MANTA implementation, acceptance and benchmark plan

This plan accompanies the architecture and scientific contracts. The stage table specifies the full 0.18.x implementation target; the progress descriptions and manual identify qualified increments. The reference-test inventory is not evidence that every proposed backend already passes it. Reproducible benchmark reports live under benchmarks/. No numerical source default changes in this plan.

1. Ordered implementation increments

Stage	Concrete deliverables	Exit evidence / permitted next step
P0: shared interfaces and references	Add provider capabilities, lossless shell/image/layout adapter, source/receipt schema and a libint tile adapter. Connect a diagnostic consumer to the existing molecular JKBuilder seam. Record fixed operator ownership.	Identical libint integrals/J/K through old and new boundaries, no duplicate normalization or changed thresholds; unsupported combinations rejected before setup. Snapshot lifetime and preflight budget gates pass. No new production default.
P1a: molecular primitive kernels	Implement FP64 Boys and MD recurrence, S/T/V, cross-basis S, moments, 2c/3c/4c Coulomb for s/p. Direct J/K and a small capped reference materializer.	Analytic/high-precision and libint parity, arbitrary-density contractions and explicit memory/work receipts. Selectable experimental manta on the admitted subset.
P1b: full molecular kernel envelope	Extend pure/Cartesian scalar orbital l through 6, auxiliary l through 7, general/partial-general contractions, batched multiple targets, erf/erfc and FT; optimize only after parity.	All admitted classes tested, contraction schemes agree, full/erf/erfc identities hold, zero-screening and all permutations work. Unsupported classes use declared fallback or refusal.
P1c: method and RI adapters	Add native JKBuilder integration, spin slots, direct and streamed RI J/K, metric admission, output/citations and explicit backend selection.	RHF/UHF/RKS/UKS parity and immutable solve capture, method energy components and terminal-density checks. ROHF/ROKS and response are individually admitted, not inferred from closed-shell tests.
P2a: molecular BUPO-J	Extent envelopes, moments/translations, deterministic hierarchy, disjoint near/far traversal, paired contraction, error accounting. Near field can use either provider.	Compare arbitrary-density J to the same unscreened/direct source; isolate tails, multipole, screening and summation errors. No exchange acceleration claim.
P2b: molecular RI-BUPO-J	Paired forward/adjoint coupling, streamed metric solves, fit/rank controls, incremental builds with full confirmations.	Exact RI versus approximate-pass comparisons, adjoint/energy-derivative tests and chain-drift safeguards. Measure actual crossover versus optimized RI and Split-J.
P3a: periodic primitive substitution	MANTA shell/FT tiles inside current Gamma and whole-mesh erfc/reciprocal/GDF sources. Keep BIPOLE domains and exchange seams.	Same-source S/T/V/J/K and energy-component parity on general complex trial densities, shifted/non-TRIM meshes and distorted cells. No molecular-limit shortcut.
P3b: periodic BUPO-J and RI-BUPO-J	Finite Ewald coefficients, compact/full-Gaussian remainders, typed q=0 hierarchy, complete finite direct J, a fixed admitted BUPO partition, retained-source infinite-Ewald errors and native all-pair-image electronic J/energy bounds and a matched electronic/point-nuclear charge, background and self policy are implemented. An explicit bounded RHF/UHF consumer now combines matched BUPO electrostatics with native kinetic and finite exact exchange, enforcing electrostatic targets at every density. Native full-image S/T enclosures now supply pre-SCF matrix admission and per-density kinetic energy admission. Explicit full-Coulomb exchange certification now jointly bounds omitted AO images and reciprocal vectors, including the overlap-dependent fixed-Madelung correction, at every evaluated spin density. A native reciprocal-cutoff factory preserves the original BUPO source while selecting certified exchange spheres and deriving their completion cube. Complete native AO/Ewald/tree/near construction now uses explicit cube policies, cumulative staged admission and a prepared source without electronic state. Typed public RHF/UHF jobs now retain the complete prepared source, managed output and evaluated-density QVF state. An exact paired q=0 RI J contraction now supplies a two-pass baseline over the unchanged retained metric and finite coupling source. The paired baseline now reuses unweighted complex forward/adjoint actions owned by the existing GDF tile producer, preserving ordered finite domains. A coupling-only screened baseline now preserves the exact finite metric and propagates source-owned omission bounds through paired J/energy actions. Ordered erfc shell-leaf multipoles now reuse the same producer support, native extents/moments and paired actions, with evaluated Gaussian error bounds and exact direct fallback. The selected auxiliary-image hierarchy now has shared Gaussian preparation and compressed forward/downward and adjoint/upward moment actions over the same q-aware coupling partition. A bounded source-owned cache now reuses selected trees and certified partitions across actions and SCF. Call-wide pair charges and auxiliary inputs, plus single auxiliary/pair projections, now reuse these producer panels across shell triples. An opt-in global AO-pair hierarchy now supplies paired moment actions and per-shell-block error ledgers. Shared isolated erfc radial and interior-moment bounds qualify explicit tighter tolerances. Shared componentwise omission and column-magnitude envelopes now tighten J/energy bounds through the actual retained metric factor; automatic whole-method profiles and general production crossover remain.	Independent Gaussian integration, unreduced ordered Bloch sums, complete reciprocal Coulomb limits, positive image envelopes, near transfers, domain enlargement and weighted energy derivatives qualify the declared electronic response. Diffuse/skew-cell whole-method accuracy remains a method gate.
P3c: low-dimensional sources	Explicit slab/wire Green functions and open-direction boundary policies with dimensional stress conventions.	Same-dimensional independent references; 3D vacuum extrapolation is supplementary, not the defining reference. Keep unsupported combinations refused.
P4: CCM and chi adapters	Individual adapters for union/WSSC, neutral Bloch, neutral real-Gamma and chi four-center/RI/RIJCOSX. Prove weight factorization before BUPO aggregation; use streamed direct terms otherwise. Inventory model-specific SECCM electrostatics.	Preserve finite domains/weights and experimental gates. Same-H Fourier equivalence only where applicable. No global supercell AO matrices or four-index tensors in production. Conditional capability decisions documented per source.
P5: qualified symmetry reduction	Method-owned admission over shell orbits, stabilizers, bubble/fit/support policies; transport in generation and digestion; explicit identity-only path.	Independent unreduced same-source comparisons, arbitrary-density equivariance, failed-parent/rank/phase negative tests, measured executed-work reduction. Existing diagnostic success alone does not enable reduction.
P6a: derivatives	Nuclear gradients for molecular exact/RI then BUPO, periodic and CCM sources; stress as a distinct extension. Include Pulay, metric/projector, moment/translation, domain, gauge and seam terms.	Distorted-geometry finite differences, sum rules, cell strain and topology/rank crossing diagnostics for each selected approximation. Nonvariational sources retain their restrictions.
P6b: further acceleration	Specialized recurrence DAGs, GPU batches, distributed target tiles, optional mixed precision and measured kernel dispatch.	Same scientific gates and end-to-end error budget; host/device transfer and replicated memory included. No imported ORCA/LibintX/EXESS speedup claims or unreviewed dependencies.

P0-P2 can land without waiting for a universal periodic Fock refactor. The periodic raw short-range fitting increment reuses the existing GDF image selector with MANTA 2c/3c kernels. Analytic Boys double sums, same-source libint metric/coupling blocks and general complex fitted-response trials check Gamma and non-TRIM transfers. Signed long contractions, pure/Cartesian angular shells, independent high-l radial/Fourier integrals, image gauges, reciprocal relabeling, engaged envelope screening and simultaneous exact/ one-short resource caps retain their separate acceptance. The output owns only raw SR components; complete RSGDF assembly and method selection remain required. Its report is benchmarks/manta_periodic_fitting.md.

The subsequent complete Coulomb source assembles SR and tiled MANTA Fourier blocks with the existing jellium kernel. Independent analytic finite sums and converged bare-Coulomb reciprocal references validate Gamma and non-TRIM transfers, two numerical splits, finite-zero subtraction independent of list membership, and complex trial responses. Polynomial quadrature checks the Cartesian and high-angular Fourier assembly. Gauges, left-handed cells, engaged SR screening and joint caps remain explicit. Fitted SCF is qualified separately below. The complete-source report is benchmarks/manta_periodic_gdf.md.

The immutable tile source now reconstructs that dense source bitwise while admitting only one metric or coupling shell tile. Its fixed-projector q-channel RI consumer is checked against independent Gaussian/Boys/Fourier sums and libint blocks, including signed angular contractions, arbitrary complex indefinite spin densities, nonuniform weights, image gauges, conjugate transfers and weighted energy derivatives. Converged numerical splits agree with an independent bare-Coulomb fit. Redundant, truncated and zero-rank auxiliary spaces, significant negative-metric refusal, owned snapshots, source identities and all five exact/one-short resource caps have separate tests. Count-only memory witnesses admit streaming below the size of one full coupling tensor; they do not execute the large numerical workload. The report is benchmarks/manta_periodic_ri_q.md.

The whole-mesh fitted Fock consumer now passes independent Gaussian/libint checks on every matrix and energy component, weighted energy derivatives, mesh reordering, and full/truncated-projector image transport through the shared symmetry density-push/operator-pull interface. Opposite transfers must preserve the actual finite reciprocal support and conjugate metric, projector and inverse before the consumer is admitted. Arbitrary trial spin densities remain independent; no spatial or time-reversal reduction is used.

Fixed independent J/K selection additionally passes separate Gaussian/libint matrix and component-energy references, weighted energy variations and reciprocity for full, truncated and zero-rank fits. Gamma/non-TRIM meshes, nonuniform/zero weights, exact component decomposition, all five joint caps and one-short refusal are tested. J-only owns no exchange-transfer metric; its actual metric/coupling calls and complete admitted bound are smaller on the multik witness. Independent image transport and owned exports cross the landed shared Fock API with explicit source flags and no symmetry admission. Eighteen prechange joint J/K states preserve matrices, scalar receipts, projectors and admission counts bitwise. Timing and modeled-memory evidence is in benchmarks/manta_periodic_ri_targets.md. Trial-density diagnostics also compose each RI target with the complementary direct reciprocal source and check independent responses, energies and derivatives with both transfer conventions preserved. Mixed HF acceptance is described below. Fitted KS, physical range fits and BIPOLE parity still require their own acceptance.

Physical finite-source RI UHF now reuses S/T/V, nuclear Ewald, the fixed-spin bounded solver and the method-owned exchange correction. Independent libint raw fits, NumPy contractions and SciPy SCF check Gamma/two-point/shifted H and Li states, unequal/empty spins, the restricted limit, all energy components, and every capped epoch. AO and auxiliary image transports check complex physical snapshots. All five aggregate caps include every retained projector, metric construction once, repeated coupling passes, scalar history and terminal confirmation. Selected scientific output adds admitted per-transfer evidence without changing the caller’s budget.

An offline compatibility probe also admitted 24 actual RI UHF states (72 spin/k channels) into the then-inspected FockBuild draft. Evaluated density, method energy, fixed source, S/X frame, physical action, metric populations, immutable storage and solver-parent identities were preserved. Capped states keep their distinct next orbital projector. That probe does not land or duplicate the draft API, replace method convergence criteria, qualify BIPOLE/CRYSTAL parity, or authorize symmetry reduction. The report is benchmarks/manta_periodic_ri_uhf.md. The RI UHF cutoff factory now passes independent integer enumeration of skew, odd/even and shifted reciprocal spheres, exact-boundary/empty-source checks, pair-complete AO image membership and independent AO/auxiliary gauge transport. Explicit-source and generated runs have identical D/F and scientific source identities. Independent libint/NumPy/SciPy checks cover Gamma and shifted H/Li SCF with both exchange corrections. All five exact/one-short caps include generation, auxiliary sources, projectors and repeated solver work. Its geometric receipt remains distinct from the fitted physical source. The report is benchmarks/manta_periodic_ri_domains.md.

Public RI UHF job selection now preserves the same independently checked finite source, every fitting control and metric projector, explicit J/K choices, evaluated spin history and lossless QVF density. Joint source/output admission, dry runs, output delivery failures, truncated/zero-rank fits, independent AO/auxiliary images and capped states have separate checks. Repository tests now check the 24 public states against the landed FockBuild API, preserving method energy, physical action, source/density/frame separation and solver-parent identities without adding dense snapshots to the bounded native solve. The report is benchmarks/manta_periodic_ri_job.md.

Restricted RI HF now reuses the same immutable fitting/physical source while running the bounded RHF numerical leaf. Independent libint metric/coupling and one-electron/nuclear sources, NumPy contractions and SciPy restricted SCF cover He/Be, Gamma, full/shifted meshes and both exchange corrections. Capped recurrences, negative/empty/truncated auxiliary spaces, redundant AO spaces, equal-spin embedding, exact/one-short native/domain/output caps, independent AO/auxiliary images and nuclear-frame QVF have explicit checks. Shared FockBuild crossings preserve the restricted total density and retained S/X frame; no source symmetry certificate is inferred. Singlet UHF has the same fitted source but its own solver/storage and method identity. Sixteen existing UHF capped/converged states remain bitwise unchanged after sharing RI HF composition. Native and public benchmark costs are recorded separately in benchmarks/manta_periodic_ri_rhf.md. Fitted KS, physical range-separated fitting and the remaining capability matrix stay open.

Mixed exact/RI RHF and UHF now pass independent libint raw-fitting, Gaussian Fourier quadrature and NumPy/SciPy SCF references for both component choices, Gamma/full/shifted meshes, empty/unequal spins and both exchange corrections. The 152-case mixed suite also checks every capped recurrence, all five native/generated/public resource boundaries, truncated and empty fits, multicenter AO/auxiliary image transport, the two K-domain conventions, evaluated QVF densities and the landed FockBuild interface. The complete method plan admits retained fitting plus direct response and composition workspace; plan.fock alone is only the fitting subplan. Thirty-two prechange complete RI states retain arrays, spectra, energies, source/projector IDs and existing resource counts bitwise. Eight isolated benchmark workers measure complete native/public jobs and independently converged references in benchmarks/manta_periodic_mixed_hf.md. Mixed finite-source qualification does not establish fitted KS, physical range fitting, BIPOLE parity or a source-specific symmetry reduction.

Explicit fitted pure/global KS now passes independent libint raw-fitting, Gaussian Fourier/direct and libxc quadrature contractions with NumPy factors and SciPy SCF. Pure RI-J LDA/PBE/BLYP and all three global exact/RI choices cover Gamma/shifted meshes, restricted/unequal/empty spins and strict/BvK corrections. Capped recurrences preserve the evaluated density and frozen projectors. Fourth-order complex congruence energy differences check the functional Fock derivative; the HF half trace is explicitly rejected as an energy reference. Empty PBE/PBE0/B3LYP endpoints keep separate measured minority-potential sensitivity witnesses, with strict occupied-spin and energy checks. This is the existing libxc endpoint limit, not a widened uniform matrix tolerance or a regularized functional.

Truncated/zero fitting spaces, independent multicenter AO/auxiliary image shifts, redundant AO shells and rectangular S/X frames preserve all physical components. Exports cross the actual shared FockBuild and BlockSpaceAction interfaces with method-owned energy and no inferred symmetry certificate. Source changes at the same HCORE state preserve the evaluated-density identity while changing source/Fock identities. Fifty-six saved direct pure/global/range KS states retain arrays, spectra, energies, source hashes and original resource counts bitwise; density/snapshot IDs intentionally adopt the separated version 2 contract.

All five native and selected scientific caps admit exactly and refuse one short before poisoned array copies. Functional/source restrictions remain fail-closed. Twelve isolated benchmark workers, each with five repeated native and selected scientific solves, report complete fixed-source errors and conservative resource models in benchmarks/manta_periodic_ri_ks.md. The selected timing includes provenance construction but no full public job or artifact writing.

Generated fitted KS adds independent integer membership/conjugacy checks for Gamma and shifted meshes, raw-fitting/functional SCF on generated supports, all exact/one-short domain/grid/output caps, capped/truncated states, empty spins, rectangular overlap frames and independent AO/auxiliary images. Owned exports preserve the shared Fock and BlockSpaceAction contracts. Twelve saved generated direct KS states preserve numerical arrays, plans and identities exactly after sharing the factories. The generated/explicit/selected states agree bitwise. benchmarks/manta_periodic_ri_ks_domains.md measures complete source and quadrature construction in twelve isolated workers with five repeats per interface.

Public fitted KS adds independent pure/global functional SCF, explicit J/K selection, complete output-budget boundaries, capped/truncated states and lossless evaluated-density QVF for restricted, unequal and empty spins. Independent AO/auxiliary image shifts, rectangular overlap frames, immutable result/evidence exports, citations, dry runs and artifact-delivery failures preserve the method contract. Sixteen saved public direct KS/RI HF states retain numerical arrays, native plans and identities exactly. The twelve-worker benchmarks/manta_periodic_ri_ks_job.md measures complete native and public jobs, including standard output and QVF, with five repeats each. Physical range fits, BIPOLE/CRYSTAL parity, source-qualified reduction and the remaining approved matrix stay required.

The initial public surface covers the P0 reference boundary and the P1 molecular MD one-electron matrices, streamed 2c/3c fitting tiles and four-center tiles/direct J/K, including erf/erfc kernels and batched AO-pair/auxiliary Fourier panels, multi-density direct digestion and a streamed dense-metric RI-J/K reference, plus bounded sharing across general and partial contraction channels, analytic one-electron basis/charge/origin derivatives and analytic 2c/3c/4c shell-center derivative tiles and a bounded all-electron molecular HF Lagrangian gradient consumer, plus explicit RHF/UHF/RKS/UKS method selection with executed-provider and terminal-density evidence, independent exact/RI range exchange sources and the native XC/VV10 composition. A bounded absolute three-dimensional shell-pair extent/tail envelope and bounded Cartesian multipole translations/interactions and a deterministic streamed bubble partition support a low-level molecular BUPO-J consumer. Independent point-charge Legendre expansions check the multipole algebra, including the compact-support remainder; Gaussian tails remain separate. Small exhaustive inventories prove that near/far blocks partition each unordered shell-pair interaction once, including when candidates are refined. Shared primitive shell-pair moment panels through degree twelve and optional full absolute radial envelopes support streaming forward/reverse consumers; independent polynomial quadrature validates the complete panels. Single-auxiliary panels through l=7 and degree twelve, and shell-centered full/tail extent envelopes, are validated against direct polynomial quadrature and radial gamma integrals. These retain the single-function distribution required by RI-BUPO rather than substituting an orbital product. A Gaussian error model combines compact truncation, exact tail penetration and the full-versus-compact moment correction. Independent libint and analytic Gaussian interactions validate its per-integral approximation ledger, separate from floating-point contraction errors. The paired J consumer passes arbitrary density, linearity, reciprocity, energy-derivative, near-only and strict far-field comparisons against independent dense integral contractions. Its selected RHF/UHF/RKS/UKS adapter confirms the returned density against an independent exact J while preserving the chosen exchange and XC treatment. Loose negative controls must fail that confirmation even when the approximate SCF itself is stationary. Performance benchmarks remain a separate gate; BUPO does not supply exchange or derivatives. Pair-bubble/single-auxiliary interactions reuse the same explicit Gaussian ledger, with independent three-center libint and unequal-Gaussian analytic checks. This establishes coupling-tile admission, not a complete RI-J error or fitting-conditioning certificate. A native paired three-center coupling now streams the same density-independent partition in forward and adjoint passes, with atomic auxiliary leaves and pair bubble translations. Independent libint/libcint comparisons through orbital l=6/auxiliary l=7, full-matrix adjoint tests, exact near limits, signed linearity, positive-metric energy derivatives and exact aggregate resource boundaries validate that primitive. A bounded RI-BUPO J consumer now combines both passes with the existing exact dense metric and fixed positive retained subspace. It reports explicit exact-RI confirmation, separate pass defects, propagated J/energy coupling bounds and discarded-space metric residuals. Independent dense references, duplicate/nearly-dependent and zero-rank spaces, energy finite differences and combined resource boundaries validate this composition. Selected RHF/UHF/RKS/UKS can now use RI-BUPO J with independent exact/RI K and native XC/range exchange. Terminal confirmation rebuilds exact RI-J with the identical auxiliary/metric source; loose stationary and NOITER controls must fail. Receipts include executed paired-source and conditioning evidence. Large streamed metric solves and selected RI-BUPO derivatives remain gates. QVF file and memory producers preserve executed molecular engine receipts in an optional vendor section, including failed exact terminal confirmation, with hash validation, coexistence and source-ownership tests. Selected molecular static populations, bond indices, natural orbitals and dipoles use the executed one-electron provider with content checks and separate work receipts. Selected single-point jobs retain J/K and range/XC sources through dispatch and RKS READ retries, output/citations and failed-confirmation checkpoints. IAO populations and closed-shell IBO/Boys/Pipek-Mezey localization use the selected main, minimal-reference and cross-basis overlaps and dipole moments. Independent libint comparisons, occupied-density preservation, source refusals and QVF exports qualify these property paths. Atomic SAD promolecules, response and other job compositions remain gated. Independent shell-tile sessions admit only provider/workspace resources and one quartet, leaving aggregate work and density buffers to the scheduler; the original ordered J/K plans retain their whole-traversal admission. These interfaces do not complete the remaining job-composition, large-metric, periodic or derivative gates; the manual records what is actually selectable. Symmetry foundations can advance independently, but P5 execution depends on the actual P2/P3/P4 source to be reduced. Derivative primitives can be developed earlier; a user-facing force/stress capability requires the complete P6 gate.

Use incremental, additive changes. Add a manifest classification through scripts/test_gate/update_suite_manifest.py for each new test file. Add user-visible changes as changelog.d/ fragments when behavior ships, not as claims in released changelog sections. The implementing chat may validate and accept its own work; no separate reviewer or review-only hold is required. Scientific acceptance and closure require an affected-method calculation through vq with a suitable matched external or justified numerical reference. Reuse valid evidence and record the actual source/native runtime. Ordinary landings skip CI; full CI belongs to release candidates. Before a large refactor, record its bounded scope on the full MANTA work tracker.

The dense RI metric response now shares the RI positive-eigenprojector factorization. Independent displaced eigensolves validate inverse and projector derivatives, including nonzero discarded modes, degenerate blocks, zero rank and absolute/relative cutoffs. Frobenius adjoints, orthogonal covariance, fixed-density fitting energies, exact factor identity, numerical rank-crossing refusals and resource boundaries are qualified separately from complete nuclear gradients. The cutoff guard is a numerical admission policy, not an interval spectral certificate.

A fixed-density RI Coulomb gradient consumer now streams the fitting RHS and three-center derivative contraction and contracts the exact metric adjoint. Independent libint energy differences validate full and truncated fitting spaces; range kernels, separate orbital/auxiliary ownership, component-wise finite differences, translation/rotation sum rules and aggregate resource boundaries cover the derivative composition. This qualifies the RI Coulomb energy component, not complete SCF forces, exchange derivatives or stress.

The paired-spin RI exchange energy gradient now forms its metric adjoint in bounded raw auxiliary blocks, including discarded modes, and streams the three-center derivative contraction. Independent libint energy and component finite differences, full/erf/erfc kernels, spin additivity, block invariance, zero rank, geometric sum rules and aggregate work/memory admission qualify this component. Receipts match the RI exchange source and spin-density identities and expose the reference schedule’s repeated integral passes. Complete selected RI SCF force composition remains a separate gate.

A complete low-level molecular HF RI Lagrangian now combines independently selected exact/RI J and K derivatives with nuclear, core and overlap Pulay terms. Component-wise independent libint finite differences cover pure and Cartesian, full and truncated metrics; relaxed RHF/UHF differences and independent full-RI force comparisons include auxiliary response. Executed counts prove that an all-RI derivative requests no four-center tiles. The combined admission covers every component before copying input matrices. The generic selected RHF/UHF adapters now retain an immutable auxiliary basis, RI policy and budget. They verify geometry, terminal density and rebuilt RI source identities. Relaxed-energy differences exercise both public and native gradient routes for independent exact/RI J and K selections. Custom same-name auxiliary bases, truncated metrics, caller option mutations, derivative-budget refusals and success-only output receipts qualify context preservation. Selected KS and BUPO derivatives remain separate gates.

The molecular HF geometry source now preserves orbital/auxiliary shell content and atom maps while rebuilding centers at each geometry. Displaced RHF/UHF energies validate all exact/RI J/K compositions; native optimizer walks and complete jobs verify stationary final forces, source identities, final custom auxiliary placement and derivative citations. The source snapshots mutable SCF/fitting options and budgets and uses explicit HCORE starts. Projected READ warm starts and other derivative compositions remain separate gates.

The finite Bloch Fourier primitive now streams translated shell panels across an explicit image list and shares them across ket momenta. Independent Gaussian quadrature, physical libint overlap at zero argument, reciprocal relabeling, global-origin phases, momentum-transfer adjoints and exact physical-support boundaries qualify its convention. The older raw Fourier table’s normalized solid harmonics require an explicit angular conversion before reference comparison, matching the existing RSGDF AO scaling helper. That difference is not hidden by a fitted numerical rescaling; complete periodic/CCM sources still require normalization-consistent method qualification. Aggregate work/storage caps and actual generation/folding receipts cover bounded batches and the opt-in periodic Fourier helper adapters.

The finite three-dimensional reciprocal Hartree consumer now composes this provider over a complete density epoch with explicit nonnegative normalized k weights and unique inversion-closed image/G supports. Tests compare pure and Cartesian results with independent Gaussian quadrature, differentiate the Hartree energy with respect to one complex Hermitian density block, and check Gamma reduction, nonuniform mesh permutation, time reversal, reciprocal relabeling and origin covariance. A normalized scalar Gaussian supplies a closed-form reciprocal-cutoff convergence reference. Existing Ewald J cell/k interfaces agree at the same finite source and physical normalization. Admission covers cumulative kernel work, all live output/input owners and the Python grid generator; low caps fail before payload/grid allocation. Raw imaginary/Hermiticity residuals are checked before legacy real-block conversion. This does not qualify nuclear/K composition, periodic SCF, CCM, periodic BUPO, forces or stress.

The one-electron point-charge provider admits erf/erfc kernels and analytic bra, ket and charge-position derivatives at fixed range. Independent libint erfc nuclear matrices, optional libcint Gaussian-charge matrices through l=6, and high-precision scalar Gaussian integrals check the radial convention. The latter retain relative accuracy checks on erfc tails below the range at which full-minus-erf subtraction rounds to zero. Range partition, translation sum rules, center finite differences, resource boundaries and unchanged default Coulomb source identities gate the primitive. This does not itself admit a periodic nuclear sum or a derivative of the splitting parameter.

Finite overlap and kinetic producers now retain real cell blocks while sharing translated MD shell tiles across all Bloch momenta. Independent libint lattice blocks, l=6 polynomial quadrature and a converged analytic Gaussian chain check the physical convention. Tests cover image-relabeling covariance with regenerated pair-complete supports, reciprocal relabeling, asymmetric/repeated image domains, raw residuals, exact cutoff boundaries and aggregate admission. The explicit cell adapter preserves the standard LatticeMatrixSet in dimensions one through three and emits executed source/work receipts. It does not enable complete periodic SCF or symmetry reduction on its own.

The finite three-dimensional nuclear operator now composes erfc point-nucleus images, damped reciprocal attraction and the positive overlap correction for zero-average G=0 treatment. Its physical nuclear sphere uses the existing midpoint-centered selector. Independent libint short-range blocks, Gaussian quadrature reciprocal blocks, analytic overlap corrections and a converged scalar plane-wave series check each component and the total. Tests exercise split convergence, basis/nuclear image relabeling, origin shifts, complex Bloch folding, l=6 screened attraction, actual image/primitive-charge counts and aggregate resource boundaries. The explicit lattice adapter agrees with the existing Ewald operator at matched finite domains and emits execution evidence. This qualifies the operator, not complete periodic SCF, exchange, forces or stress.

A finite reciprocal full-Coulomb exchange consumer now accepts explicit per-transfer Q supports and an immutable all-k/all-density snapshot. Its B-dagger-D-B convention agrees with independent Gaussian quadrature, analytic scalar Gaussian sums and the existing negative-source-phase contraction after physical AO normalization. Reversed transfer supports are checked so that the weighted density response is self-adjoint; perturbing one k density verifies the exchange-energy derivative and changes responses across the mesh. Separate spin/trial channels share Fourier work but retain separate responses/identities. Tests cover image-gauge density pushforward, reciprocal relabeling, arbitrary complex Hermitian densities, raw residuals, batching and aggregate admission. The explicit source omits Q=0 and adds no Madelung correction. It does not qualify singularity-corrected exchange or complete periodic SCF.

The same consumer now supports explicit erf/erfc kernels. A positive-range erfc request includes its finite zero mode only when supplied in the domain; full Coulomb/erf retain the omitted-zero convention. Independent quadrature, energy derivatives, high-precision positive-tail tests and a scalar Gaussian real/reciprocal Poisson identity qualify this distinction. Kernel/range and actual zero-mode work are recorded; no singularity correction is inferred.

The native spin Fock consumer now freezes H+J[D_alpha+D_beta]-a*K[D_spin] and the corresponding electronic-energy components in one owned epoch. Independent quadrature, spin/k energy derivatives, restricted factors, time reversal and atom-image gauge tests qualify the composition. Source, density and evaluated-payload identities remain distinct; aggregate admission reserves both component peaks and enclosing owners before copying inputs. The H matrix is explicitly supplied and authenticated, not asserted to be a MANTA nuclear source. This is a fixed matrix snapshot; complete physical periodic SCF and correction policies remain separate qualification stages.

The neutral all-electron three-dimensional RHF driver now composes physical S/T/V, point-charge Ewald energy and the whole-mesh reciprocal J/K source. The bounded numerical solver retains the last evaluated density/Fock pair, checks the occupied/virtual gap and projected eigenproblem, and requires a fresh terminal Fock/energy confirmation. Explicit strict zero-mode omission and a separately admitted BvK probe-charge Ewald correction are qualified against independent quadrature/libint components and optional refined PySCF AFT calculations. Full regular Gamma, multi-k and shifted meshes are covered; cutoff convergence remains distinct from SCF convergence.

The cutoff factory admits physical AO-pair image spheres and certified reciprocal kinetic-energy spheres before allocation, checks reversed momentum-transfer conjugacy, and preserves independent domain/source identities. Its selected run_periodic_job adapter now provides separate engine/J/K controls, explicit domains, output memory reservations, standard artifacts and executed provenance. QVF preserves evaluated densities on converged and capped exits and transports independently displaced AO shells into the archive’s nuclear-center gauge. Capability refusals and output delivery failures retain the shared job lifecycle semantics. Native-source and complete-job benchmarks separately report numerical error, time, work and memory. General periodic KS, RI/BUPO, reduced-dimensional boundaries, CCM, qualified symmetry reduction and periodic derivatives remain open stages; these RHF results do not qualify them.

The physical RHF driver also retains scalar snapshots of every evaluated iteration through the bounded solver’s existing observer contract. Native copies and Python/QVF records are admitted against the maximum iteration count; matrix histories are not retained. Independently capped runs check each energy/residual/gap snapshot, and confirmation calls do not create extra iterations. Selected jobs deliver the complete history after the solve while retaining the evaluated terminal density separately.

The bounded UHF numerical leaf is now a separate fixed-spin solver with D[2,K,n,n], shared physical S/H[K,n,n], independent alpha/beta occupations and a single whole-density callback per iteration. It shares the RHF leaf’s audited Jacobi, overlap and metric routines. Complex NumPy fixed-point references qualify unequal/empty spin populations, spin exchange, AO phases, per-spin band gaps, metric idempotency and last-evaluated-density exits. Exact-cap and one-byte-short cases check owned and enclosing resource budgets. The explicit-support physical UHF driver now composes this leaf with the neutral 3D all-electron S/T/V and nuclear Ewald source, whole-mesh spin J/K, and separately admitted BvK correction. Independent quadrature/libint UHF fixed points validate empty and nonempty beta channels, Gamma and shifted meshes, component energies, shell-image gauge transport and same-density confirmation. Physical RHF/UHF share the spin-independent source receipts; the full UHF identity additionally binds its fixed spin populations. Refined Gamma and shifted-mesh hydrogen cases also compare S/H, both spin densities and Focks, nuclear and total energies, and the Madelung constant against optional PySCF AFT KUHF. The reference uses explicit fixed-spin occupations to avoid its empty-beta diagnostic bug, with supercell electron counts set explicitly. These are finite-basis checks, not spin-stability or basis-convergence claims. Cutoff-generated UHF now shares the certified geometric source with RHF and admits a separate complete spin-aware physical plan. Independent integer enumeration, spin SCF, shell-image transport and exact-budget refusals qualify this route. Selected public UHF jobs now deliver separate evaluated spin densities, owned spin orbitals/occupations, complete scalar spin history and standard artifacts. Independent job-level integral/SCF comparisons and QVF readback cover empty beta, unequal populations, capped states and shifted AO gauges. Job resource admission and delivery failures preserve the shared lifecycle. Pure-KS jobs are qualified below; general KS and later stages remain open.

A separate joint functional numerical contract now reuses the bounded restricted/unrestricted iteration kernels while preserving the HF APIs. The provider supplies potential and interaction energy from one evaluated D. Nonlinear polynomial fixed points and energy derivatives distinguish this from the HF half-trace formula; capped, cancelled and missing-output cases check epoch consistency. This is groundwork for periodic KS, not physical XC quadrature or selected KS job qualification.

2. Independent reference hierarchy

Agreement with one backend does not establish correctness if both share a normalization or contraction bug. Use all applicable levels:

1. Analytic ssss, overlap, kinetic, point-charge and Gaussian moment formulas; high-precision one-dimensional Boys quadrature and small Gaussian Coulomb cases independent of the production recurrence.

2. Existing libint integral tiles, with a separately checked AO convention; small independent NumPy contractions over full tensors, not the same MANTA digestion loop reused as an oracle.

3. Existing unreduced native/Python lattice and reciprocal builders under matched supports, weights, metric ranks, background and q=0 conventions. Distinguish finite-source parity from convergence to an infinite source.

4. Independent external programs only in optional tests or regression subprocesses, never in python/vibeqc/ or cpp/. Pin basis coefficients, pure/Cartesian order, pseudopotentials, auxiliary basis, exchange treatment, numerical cutoffs and gauge. A converged SCF comparison without those matches is a scientific comparison, not an implementation identity test.

For periodic Coulomb use an independently accumulated high-accuracy Ewald or reciprocal reference; validate nuclear, J and combined electrostatic energy separately. A direct bare lattice cutoff is not a valid 3D Coulomb reference without its surface/neutrality convention. For CCM use explicit small-domain weighted sums as oracles; a generic periodic program cannot certify a different finite Hamiltonian. Published lattice-sum numbers in Kudin 2004 Tables I-II provide an additional convention-converted witness.

Existing tests to inspect and extend, preserving their established thresholds:

Layer	Existing files
Molecular primitives and fit	tests/test_integrals.py, tests/test_df_core.py, tests/test_df_rhf.py, tests/test_df_uhf.py, tests/test_df_gradient.py
Frozen operators	tests/test_operator_contract.py
Periodic finite kernels/resources	tests/test_periodic_gaussian_source_context.py, tests/test_periodic_gaussian_metric.py, tests/test_periodic_gaussian_three_center.py, tests/test_periodic_gaussian_fock.py
Whole-mesh and GDF	tests/test_periodic_fock_multi_k.py, tests/test_rsgdf_shared_q_batch.py, tests/test_gdf_cross_route_parity.py, tests/test_periodic_gdf_memory_preflight.py
BIPOLE identity and final density	tests/test_bipole_jk_domains.py, tests/test_bipole_domain_contract.py, tests/test_bipole_final_density_phase.py, tests/test_pbc_bipole_multik_ewald_split.py
CCM/chi	tests/test_ccm_bloch_reference.py, tests/test_ccm_direct.py, tests/test_periodic_ccm_neutral_bloch_adapter.py, tests/test_chi_transform_inputs.py, tests/test_chi_fitted_controls.py, tests/test_chi_hf_reference.py
Symmetry	tests/test_symmetry_shared.py, tests/test_symmetry_integrals_reduced.py; the symmetry workstream’s retained-GDF tests after integration

3. Numerical acceptance suite

The numbers below are proposed initial small-fixture gates, to be confirmed with independent references. They do not relax existing tests or promise these tolerances for arbitrary ill-conditioned inputs. Fixtures have bounded norms and non-singular retained spaces. If a gate fails, establish conditioning/reference error before proposing a change; do not silently widen it. Publish absolute max, absolute Frobenius and scaled Frobenius residuals.

Test family	Required cases and measurements	Initial gate
Normalization and integral tiles	All s/p classes and representative classes through advertised l; mixed pure/Cartesian, same-center, far/diffuse/tight, signed and deep contractions, ghosts; 2c/3c/4c; every coincidence/permutation	Element error <= 1e-11 + 5e-12 * abs(reference) a.u.; additionally report norms and analytic ssss/S diagonals. Higher-conditioning cases use high-precision witnesses.
Range and moment/FT kernels	omega near zero, intermediate and large; full=erf+erfc; analytic finite SR Q=0; moments at several origins, translation composition and derivative orders; FT conjugation and q wraps	Same integral gate; zero/large limits and exact low-order identities tested independently
Arbitrary-density J/K	Seeded PSD, Hermitian indefinite, sparse, random complex, spin-separated and small delta densities; batches of 1/2/8 targets; response non-Hermitian mode separately	Max error <= 2e-10 Eh for fixed bounded fixtures versus independent full contractions; linearity/adjoint and raw Hermiticity <= 1e-11 in their stated norms
Energy consistency	Central difference of quadratic J/K energy with nonsymmetric-in-space Hermitian perturbations; density-pair reciprocity; spin factors and separate exchange ranges	Directional derivative agrees to 1e-8 Eh on the step-size plateau; cross-density bilinear residual <= 1e-10 before any symmetrization
BUPO-J	Exact near-only, far-only admitted pairs, translated and rotated geometries, signed contractions, diffuse always-near bucket, repartitioned trees, reordered tasks	At strict target, max delta-J <= 1e-8 Eh and absolute delta-EJ <= 1e-8 Eh for small fixtures; tighten each approximation until the same-source analytic limit is recovered
RI-BUPO-J	Exact B/V baseline; approximate forward only, adjoint only and paired passes; rank-degenerate/near-threshold auxiliary spaces; small/large solve residuals	Same BUPO gate relative to exact RI; forward/adjoint dot test <= 1e-11 relative. Separately report exact-RI minus exact-4c error, never charge it to BUPO
Incremental builds	Alternating and cancelling deltas, different alpha/beta slots, restart, threshold/rank/kernel/tree changes, at least two rebuild intervals	Final full build agrees with independent nonincremental map within its allocated error; forced drift prevents convergence and reseeds state
Periodic finite-source parity	Gamma, 2x1x1, 3x1x1, 2x2x2 and shifted meshes; non-TRIM complex densities; one k perturbed at a time; nonuniform normalized quadrature outside finite-character tests	Raw J/K max error <= 1e-9 Eh for small matched sources; component energies <= 1e-8 Eh/cell; no final averaging to conceal phase defects
Periodic convergence	Independent real/G/eta, near-cell, pair-image, multipole order and mesh ladders; diffuse/skew ionic cells, neutral and explicitly compensated charged controls	Same-source errors meet the specified budget; successive independent converged controls change total energy < 1e-7 Eh/cell and J/K < 1e-7 Eh before claiming convergence for that fixture
Cell identity/gauge	Shift atom by lattice vector; change unit-cell origin; equivalent supercell folding and k labeling; G=0 background and nuclear self removal; full versus SR exchange seam	Covariant matrices and invariant matched energies satisfy the periodic gates; expected potential-zero changes are identified component by component
CCM identities	Explicit weighted small sources, WSSC ties on odd/even meshes, all route names, neutral real/Bloch Fourier equivalence, chi finite characters and fitted projectors	Same-source matrix/energy gates; intentionally different sources must remain distinguishable; unsupported weight factorization/dimensions refuse
Symmetry	Proper/improper operations, stabilizers, fractional translations, scalar TR, Cartesian metric, dense auxiliary gauges, broken-state trial densities, orbit-adjoint contraction	Reduced/unreduced max delta-J/K <= 1e-10 Eh on bounded fixtures, separately from approximation error; every deliberately invalid source/rank/action is rejected or runs identity-only
End-to-end SCF	H2O, stretched/open-shell molecule, signed/general/diffuse basis; ionic and covalent distorted solids; each experimental source separately; HF, pure KS, hybrid, screened hybrid, smeared metal where supported	Same basin/occupations and original convergence tolerances; total energy <= 1e-8 Eh (per cell for periodic fixtures), component errors reported, density subspaces compared in S rather than arbitrary orbital gauges
Gradients	Distorted molecules/cells, selected exact/RI/BUPO energy, multiple displacement steps; total and component finite differences; tree/rank/support crossings	Max force error <= 3e-6 Eh/bohr on a stable FD plateau; translation/rotation sum rules; separate reports for crossing cases and nonvariational sources
Stress	Hydrostatic and shear strains, skew cells, fixed fractional k, nuclear/background/seam terms, finite-temperature free energy where applicable	Max error <= 3e-6 Eh/bohr^3 for 3D fixtures; dimensional units for 1D/2D; compare several strain steps and cutoff ladders

Convergence ladders must vary one approximation at a time and then test their combination. Finite-difference energy noise must be well below the targeted force times displacement (or stress times volume and strain). Smearing tests compare the appropriate free energy and occupations. Degenerate orbital rotations are assessed as subspaces; energy ordering alone is not a state identity check.

For every budgeted path test exact-cap acceptance, one-byte/work-unit-short refusal, integer overflow, cancellation, invalid dtype/layout, NaNs and stale source identity before expensive allocation. Verify that tile views cannot outlive their workspace and that mutating a builder after snapshot creation does not change a captured operator. Concurrent density mutation is prohibited; use ownership or the existing checked borrowed-input pattern. Force a fallback and verify its source identity, memory admission and output counts.

Initial local test ceilings: analytic/tile fixtures 60 seconds and 512 MiB per case; small J/K and periodic cases 15 minutes and 4 GiB per process. These are proposed admission limits, not measured runtimes. Medium numerical and scaling cases need a separately sized plan after small gates pass. No full native lane, large all-q inventory or large supercell run is required by this documentation change. Actual implementation tests must rebuild and verify the loaded native extension belongs to the edited checkout.

4. Benchmarks with attributable speedups

Benchmark the requested scientific accuracy, not only a kernel’s throughput. Use reproducible public input definitions, pinned source/build/compiler/BLAS, CPU/GPU model, thread/rank settings and numerical controls. Record operational logs, machine identifiers and absolute paths outside the product checkout. Only sanitized portable summaries and approved fixtures belong in the tree. Acquire licensed literature SI inputs on demand unless redistribution has been reviewed. SI geometry presence does not confer a license to bundle it.

Workloads should cover:

• Low-l segmented molecules where libint can win; deep general contractions; high-l quartet and 3c classes; multiple response right sides.

• Compact water/organic clusters, extended glycine chains and a diffuse charged molecule. Vary shape and basis separately from atom count.

• Gamma and multi-k covalent/ionic solids, anisotropic cells and slabs/wires only after their source gate. Vary cell size, k mesh and support separately.

• Small and growing finite sources for each CCM/chi route, including cases where weight structure prevents efficient BUPO aggregation.

For each workload run these matched variants, including no-win cases:

Variant	Provider	J algorithm	Symmetry	Question answered
A	libint	existing exact/direct or RI	off	Baseline including existing optimized digestion
B	libint	new tile/consumer exact or RI	off	Interface/digestion overhead or benefit
C	MANTA	same exact or RI algorithm as B	off	Integral-provider contribution
D	MANTA	BUPO or RI-BUPO matched to C	off	Coulomb approximation/traversal contribution at measured accuracy
E	MANTA	same as D	qualified reduction	Symmetry contribution for the same numerical source
F	libint near field	same BUPO plan as D	off	Provider versus BUPO interaction/crossover

Measure A/B, B/C, C/D and D/E separately; show A/E only as total observed benefit. Also compare to the best existing admissible route. Approximate sources with different RI/K choices do not form a speedup ratio without showing their accuracy difference. End-to-end timings are not products of microbenchmark speedups.

Each record contains setup and total wall/CPU time, SCF iterations and final confirmation time; basis/extent/tree setup; E/R/Boys formation; primitive and contracted transforms; screening; near-field integrals; moments/M2M/M2L/L2L; metric setup/solve; RI forward/adjoint passes; J/K digestion; reciprocal work; symmetry planning/transport; XC; eigensolve; output; synchronization, I/O and host/device transfers. Report peak process-tree RSS and device memory, measured workspace high-water mark, per-rank/worker replication and spill volume.

Actual work counts include candidate/retained shell and primitive pairs, quartets/triples/metric tiles, screened terms, executed GEMMs and recurrence classes, bubble visits/accepted interactions/orders, near-cell and reciprocal vectors, q/k contractions, fit iterations, symmetry representatives and reconstructions, incremental/full rebuilds and fallback tiles. Do not present planner cardinalities as executed work. Explain time components that overlap instead of adding overlapping timers.

Run one warm-up and at least three measured repeats for stable medium cases; report median and range, with cold setup separately. Longer cases may use fewer repeats with that limitation visible. Confirm accuracy on the timed run’s actual output, including J/K, energy components and terminal density. Control thread counts and node contention; an isolated rerun distinguishes a timeout from a numerical regression. Show absolute seconds and memory even when a speedup is below one. Fit scaling only over the measured regime with fixed accuracy, and disclose dense metric/solver bottlenecks and diffuse near-field growth. No ORCA speedup is transferred to vibe-qc.

5. Decisions and review checkpoints

Adopt now as design constraints: explicit provider selection, separate J/K algorithms, fixed solver snapshots, source-specific periodic/CCM identities, bounded production storage, paired RI approximation, unreduced reference and visible provenance. These do not change a public API or an existing source.

Before the relevant implementation stage, review the proposed public option names/schema, qualified l/derivative envelope, calibrated accuracy profiles, periodic tail representation, compatible CCM weight factorizations and the large-metric solver/preconditioner. A new hard dependency, licensing decision, public API break or physical-source/default change belongs to the maintainer. Ordinary additive provider implementation and focused validation can proceed within the agreed stage. Preserve the libint reference throughout the rollout.

Periodic direct-Bloch local-exchange increment

The finite local-exchange source is qualified separately from physical KS SCF. tests/test_manta_periodic_local_exchange.py compares complex direct Bloch densities and potentials with independently evaluated Gaussian polynomials and libxc LDA exchange. Its gates cover weighted k/spin energy derivatives, restricted spin scaling, empty spin, shell-image gauge changes, source identity/ownership, image and grid refinement, and exact/one-short resource admission. No real inverse-Bloch density assumption is made.

This leaf admits explicit 3D image/grid supports and l<=4; it alone does not close the periodic KS capability row. The following increments qualify pure LDA/GGA physical composition, grid/domain generation and public job outputs. General XC, production accuracy profiles and other unqualified stages remain required.

The subsequent native LDA/GGA component shares that finite Bloch support and adds bounded AO gradients, spin-density invariants and their exact adjoint. Independent Gaussian polynomial derivatives and libxc point evaluations, complex real/imaginary energy differences, mixed-spin gradients, restricted limits, empty spins, image gauges and exact resource boundaries qualify it. The finite physical periodic KS composition below consumes this joint functional energy contract, preserves the same k weights and confirms the terminal evaluated density against the complete finite physical source.

The explicit physical pure-LDA/GGA KS driver now composes the qualified Hartree and semilocal sources with physical S/T/V and nuclear energy. The same-density joint energy contract applies to both restricted and fixed-spin unrestricted occupations. Independent Gaussian/libxc contractions and SciPy eigensolves check full SCF, capped evaluated epochs, separate energies and final physical confirmation. Exact/one-short aggregate budgets include both sources and the functional solver’s retained energy scalar. The finite Hartree pair support and canonical XC image support remain distinct; grid charge, XC energy and XC potential require independent refinement. Public pure-KS jobs have their own acceptance below. General functional profiles are not inferred from this finite-source increment.

The explicit global-hybrid adapter separately adds full-Coulomb exchange to the semilocal component on the same evaluated density. Resolved method components supply the coefficient; the pure API still refuses hybrids. Independent Gaussian pair Fourier integrals and AO gradient contractions, libint one-electron matrices, libxc integrands and SciPy fixed-point solves check PBE0, B3LYP and custom LDA/GGA hybrids. Both zero-mode policies have independent probe-charge and spin-factor witnesses. Complex congruence energy differences check the Fock derivative, including k weights and conjugation. Capped epochs, source/image gauges, rank truncation and all five exact/one-short aggregate resource limits pass. Separate empty-spin PBE0 and B3LYP tests measure libxc endpoint sensitivity without changing runtime regularization or claiming uniform minority-potential accuracy. Full-matrix empty-spin acceptance uses a well-conditioned B88/LYP global hybrid.

Exported hybrid snapshots were checked against the actual shared FockBuild draft, including physical S/X frames, owned evaluated densities, separate method energy components, solver-modified operator parentage and next orbital projectors. This qualifies export compatibility with that inspected draft, not a landed runtime adapter or an in-loop Python allocation contract. No symmetry-reduced or BIPOLE producer is admitted by this evidence. General periodic accuracy qualification remains required. Explicit range separation has the separate acceptance below. Reproducible finite-source timing and independent errors are recorded in benchmarks/manta_periodic_ks.md in the repository.

The explicit range-separated adapter now independently qualifies complete finite-source RKS/UKS for HSE06, CAM-B3LYP, LC-omegaPBE, omegaB97X, mixed ranges and empty-spin LC-BLYP. The reference uses fixed published coefficients, independent Gaussian Fourier panels and analytic screened kernels, libxc AO contractions and SciPy SCF. Tests isolate the finite erfc zero and its k weight, the long-range coefficient of the Madelung term, and the absence of that term for screened-only exchange. Both requested zero-mode choices, complex density energy derivatives, capped evaluated states, next projectors, closed-shell limits, retained-rank solves, cancelled components and source-image gauges pass. All five exact and one-short aggregate budgets include every kernel and the expanded transfer source; invalid numerical arrays remain unread after a resource refusal. Unsupported functional families stay gated.

The actual shared FockBuild/OperatorFrame draft also consumed nine exported range-separated states, including early capped exits and converged results. All 45 spin/k operators preserved physical frames, evaluated density, component energy, immutable ownership and solver-modification parentage. Independent generalized spectra and next projectors agree. This qualifies export compatibility with that draft, not a landed in-loop adapter or a symmetry certificate. Canonical Coulomb-plus-erfc zero-mode semantics are explicit; no equivalence to another finite-mesh singularity prescription is inferred. Timings and errors are recorded in benchmarks/manta_periodic_range_separated_ks.md. Range-separated cutoff/grid generation and public output have separate acceptance below; source refinement and production accuracy profiles remain required. BIPOLE/CRYSTAL and symmetry gates retain their own sources.

The range-separated cutoff and joint-grid factories reuse the qualified HF/global-hybrid geometric producer, with complete range-separated admission. Independent integer spheres check Gamma and shifted skew-cell G/Q support, exact boundaries and distinct pair/XC image domains. HSE06, CAM-B3LYP, mixed ranges and empty-spin LC-BLYP match explicit composition bitwise and an independent Gaussian/libxc and SciPy SCF reference. Every erfc leaf retains its finite diagonal zero; domain receipts describe the common nonzero base. Both spin conventions, singularity choices and grid partitions, capped evaluated states, AO-image gauges and standalone receipt lifetimes pass. All five jointly exact and one-short caps precede payload copies or invalid grid generation. The grid, geometric source and all exchange components remain charged together. A further nine-state/45-block check against the current FockBuild draft preserves domain/quadrature provenance and evaluated state ownership. Public jobs have separate acceptance; no symmetry admission follows from these factories.

Hybrid cutoff and joint-grid factories now have independent acceptance too. They reuse the HF geometric planner and certified reciprocal generator with complete hybrid admission; no HF solver proxy is used. Independent integer enumeration covers skew Gamma and shifted multi-k G/Q spheres, exact cutoff boundaries, pair-complete source translations and distinct canonical XC images. Identical pair/G/Q supports retain the same child geometry identity as HF. RKS, UKS, unequal/empty spins and both zero-mode policies match explicit source composition and independent full SCF, Fock and individual energy terms. Both atomic partition choices and capped evaluated states are covered. All five whole-request exact/one-short caps precede enumeration or poisoned array copies, and a coincident-center fixture proves joint refusal before partition generation. Grid/source ownership is charged through the full hybrid solve. These tests do not establish automatic grid accuracy, BIPOLE parity or a symmetry-reduced producer. Public output and QVF qualification follows below.

Pure-KS cutoff generation now reuses the pair-complete direct source and certified reciprocal source, with a separately selected canonical XC image sphere. Count-only admission bounds all traversal, source ownership and the complete physical KS solver; no exchange-transfer tables are constructed. Independent integer spheres, generated/explicit equality, independent SCF, AO-image gauge transport and exact/one-short budgets qualify these domains. The standalone cutoff interface keeps caller-supplied quadrature; the joint producer below supplies it explicitly, including in selected pure-KS jobs. The empty-beta PBE witness also requires a separate minority-potential conditioning check: the observed libxc fp64 endpoint response amplifies one-epsilon input perturbations even when energy and occupied-spin results agree tightly.

A bounded periodic atomic quadrature adapter now qualifies a finite 3D source: shared generic radial/Lebedev rules and periodic Becke/Stratmann partitions, canonical nuclei and folded points, owned exports and count-only work/memory admission including OpenMP neighbor scratch. Independent radial, angular and integer-image partition reconstruction checks the generated weights. Separate Gaussian/libxc contractions check the same-grid energy/potential, and two independent tensor-cell resolutions qualify the refinement reference. Observed grid errors remain explicit: a larger grid is not an automatic accuracy qualification, and partition-radius refinement matters separately. This does not close automatic profiles or low-dimensional grid rows.

Joint grid/domain/KS admission now reserves every retained grid owner and explicit source copy, subtracts grid work before downstream admission, and checks the whole request before generating numerical points. Independent finite-source SCF and bitwise equality with explicit composition cover RKS, UKS, empty-spin BLYP, both partitions, converged and capped epochs. Exact simultaneous and one-short memory/shell/primitive/scalar/kernel limits cover the joint plan; invalid partition generation is not reached after aggregate refusal. Source receipts and histories retain their existing semantics.

Selected public RKS/UKS jobs now use the joint grid/domain/SCF source with explicit finite XC controls. Job-level independent Gaussian/libxc contraction and SciPy SCF references cover PBE restricted and fixed-spin states, the restricted UKS limit and empty-beta BLYP. QVF validation and exact density readback cover the actual evaluated state, including capped epochs; separate generalized eigensolves check terminal orbitals without reconstructing energy from them. Gauge tests distinguish source-frame arrays from nuclear-frame QVF and require a changed frame identity. Owned exports remain independent.

Before numerical generation, selected KS jobs reject unsupported functional components, exchange sources, BIPOLE controls, symmetry reduction and each insufficient resource cap. Grid-only dry runs and artifact delivery failures preserve the standard lifecycle. Functional/grid citations, child source identities and raw component energies survive output. Whole-job benchmarks include artifact writing and report independent errors with modeled memory. This is finite-source job acceptance, not BIPOLE/CRYSTAL parity, a certified symmetry source, or general functional/grid accuracy qualification.

Selected global-hybrid RKS/UKS jobs now pass independent Gaussian/libxc contractions and SciPy SCF checks under both exchange zero-mode conventions. PBE0, B3LYP and custom LDA/GGA components cover Gamma, shifted meshes, restricted, unequal and empty spins. Method-scaled exchange, its separate correction and the unscaled K child receipt survive manifest, structured log and QVF delivery. Component sums refer to the evaluated density, including capped exits; independent generalized eigensolves verify the separate next projector. Nuclear-frame QVF readback and source-frame Fock/gauge checks preserve that distinction. All simultaneous resource caps pass exactly and refuse one short after reserving job and provenance owners. Unsupported functional components, BIPOLE and symmetry requests fail before generation; dry-run and artifact-failure checks preserve the existing output lifecycle. The public-job benchmark times complete artifact delivery and independently checks SCF, every energy component and lossless QVF density. Finite-source acceptance does not establish BIPOLE/CRYSTAL parity or a symmetry certificate.

Selected public range-separated RKS/UKS jobs now pass independent full SCF, same-density energy/Fock, evaluated-epoch QVF and component-provenance checks. HSE06, CAM-B3LYP, LC-omegaPBE, omegaB97X, distinct-range composites and empty-spin LC-BLYP cover Gamma and shifted meshes. Cancelled descriptors retain complete method admission. Screened-only jobs report the requested convention separately from its inactive actual correction, with identical source/D/F under changes to inactive controls. Signed component energies, raw child K receipts and complete semilocal requirements survive JSON output. All five exact/one-short job budgets include component receipt and serialized owners; unsupported kernels and sources fail before generation. Capped states, image gauges, immutable public exports, dry runs and delivery failures retain their contracts. Nine public states also pass the actual FockBuild draft adapter check with full delivered provenance. Method-owned convergence norms and confirmation criteria remain native; a generic operator diagnostic does not replace them. Whole-job benchmarks include standard artifact delivery.

The frozen-density grid assessment now has its own native aggregate admission and an explicitly partial hybrid entry point. Independent Gaussian/libxc contractions check global and range-separated LDA/GGA components, including multiple ranges and empty spin. Complete hybrid builds at the same HCORE density independently confirm that only the semilocal Fock/energy changes when the grid changes. Pure-entry refusal, complete hybrid admission, cancelled descriptors, source/gauge ownership and exact/one-short aggregate resource caps retain their gates. Exchange and singular corrections remain with the complete method, and partial potentials are never labelled Fock.

The pure grid assessment also has independent contraction checks. LDA/PBE restricted and unrestricted states, BLYP, empty-beta BLYP and complex non-TRIM k matrices check signed XC energy, each spin population, the reference potential, and every spin/k maximum-entry and Frobenius difference. All five resource caps pass exactly and refuse one short before copying invalid numerical inputs. Tests cover count overflow, retained reference and external storage, batch-independent source identities, separate fixed-density identity, owned exports and AO-image gauge transport.

Its benchmark separates same-grid correctness from reference convergence. The chosen atomic reference still has measurable energy and potential errors against independent tensor-cell integration. The optional physical HeH/PBE probe holds a confirmed finite-source UKS density fixed across four atomic grids and three independent tensor resolutions. It tests reference adequacy, not another SCF sequence; a stable charge integral cannot qualify a changing minority-spin potential. No automatic accuracy profile follows from these diagnostics. Image, functional, boundary, BIPOLE parity and source-specific symmetry gates remain independent.

The harder HeH/PBE reference is now also tested with independent adaptive cell integration. The benchmark uses Genz-Malik and two product Gauss-Kronrod rules with explicit subdivision caps; energy, populations and all real/imaginary spin/k potential entries participate in adaptation. The vector witness is checked against same-point native contractions and complex density energy derivatives, including restricted LDA/PBE and empty-beta BLYP. Actual convergence status and inter-rule differences remain distinct from estimated errors. This strengthens the fixed-fixture reference without claiming an automatic grid profile or changing a product quadrature source.

Finite lattice compact remainder

tests/test_manta_lattice_remainder.py compares the native positive integral envelopes with independently evaluated incomplete-gamma formulas, including optional 70-digit references. Signed compact point clouds test complete finite Ewald cross energies, every charged pair and order selection. Near-set transfers, cubic/skew cells, origin limits, support contact, charge/radius scaling, covariance, positive underflow, source identity and exact/one-short resource caps exercise the conditional contract. Previously accepted coefficient matrices and identities remain unchanged.

The remainder benchmark separates bound cost from coefficient construction and independent validation. The recorded vq calculation covers 24 finite Ewald energies, all nine charged pairs per case and four adaptive-order calculations. Every measured error is below its admitted bound; at order 12 the maximum cross-energy error is 2.38e-15 Eh. Source and native identities accompany the benchmark. These compact finite-source calculations have no matched ORCA/CRYSTAL case. Gaussian tails, omitted Ewald images and numerical roundoff are excluded from this Taylor ledger; no production periodic BUPO or symmetry omission follows.

Finite lattice Gaussian error ledger

tests/test_manta_lattice_gaussian.py checks all four native orbital-pair and auxiliary-envelope combinations against independent analytic Gaussian convolutions. Signed off-center p/d contractions use bivariate polynomial Gaussian integration and refined radial quadrature, independent of native Taylor coefficients and moment recurrences. Tests also cover complete neutral three-Gaussian energies, separate compact/penetration/full-moment terms, an explicit tight-source error target, absolute norms for neutral components, units and density scaling, retained-moment requirements, immutable identities, positive underflow and exact/one-short joint budgets. Previously accepted coefficient matrices and identities remain unchanged.

The Gaussian ledger benchmark measures joint coefficient, remainder and error construction. The recorded vq calculation passed 24 finite Gaussian energies, all nine pairs per case, four signed angular combinations and four tight-source target calculations. At order 12 the largest energy error was 8.89e-16 Eh. All four tight-source cases met a 1e-8 bound at order 5. Diffuse-source bounds can be conservative and need not decrease with order; the consumer must check the actual bound. The benchmark records source and native identity and measured errors.

No matched ORCA/CRYSTAL reference exists for this arbitrary finite-source profile. This ledger excludes omitted lattice/pair-image domains and floating-point errors. Its envelope fingerprints do not authorize a Fock source or symmetry omission. Production periodic BUPO/RI-BUPO, complete accuracy profiles and point-nuclear self conventions remain separate work.

Infinite Ewald cube-domain remainders

tests/test_manta_lattice_domain.py checks the complete integer-cube omission bounds against independent infinite positive shell envelopes, explicit real/reciprocal refinement and complete neutral two-ion Ewald energies with regular point self. Signed compact charge clouds and translated copies verify the finite periodicity-defect bound. Rotations, handedness, skew cells, scaled units, zero norms, positive subnormals, kernel identity, near transfer, invalid/incomplete domains and count-only resource refusal are covered. Native matrix coefficients and compact remainders preserve the saved prior bitwise fixtures.

The domain-bound benchmark records native bound construction and complete ionic energy comparisons. Adaptive cube enlargement must meet an explicit 1e-8 Eh bound, with measured error also below that target. The high-cutoff reference is an independent SciPy erfc/cosine sum, including the self correction in Ewald (1921), IV.1, Eqs. 38-40. A finite periodicity defect is measured rather than set to zero. This qualifies conditional compact-source domain errors, not unbounded Gaussian lattice errors, AO pair-image convergence or a full SCF profile.

Actual local vq evidence includes 24 fixed complete ionic energies, eight adaptive target calculations and two signed compact translation checks. All eight 1e-8 Eh targets are met at cube radii 5 through 8; the largest accepted bound is 9.657e-9 Eh and measured error 3.89e-16 Eh. Explicit finite periodicity defects are covered by conservative real-domain bounds. Source/native pins, fetched numerical artifacts and reference limitations are recorded in the benchmark.

Periodic pair-image density source

tests/test_manta_periodic_pairs.py compares native shifted-shell moment panels and density contractions with independent polynomial Gaussian quadrature, including signed contractions and pure/Cartesian l=6 shells. An unreduced ordered Bloch sum independently checks the q=0 conjugate-pair identity. A nonreciprocal Fourier counterexample preserves its boundary. General complex Hermitian densities, non-TRIM momenta, nonuniform/zero weights, weighted adjoints and complete quadratic energy derivatives are tested without assuming time reversal between k points. Ownership, source identity, canonical image order, origin shifts, retained norms, zero density, invalid domains and all five joint resource caps have separate gates.

The periodic pair-source benchmark separates immutable source setup, forward density moments and adjoint AO responses. Its complete finite Fourier Coulomb calculations use native moments with a declared Taylor density approximation. Independent ordered Gaussian Fourier integrals measure that approximation error; retained absolute radial moments bound it. Same-order polynomial quadrature checks the source itself. A converging diagnostic Taylor approximation does not establish an SCF accuracy profile. The molecular extent helper refactor preserves every field and identity in the saved regression fixtures.

The complete local calculation evidence covers 24 finite Fourier Coulomb energies and four fixed quadratic density functionals through vq. Native same-order Fourier discrepancies are at most 4.75e-15, half-trace errors 5.00e-16 Eh and finite-difference derivative errors 5.41e-15. All explicit Fourier/energy bounds cover their errors. The expanded density set still has order-12 truncation up to 2.264e-5 Eh; no universal convergence ratio or SCF accuracy target is inferred. Source/runtime provenance and measured results are recorded in the benchmark.

Periodic traversal, source-bound aggregate Coulomb error control, full charge policy, omitted-image/lattice convergence and production Fock integration remain required. The molecular bubble-tree inventory guard is unchanged. No spatial symmetry, exchange or nonperiodic translation identity is inferred.

Physical range fitting sources

tests/test_manta_periodic_range_fitting.py compares dense and streamed erfc/erf metrics and couplings with libint short-range and independent Gaussian Fourier references, including signed angular contractions. It checks physical/numerical range separation, finite-zero ownership, the complementary-kernel identity, image gauge and transfer conjugacy, fixed RI contractions, source/frame/density identity separation, immutable controls and all five resource refusals. Saved default Coulomb matrices, identities and counts remain unchanged.

Four complete finite Gamma SCF diagnostics combine the native fixed Coulomb-J, physical-range K and semilocal XC components outside the bounded driver. Their full functional energies and states are compared with independent libint/Gaussian/NumPy responses and SciPy fixed points. These deliberately specified finite functionals have no matched ORCA or CRYSTAL reference; external parity is untested. They do not qualify production fitted range KS composition, public jobs, source reduction, derivatives or a converged accuracy profile. The measured source and calculation results are in the range-fitting benchmark.

tests/test_manta_periodic_ri_range_fock.py extends physical-range acceptance to one, two and four k points, including zero/nonuniform weights, signed exchange coefficients, positive truncated and empty projectors, weighted variation and reciprocity, image transport, exact resource boundaries and screened-J refusal. Four complete shifted two-k functional SCF diagnostics independently compare the whole-mesh native range K with per-q libint/Gaussian/NumPy contractions. They retain separate bare-Coulomb J and actual functional energy. The original Coulomb Fock baselines remain bitwise unchanged. See the whole-mesh range benchmark.

Bounded fitted range KS

tests/test_manta_periodic_ri_range_ks.py independently reconstructs each Coulomb/erfc metric and coupling using libint and Gaussian Fourier references, retains fixed NumPy projectors, and compares complete native SCF states with SciPy fixed points. RI-J/exact-K, exact-J/RI-K and RI-J/RI-K cover Gamma and shifted two-k RKS/UKS, HSE06, CAM-B3LYP, mixed physical ranges, other long-range hybrids and empty beta spin. Tests retain actual functional energy, signed and cancelled terms, finite screened zero and method-owned singular correction.

Further witnesses cover functional derivatives, capped evaluated epochs, truncated/empty metrics, rectangular overlap spaces, immutable exports, all five exact/one-short resource caps before payload copies, and selected Python provenance admission. Shared Fock snapshots and complex multicentre AO/auxiliary image transport keep the operator and symmetry seams qualified for these sources. Sixteen saved prior fitted pure/global and direct range KS states, plans and identities are unchanged. The bounded range KS benchmark records 18 isolated complete calculations. No matched ORCA/CRYSTAL finite-source reference is available; external parity and domain/grid convergence remain untested. Generated range-fitting methods are qualified separately below; public jobs follow below, while source reduction still needs its own acceptance.

Generated fitted range KS

tests/test_manta_periodic_ri_range_ks_domains.py checks integer reciprocal spheres in skew cells, full transfer reversal and kernel-independent geometry. Complete generated RKS/UKS on Gamma and shifted meshes covers HSE06, CAM-B3LYP, mixed physical ranges, exact/RI J/K choices and empty beta. Generated and explicit matrices, spectra, energies and physical-source identities agree bitwise. Independent libint/Gaussian/NumPy/libxc/SciPy SCFs compare complete evaluated matrices, functional components and grid populations.

All five joint resource boundaries, selected output reservation, invalid-source refusal before payload generation, owned arrays, geometry/projector identity separation, shared Fock snapshots, rectangular overlap frames and complex multicentre AO/auxiliary image transport are exercised. These tests do not grant source-qualified symmetry skipping. The generated range KS benchmark records isolated complete native and selected calculations. Grid/cutoff convergence and external ORCA/CRYSTAL parity remain unqualified.

Public fitted range-KS jobs

tests/test_manta_periodic_ri_range_ks_job.py compares complete public RKS/UKS calculations with native generated sources and independent functional SCFs. HSE06, CAM-B3LYP and mixed ranges cover Gamma/shifted meshes and strict/BvK conventions. Separate witnesses cover LC-wPBE, empty beta, truncated/empty projectors, capped evaluated states and every exact/one-short resource limit. Unqualified selections refuse before generation or calculated artifacts.

Returned results, manifests, logs and QVF retain the same energy, density, frame and per-kernel source/projector evidence. QVF schema validation and bitwise density recovery, complex AO/auxiliary image transport, rectangular overlap frames and immutable shared Fock states guard the common interfaces. Dry runs and synthetic delivery failures check writer lifecycle. The public range-KS benchmark measures complete jobs and records independent comparisons, output sizes and resource reservations. These finite-source calculations do not qualify an accuracy profile, external parity, source reduction or derivatives.

Full Gaussian infinite-domain remainder

tests/test_manta_gaussian_domain.py checks native pointwise Gaussian majorants against every signed angular Cartesian/pure component, periodic pair translations and large-coordinate product centers. All pair/auxiliary source combinations compare their omitted Ewald errors with full Gaussian convolutions and independent reciprocal Coulomb sums. Angular fixtures also use polynomial Gaussian quadrature. Complete neutral smooth-charge energies include Gaussian self integrals and adapt the cube to a declared 1e-8 Eh bound. A native moment/finite-coefficient calculation combines the finite Gaussian ledger and new domain bound with matching physical kernel identities.

The 48 focused checks include owned immutable sources, zero/subnormal and unrepresentable bounds, exact resource caps, canonical identities, reciprocal symmetry and payload-free resource refusal. Six previous extent inventories and four compact-domain receipts remain bitwise unchanged. The measured benchmark reports six isolated workers and the external-reference limitation. This primitive does not qualify omitted AO pair images, density aggregation, whole-method accuracy, periodic traversal, symmetry or derivatives.

Periodic bubble source aggregation

tests/test_manta_periodic_bubbles.py checks the native hierarchy against independent multinomial and Gauss-Hermite moments, absolute radial bounds, weighted forward/reverse identities and energy derivatives through order 12. Signed arbitrary complex whole-mesh densities, nonuniform weights, image cutoffs, Cartesian/pure shells, deterministic reordering, source lifetime, owned exports and zero/subnormal cases remain explicit. Exhaustive index expansion proves that accept/refine traversals cover every retained unordered pair interaction once. Molecular inventory validation is unchanged.

Complete finite Fourier Coulomb actions compare to unreduced ordered Gaussian Bloch sums. The tests distinguish source pairing from Taylor error and compare the latter to absolute full-moment bounds. Joint resource caps and shape-only refusal protect hierarchy construction and driver copies. The hierarchy benchmark records timings, runtime provenance, references and limitations. This advances P3b aggregation and traversal geometry; kernel-dependent admission, omitted pair-image error and production periodic BUPO accuracy remain open.

Complete canonical finite Ewald direct response

tests/test_manta_periodic_ewald.py compares every complex J element and separate real, reciprocal and gauge energies with independent full Gaussian convolutions. Signed contractions, Cartesian/pure p and d components, coincident Gaussian self integrals and cubic/skew cells are included. Angular references use bivariate Gauss-Hermite and Laplace quadrature, with quadrature refinement. The reference uses a stable erf difference near coincident Gaussian centers and an erfc difference at long distance.

General complex Hermitian whole-mesh densities, nonuniform and zero weights, two-step energy derivatives, linearity and cross-k responses test the weighted action. Reciprocal energies also compare to unreduced ordered Bloch Fourier sums. Enlarged real/reciprocal domains converge to an independent reciprocal Gaussian Coulomb limit at two eta values. This is evidence for the tested finite sources; it is not a general omitted-domain or accuracy-profile proof.

The 31 focused tests include exact caps, count-only refusal before payload reads, strict/unaligned arrays, immutable ownership, subnormal-scale response, domain reordering and origin/reciprocal/time-reversal covariance. Three old lattice matrices/identities and one pair contraction/identity remain bitwise unchanged. The direct Ewald benchmark records measurements, runtime and actual calculation evidence. No matched ORCA/CRYSTAL profile is available for this arbitrary-density folded finite quadratic form. Production kernel-admitted BUPO traversal, pair-image and aggregate error controls, full charge policy and SCF selection remain open.

Bound-admitted finite periodic BUPO response

tests/test_manta_periodic_bupo.py exercises accepted and direct blocks of one complete finite Coulomb calculation. Full signed Gaussian convolutions provide an independent scalar reference. Cartesian/pure angular sources compare every complex J element and energy with the already independently qualified native direct Ewald source. Cubic/skew cells, nonzero pair images, nonuniform/zero mesh weights and raw moments through order 12 are covered. The fixed partition gives linear J and the weighted derivative of a single quadratic energy, tested with two finite-difference steps.

The tests check aggregate energy and per-AO J bounds, density scaling, subnormal response, immutable source matching, exact resource caps and refusal before payload reads. Periodically overlapping candidates refine even when their central-cell geometry is separated. Zero tolerance and wide Gaussian extents with inadequate error bounds use the complete direct action. Moving identical real images between bare-near and complementary-tail terms preserves the finite kernel and full Cartesian trace contributions.

The finite BUPO benchmark records actual calculation evidence, timings and source/runtime provenance. Four saved direct-source calculations are bitwise unchanged by the shared block-helper extraction, and the existing direct and Gaussian-error checks pass. These bounds compare with the same retained finite canonical kernel; they exclude floating-point roundoff, omitted pair images and infinite-domain error. They do not qualify production BUPO/RI-BUPO profiles, the complete electronic+nuclear charge policy, exchange, source reduction or derivatives with respect to geometry.

Retained-source infinite-Ewald error aggregation

tests/test_manta_periodic_bupo_domain.py compares complete complex J and energy with independently integrated bare reciprocal Gaussian Coulomb limits. Scalar and Cartesian/pure angular sources, both cells and boundary-crossing pair images are included. Reciprocal-reference refinement is checked. Tight mixed BUPO partitions compare with enlarged independently integrated Ewald domains. An independent dense contraction of the public primitive domain bounds verifies diagonal half-energy factors, coefficient norms and both Bloch scatter arms, including same-AO nonzero images.

Density scaling, zero weights/density, positive underflow, exact resource caps and immutable owned exports remain explicit. Domain checks refuse incomplete cubes and inadequate omitted-center separation. Near transfers leave the domain-bound identity and values unchanged. A complete atomic periodic pair source enlarges its domains until both energy and J bounds fall below 1e-8 at two eta values. This target concerns the retained source, not omitted pair images or a production SCF profile.

Four saved finite BUPO responses, bounds and identities remain bitwise unchanged. Existing Gaussian-domain and finite-BUPO checks pass. The domain-bound benchmark records calculations, runtime provenance and measured overhead. The infinite-minus-finite bound includes the finite kernel’s covariance error relative to the limiting retained periodic source. Omitted AO pair images, roundoff, full-cell charge policy, production selection, RI and geometry derivatives remain open.

Matched electronic and point-nuclear composition

tests/test_manta_periodic_electrostatic.py resolves signed s/p/d Gaussian attraction against independent Laplace quadrature and Gaussian characteristic functions, and point energies against independent ordered Ewald sums. Cubic and skew cells, pure and Cartesian components, original mesh weights, zero weights, point permutations and zero charges are covered. A tight neutral source is compared with a complete ordered-image bare reciprocal electronic reference plus independently converged point Ewald energy at two physical eta values. Separate image and reciprocal refinements check the reference.

The checks distinguish retained charge from omitted-image uncertainty, neutral refusal from explicit uniform background, Gaussian self interaction from point self removal, and J+V from half-trace energy. Whole-mesh density derivatives preserve the fixed electronic partition. Deliberately missing central targets and small Ewald domains exercise attraction/point bounds; all five resource limits precede payload reads. Source/result arrays are owned and receipt fields immutable. The electronic source itself retains its previous qualification and independent numerical evidence.

The electrostatic benchmark records local queued calculation evidence, references, measured errors, setup/build cost and remaining limitations. No matched ORCA/CRYSTAL arbitrary-density component profile is available; this is not an external SCF parity claim. Production BUPO accuracy-profile/SCF selection, q-aware RI-BUPO and the remaining method matrix stay open.

Native reciprocal-cutoff selection over that immutable BUPO HF source now passes 12 focused and 38 related checks, plus five complete queue-interface calculation scenarios. Independent integer enumeration validates every executed sphere; Gaussian/Fourier integration and separate SCF validate Gamma/skew RHF, shifted empty-beta/doublet UHF and a capped doublet. Ten accepted native runs preserve factory/explicit-control D/F/H/S/E bitwise. Maximum Fock, same-density energy, relaxed-energy and density discrepancies are 2.621e-13, 1.765e-11, 1.892e-11 and 9.750e-10 in atomic units, within the unchanged comparison tolerances. Two insufficient cutoffs refuse their accuracy targets. Shifted odd meshes, left-handed/skew cells, source immutability, opposite support, all five resource caps, output provenance and evaluated shared-Fock state retain their separate checks. The cutoff report records complete timing/memory and reference limitations. This selects only exchange spheres over a supplied source. Automatic AO/Ewald selection, whole-method profiles and q-aware RI remain open. The public job route below composes the subsequent native source preparation.

Public BUPO HF job acceptance

The typed public job increment composes the already accepted prepared native BUPO source. Five actual vq calculations preserve the accepted RHF/UHF D/F/H/S/E and source identities exactly. Independently integrated Gaussian/Fourier/eigensolver references are reused with pinned artifacts and unchanged physical inputs. Maximum same-density energy and Fock differences are 1.765e-11 hartree and 2.621e-13; evaluated spin-density QVF round trips have zero discrepancy for the accepted five cases. Capped states remain nonconverged and unconfirmed. All evaluated-density integral targets pass without tolerance changes. The shared Fock state contract and unreduced periodic domain ownership are preserved; molecular symmetry consumer qualification does not authorize periodic reduction.

Focused checks additionally cover independent basis-image gauge transport, dry-run output discovery without source construction, and exact/one-short complete-job resource caps. See the public job benchmark for source/runtime provenance, measured costs and reference limitations. Automatic whole-method profiles, q-aware RI-BUPO, lower-dimensional Green functions, CCM/chi adapters, producer-qualified symmetry, derivatives and acceleration remain open matrix items.

Exact paired periodic RI Coulomb baseline

The fixed q=0 J-only source now executes two raw coupling sweeps when its retained-mode schedule needs more than two. Rank, native metric factor, finite Gram matrix, phase convention and physical support stay fixed. The actual local vq run covers seven complete public states and seven retained-mode controls: RHF, UHF including empty beta, pure RKS/UKS and capped HF/KS states. Independent raw integrals, Gaussian Fourier sums, factorization and SCF pass with maximum Fock and same-density energy differences 5.152e-14 and 9.415e-14 hartree. Evaluated-density QVF and shared Fock state checks pass without granting source symmetry.

The rank-six trial benchmark reduces coupling evaluations from six passes to two under the unchanged conservative admission. Twenty-five new tests cover independent full/truncated/zero-rank fits, weighted adjoints and energy derivatives, image gauges, target separation and all five caps. See the paired RI benchmark for measurements, provenance and the lack of a matched ORCA/CRYSTAL finite source reference. This is the exact baseline for later paired approximate couplings; approximate periodic RI-BUPO and the rest of the matrix remain.

Shared periodic coupling action acceptance

The exact paired RI baseline now consumes the producer-owned forward and adjoint actions on PeriodicGDFTiles. Independent complex transition inputs at Gamma and nonzero transfer, Coulomb/erfc/erf kernels, angular contractions, image frames, optional metric storage and all five action resource caps pass. An actual local vq calculation checks seven complete HF/KS paired states and seven retained-mode controls against independent finite-source SCF references. Shared Fock and QVF evaluated states remain consistent. The report records measured errors, unchanged acceptance gates, runtime provenance and action costs. This establishes the source boundary for the next approximation; approximate periodic RI-BUPO and the other required 0.18.x capabilities remain open.

Fixed-metric periodic coupling screening

The first approximate periodic RI-J coupling uses the existing ordered GDF Gaussian-envelope selector. Its zero-screen finite metric and native retained factor remain unchanged. Paired actions supply density-specific J and energy omission bounds; positive coupling screening refuses fitted exchange. Focused qualification covers independent libint short-range and Gaussian Fourier contractions, complex adjoints, nonuniform/zero weights, retained ranks zero through six, energy derivatives, joint admission and complete evaluated HF states. Public KS uses the same J source and keeps its own XC.

The screening acceptance record records calculation evidence and measured costs. These bounds exclude arithmetic, finite-domain, RI basis and relaxed-density errors. This is an experimental bounded screening baseline, not completed hierarchical RI-BUPO or an automatic production accuracy profile. P3b and the full 0.18.x capability matrix remain open.

Ordered periodic RI multipole integration

The experimental coupling_multipole_error path replaces admitted far erfc image interactions inside the existing GDF producer. Validate raw complex maps at Gamma and nonzero q, dense/tiled equivalence, signed Cartesian/pure shells, image gauges, reciprocal relabelling, exact metric/factor identity, rank-zero and weighted limits, energy derivatives and all joint resource caps. Public RHF/UHF and RKS/UKS states must retain their evaluated shared Fock, independent exchange/XC, QVF density and approximation receipt. An actual local vq calculation is required for acceptance, with source/native pins and independent finite integrals and SCF algebra. ORCA/CRYSTAL comparisons remain unavailable for this custom finite-domain test; no bulk parity claim is inferred. See the multipole benchmark.

The shell-leaf prototype is not the completed hierarchy. Bubble aggregation, upward/downward translations, useful automatic error allocation and large-cell scaling remain part of P3b and the full 0.18.x goal.

The ordered GDF auxiliary-image hierarchy is an additional P3b increment. Validation reuses the exact finite-domain and paired-map references, and adds nontrivial multi-image nodes, upward translation counts, image/reciprocal gauge checks, density-independent partitions and joint tree/moment/envelope admission. Public HF and KS calculations must exercise the hierarchy through vq and retain the shared Fock receipt. The global density-compressed hierarchy, global AO-pair aggregation, automatic accuracy and source-qualified symmetry remain open; this bounded increment does not close P3b or the full design.

Producer-owned Gaussian preparation is shared across periodic RI paired actions and complete SCF builds. tests/test_manta_periodic_ri_preparation.py checks bitwise cold/warm/streaming/dense equality, concurrent first publication, independent source lifetimes, unchanged identities and exact metrics, full storage/work admission before bad inputs, and lazy always-near behavior. Public HF/KS tests check reused preparation in the evaluated Fock receipt; grouped-node HF uses auxiliary cutoff 12 bohr. Complete changed-method acceptance still runs through local vq with independent finite references. This closes repeated Gaussian preparation. Compressed actions and bounded partition reuse are qualified below; global AO-pair aggregation and automatic whole-method accuracy remain open within P3b and the full approved design.

Compressed hierarchical periodic RI actions now qualify the input-moment and output-field path over the existing selected auxiliary-image tree. Every operator column and complex adjoint is compared with independently materialized tiles; additional checks cover angular signed contractions, atom/reciprocal gauges, density-independent partitions, positive magnitude envelopes, all resource limits, fixed metric/rank and weighted energy derivatives. Public HF/KS calculations exercise compression through vq and retain shared Fock, energy and saved-density evidence. Benchmarks compare materialized and compressed actions on the same source. This advances P3b but leaves global AO-pair aggregation and automatic accuracy open; bounded partition reuse is qualified below.

tests/test_manta_periodic_ri_partition.py qualifies source-owned bounded partition reuse for compressed and materialized actions at Gamma/nonzero q and orders zero/two/four. It checks bitwise cold/warm/reconstructed maps and dense tiles, preserved identities/error ledgers, zero and arbitrary complex inputs, concurrent publication, source lifetime isolation, eviction and oversized fallback, cold/warm resource admission before invalid inputs, inactive exact/leaf/reciprocal routes and public HF/KS Fock receipts.

243 affected scientific source checks pass. Benchmarking compares explicit zero and 64-MiB capacities on the same source and metric, recording actual runtime/content pins, first and warm calls, partition work and admitted peaks. Acceptance requires complete local vq calculations and independent assessment of fetched arrays; the benchmark record contains that evidence. External ORCA/CRYSTAL parity remains unavailable for the custom finite-domain fixtures. Global AO-pair aggregation, useful automatic accuracy and the other approved 0.18.x capabilities remain open. See the partition benchmark.

Call-wide periodic RI moment actions add 40 focused source checks in tests/test_manta_periodic_ri_global.py. They compare both complex maps with per-tile compression and separately materialized coupling, including every operator column, Gamma/nonzero-q, orders zero/two/four, signed Cartesian and spherical d shells, atom/reciprocal gauges, linear and zero inputs, fixed metric ranks and weighted energy derivatives. Concurrent calls verify private input state. Source and parent resource checks run before invalid inputs; inactive routes reserve no global storage. Public HF/KS checks retain the shared evaluated Fock and new execution counters.

Benchmark the unchanged source and metric with the policy both disabled and enabled, recording native/content pins, first and repeated calls, action work and admitted peaks. Complete local vq calculations must then exercise the changed HF/KS path and independently assess fetched arrays, approximation bounds and output density. Custom finite-domain references use independent Gaussian/Boys/Fourier and libint integrals, NumPy contraction and SciPy SCF; they do not supply ORCA/CRYSTAL bulk parity. See the global-action benchmark. This qualifies call-wide gather/scatter only. Global pair-bubble traversal, automatic accuracy and the remaining full 0.18.x matrix remain open.

tests/test_manta_periodic_gdf_pair_tree.py qualifies the shared ordered GDF pair tree independently of a new Fock route. It compares every pair/image with an unreduced integer sphere, every classified node and complete partition with brute-force capsules, and the full auxiliary union with independent image enumeration. It checks cutoff equality, separate AO/auxiliary image frames, reciprocal relabeling, signed angular extents, source lifetime, concurrent queries and every resource cap before preparation. Exact s-Gaussian coupling reconstructed through the native tree masks and phases must agree with libint over the complete finite support.

Local vq acceptance now passes four complete finite-source calculations through the native masks and phases, seven public HF/KS states and six raw complex-action regressions. Independent assessment of fetched arrays verifies both complete Coulomb maps and retained-metric responses. All 1,874 source/reference pins and 63 managed output hashes match; 361 source checks and five documentation checks pass. Maximum tree-source coupling and response discrepancies are 1.111e-15 and 1.195e-14; public Fock/energy/density remain within their existing gates. Gaussian/Boys/Fourier, libint and independent NumPy/SciPy references qualify these finite fixtures; no matched ORCA/CRYSTAL reference is available. Those source-geometry calculations used the earlier per-pair hierarchy; the subsequent global-action acceptance is recorded below. Automatic accuracy and the remaining P3b and full 0.18.x gates remain open. See the pair-tree benchmark.

tests/test_manta_periodic_ri_pair_tree.py and the corresponding local vq calculation now qualify the opt-in global pair-tree contraction. All 61 new checks and 611 affected checks pass, including both complex maps, independent finite-source error witnesses, Gamma conjugate-support refusal, dense/raw exports, physical erfc, gauges, fixed metric ranks, energy derivatives, concurrent call-private state and complete resource boundaries. Seven complete public HF/KS states and ten raw cases pass on the same pinned native runtime; 63 managed outputs and 17 fetched arrays verify. The independently contracted Fock, energy, density and approximation ledgers retain their existing gates. No matched ORCA/CRYSTAL finite-domain reference is available. Benchmark and provenance are in the pair-tree action record. This is an explicit pair-tree by auxiliary-image traversal. Useful automatic accuracy, dual-tree/general production scaling and all other unqualified 0.18.x capabilities remain required.

The same pair-tree suite now qualifies per-shell-block error and magnitude ledgers. Its 80 checks include 19 new sparse/complex-input, duplicate-output, large-scale Euclidean-bound and fixed-rank propagation cases; 437 affected checks and 12 documentation checks also pass. Complete local vq acceptance passes the same seven public HF/KS states and ten raw cases on the new native runtime. An independent NumPy-only assessment verifies both action norms and all fixed-density energy/J bounds. Against the accepted predecessor, 146 arrays and the numerical source/factor identities are unchanged. Updated bounds and costs are in the pair-tree action record. These tighter bounds still do not establish automatic useful accuracy; the unchanged custom-domain reference limitations and remaining full matrix requirements apply.

Joint erfc radial and interior-moment bounds

The shared isolated erfc producer now qualifies a joint polynomial/Gaussian radial envelope and an interior absolute-moment scale. Its explicit Taylor derivation is in the scientific contract. This changes accepted partitions, so approximate source identities are versioned; exact metric and finite reference identities remain unchanged. Gaussian penetration and full-moment tails are retained, and finite lattice complement bounds are unchanged.

The increment has 685 passing scientific checks (31 new), one skip and 12 documentation checks. After integrating current BIPOLE symmetry/Fourier work and rebuilding, 134 directly affected checks pass on the final runtime. Complete local vq acceptance adds nine public HF/KS states and fourteen raw cases, including tight Gamma/nonzero-q actions and complete RHF at orders two/four with requested coupling error 1e-8. A NumPy-only fetched-array assessment verifies component/Euclidean action bounds, propagated fixed-density J/energy bounds, independent SCF references and managed output. Seventeen predecessor cases retain bitwise-identical exact reference arrays.

The explicit accuracy benchmark records source/native provenance, timings, measured errors, conservative bounds and reference limitations. Fixed-density energy bounds reach below 8.2e-10 hartree on its small fixture, while complete RHF remains slower than exact RI. Coupling tolerance is not whole-method accuracy; no automatic profile, general production speedup, external bulk parity or additional symmetry permission is claimed. All remaining required MANTA 0.18.x capabilities stay open.

Lossless high-order partition retention

The global pair-tree source now retains only structurally allowed interaction coefficients and its actual accepted antichain. A single expansion restores the same dense matrix before contraction. The existing separately admitted construction workspace permits cache charging and eviction by actual entry bytes; oversized entries are used once without retention. The numerical source, partition decisions and all error ledgers remain unchanged.

All 373 focused scientific checks pass, including 13 new cache/high-order cases; twelve documentation checks pass. Complete local vq acceptance passes ten public HF/KS states and sixteen raw cases, adding order-six RHF and strict-tolerance Gamma/nonzero-q maps. A separate NumPy-only assessment finds 340 result arrays bitwise unchanged across all 23 accepted predecessor cases. The accuracy and cost record provides source/native provenance, references and remaining limitations. Order-six repeated RI-J improves about sevenfold on the bounded fixture, while complete RHF remains slower than exact RI. This qualifies lossless storage reuse, not automatic whole-method accuracy or a production crossover. The full remaining 0.18.x capability matrix stays required.

Componentwise retained-factor bounds

The shared GDF actions now expose per-output omission and exact-reference auxiliary-column magnitude envelopes. Periodic RI propagates these through the actual retained metric factor and keeps the older scalar bounds when tighter. Numerical values, partitions, fixed metric/projector and source identities are unchanged. Gamma envelopes follow the same conjugate pair completion as the source; no new symmetry permission is inferred.

383 scientific checks and eleven documentation checks pass. Thirteen new cases cover five producer routes, complex Gamma/non-Gamma maps, zero and large inputs, owned exports and adversarial errors at ranks zero/one/six. Local vq passes ten public HF/KS states and sixteen raw cases. Independent NumPy assessment verifies component bounds, exact-reference column magnitudes and retained-factor error transport. All 1,878 source pins, 90 outputs and 26 archives verify. Across the same 26 predecessor cases, 364 numerical and reference arrays remain bitwise identical, with matching source/factor IDs.

The accuracy benchmark records provenance, limits and cost. Fixed-density J bounds improve by 5.8-14.3 times and energy bounds by 1.28-4.06 times on its small rank-six fixture. Complete strict RHF energy bounds improve only about one percent; automatic useful accuracy and production crossover are not established. No matched ORCA/CRYSTAL custom-domain reference is available. Existing Gaussian/Boys/Fourier, libint and NumPy/SciPy references apply; KS shares libxc. Basis/domain, arithmetic and relaxation errors remain separate. All other unqualified MANTA 0.18.x capabilities remain required.

Fixed-envelope automatic periodic RI coupling selection

The selector admits all trial work and overlapping source storage, then uses shared producer omission/magnitude envelopes and the actual retained metric factor to certify J and Coulomb-energy targets for a declared AO density L1 limit. It fixes the source before SCF, checks the limit on every evaluated density and refuses unsupported routes or unmet targets. The public receipt records selected/requested controls and the certificate. Independent K/XC, unified Fock and source-qualified symmetry ownership remain unchanged.

899 focused checks pass, including 25 new cases for metric ranks zero/one/six, complex weighted densities, exact resource limits, invalid/exhausted controls, HF/KS, global-hybrid and physical range composition. Local vq passes ten public states and four hybrid/range cases. Independent NumPy assessment verifies the envelope at 160 additional Hermitian densities, all source/output pins and unchanged exact-reference metrics/couplings. The accuracy and cost benchmark records source/native provenance, references and memory/cost limitations.

Both 1e-6 J/energy targets pass for the complete RHF fixture after two source trials, but its automatic runs remain slower than exact finite RI. No matched ORCA/CRYSTAL custom-domain reference is available; existing independent finite Gaussian/Boys/Fourier, libint and NumPy/SciPy witnesses apply. This qualifies automatic coupling selection only. Whole-method error, useful performance, remaining source adapters, lower-dimensional boundaries, source-qualified symmetry, derivatives/stress and every other unqualified 0.18.x row stay open.

Overlap-derived automatic periodic RI density limits

The complete HF/KS path now obtains a fixed density L1 envelope from the shared bounded solver’s canonical overlap and occupation contract when the requested limit is zero. Raw RI builders retain the explicit-limit contract. Count-only admission covers the added eigenanalysis, work and owned exports. The method selects its coupling source once and still checks every density.

712 focused checks pass, including 26 new cases for independent complex occupied subspaces, overlap rank/gauge/scaling, resource refusal and complete method equivalence. Local vq passes ten public HF/KS states plus four global-hybrid/physical-range cases. A separate NumPy assessment reconstructs the envelope, checks 480 independent occupied subspaces and 160 further Hermitian densities, verifies source/output pins and reuses unchanged exact metric/coupling references. Automatic and explicit resolved-limit states match bit for bit. Unified Fock, physical K/XC, BIPOLE/CRYSTAL and symmetry contracts are preserved.

The RHF benchmark derives L=784.535933 and reaches the 1e-6 J/energy targets through exact finite-coupling fallback at orders two/four/six. The UHF hydrogen case retains nonzero approximate far blocks. The accuracy and cost benchmark records source/native provenance, numerical comparisons and the conservative runtime cost. No matched ORCA/CRYSTAL custom-domain reference is available; Gaussian/Boys/Fourier, libint and NumPy/SciPy witnesses apply, with shared libxc for KS. Basis/domain, metric solve, arithmetic and relaxation errors remain separate. Automatic whole-method accuracy and production performance are unfinished, along with every other unqualified full-design capability.

Componentwise automatic periodic RI allocation

The shared canonical-overlap helper now supplies an entrywise envelope for the weighted spin-total density as well as its total L1 limit. Source-owned absolute action and omission envelopes preserve shell-block information, Gamma conjugate-orbit transport and exact residuals. The selector propagates them through the actual retained factor and probes the same adjoint partition. It admits all work/storage before setup, fixes both contracts before SCF, and rejects any evaluated density exceeding either constraint. Explicit positive L without entry limits retains the scalar selector.

884 numerical checks and 48 documentation checks pass. Local vq passes ten public HF/KS states and four hybrid/range cases. Independent NumPy assessment checks 480 occupied subspaces, 160 further densities, both constraint families and the full certificate. Exact reference arrays and metric/factor identities are unchanged. Explicit resolved total/entry controls reproduce automatic states bit for bit. No new Fock ownership, physical K/XC, BIPOLE/CRYSTAL or symmetry policy is introduced. The accuracy and cost benchmark records source/native provenance and matched scalar controls.

The small RHF fixture accepts looser tolerances but still falls back to exact finite coupling and pays extra setup cost. UHF hydrogen retains approximate far blocks under both requested targets. No matched ORCA/CRYSTAL custom-domain reference is available; finite Gaussian/Boys/Fourier, libint and NumPy/SciPy witnesses apply, with shared libxc for KS. Basis/domain, metric solve, arithmetic and relaxation remain separate errors. Automatic useful whole-method accuracy and production performance remain open with the other required rows.

Automatic RI trial selection without premature exact fallback

Measured fixed-source curves exposed a certified approximate interval that the former target-ratio step skipped. The selector now uses a less aggressive bounded proposal and handles positive-double underflow. Shared producer bounds still decide every acceptance, and source/metric identities remain fixed before SCF. No additional physical source or symmetry policy is added.

1,120 numerical checks and 48 documentation checks pass. Ten new cases cover three starting tolerances at orders two/four/six and an underflowing estimate. Local vq passes ten public HF/KS states and four hybrid/range cases; separate NumPy assessment verifies all certificates, 480 occupied subspaces, 160 further densities, numerical reference identities and source/output provenance. The three RHF orders now retain nonzero far blocks while meeting both 1e-6 targets in two trials, with explicit-source state equivalence. Exact finite RI remains faster on this small case. The accuracy and cost benchmark records measured bounds, costs and source/native identities.

No matched ORCA/CRYSTAL custom-domain reference is available; independent finite Gaussian/Boys/Fourier, libint and NumPy/SciPy witnesses apply, with shared libxc for KS. This is finite-coupling allocation, not whole-method accuracy. Basis/domain, metric solve, arithmetic, density relaxation, useful performance and every other unqualified full-design capability remain open.

Complete periodic RI image-accuracy admission

A separate pre-SCF ledger now reuses the shared full-image overlap/kinetic producer and canonical density envelope in RI HF, pure KS, global hybrids and physical range compositions, including exact J with RI K. Explicit completion cubes can be smaller than retained inventories while preserving a conservative positive exterior bound. Same-support physical states and unified Fock identities are unchanged. All five resource caps, invalid controls, immutable target snapshots and tight-target refusals are checked.

Source b33fa2d7be9c40621964c6f17c3a1326232836b4 passes 46 image checks and 1,904 affected regressions. Local vq acceptance covers twelve public states, independent Gaussian quadrature, NumPy/Decimal contraction and 1536 occupied subspaces. A tighter-support complete RHF comparison uses independent finite integral construction and SciPy SCF. Existing hybrid/range reference evidence is reused; no matching external custom-domain reference is available. The RI image benchmark records measured bounds, overhead, resource provenance and limitations.

This qualifies only S/T image errors and kinetic energy in the same finite canonical density family. Nuclear, two-electron, metric/solve, arithmetic, overlap-rank changes and relaxed-state accuracy remain outside the ledger. Automatic whole-method RI-BUPO profiles, useful performance crossover, low-dimensional sources, conditional CCM/chi adapters, qualified symmetry, remaining derivatives/stress and acceleration rows remain unfinished.

Uniform canonical exchange envelope

The shared producer is exercised on signed contracted s and Cartesian p sources, complex occupied subspaces, unequal and empty spin populations, rank truncation, original mesh order, and strict uniform-weight refusal. Independent contour-shifted Gaussian quadrature compares retained exchange with enlarged AO and reciprocal sums. Complete local RI HF calculations exercise the new bound at their evaluated states; these do not yet impose a complete RI exchange target. Count-only exact and one-short caps precede input values, typed reuse preserves the certificate, and exports own their read-only arrays. The occupied-space benchmark records constructor, overlap analysis and reused-envelope costs separately. No production speedup or whole-method accuracy follows from this prerequisite.

Local vq acceptance of this increment passed eight cases and four complete finite HF calculations, including three RI and one BUPO case. Independent Fourier/occupied-space references and 70-digit positive contractions checked 576 random spin-pair states. The benchmark records actual source/native identities and limitations. A missing import in three test wrappers was corrected separately; numerical code and the source-pinned calculation payload were unaffected. That prerequisite did not yet impose complete RI exchange targets; the adapter below now adds them for qualified full-Coulomb methods.

RI exchange and fixed-BvK admission

Exercise optional pre-SCF targets in RHF, unequal-spin UHF, empty beta and restricted/unrestricted global hybrids. Enabled/disabled controls must retain bitwise-identical evaluated states and source identities, including capped iterations and output densities. Reconstruct BvK positive bounds independently and compare finite/full Gaussian overlaps at fixed occupied subspaces. Admit exact and one-short memory, shell, primitive, scalar and kernel budgets before poisoned numerical payloads. Refuse unqualified fitted K, pure KS and physical range sources. Test the explicit AO cube’s retained-support guard and preserve standalone default-source identities against accepted evidence. A compact complete RI calculation must pass tight targets; loose diffuse bounds must remain visible rather than be relabeled as practical accuracy.

This increment passed local queue acceptance on eight complete RI states, 512 random spin-pair subspaces, independent Gaussian/BvK witnesses and 70-digit positive contractions. Two prior standalone source certificates and one PBE0 state were reused with bitwise comparisons. Independent finite HF Focks/energies and converged SCF references passed. The compact strict and fixed-BvK sources both meet 1e-8 matrix and energy targets. Source checks pass 1,066 affected cases. The RI exchange benchmark records exact implementation/native identities, measured errors and costs. No matching ORCA/CRYSTAL custom finite-domain reference is available. This leaves the whole-method error budget and remaining capability matrix unfinished; ordinary diffuse-source bounds are still loose.

Automatic physical component supports before RI SCF

Source d70e86fa5c690c40364248d0c15ef8b6778a1a59 qualifies bounded source selection through the shared cutoff, overlap-envelope, S/T, nuclear and exact-exchange producers. Twenty-one focused tests exercise multi-step growth, complete RI HF/KS routes, unchanged explicit-source states, all five resource caps, owned option snapshots, dry runs, hard limits and retained source refusals. 420 affected shared-producer/RI checks pass. A separate documentation and citation run exposes only an existing unrelated changelog-format defect.

Local vq acceptance runs a converged compact RHF calculation and tight diffuse RHF/UHF calculations capped at one evaluated iteration. Independent Gaussian S/T, polynomial/Boys/Fourier nuclear sources, libint finite RI metric/coupling, NumPy factors, analytic Fourier exchange and SciPy occupations check their complete finite states. The scalar-Gaussian Fourier reference is cross-checked with general shifted-contour quadrature. The compact case additionally passes independent SCF closure and bitwise automatic/explicit source equivalence. QVF and shared Fock exports agree.

All requested 1e-8 component bounds pass, including diffuse sources whose initial nuclear attraction and exchange estimates were much larger. The diffuse source requires nearly one million exact-exchange vectors; no useful production crossover follows. The unchanged auxiliary 12-bohr boundary case still refuses its non-conjugate capsule support; acceptance explicitly uses 12.1 bohr rather than altering the shared selector. No matched ORCA/CRYSTAL custom-domain reference is available. Source/native identity, exact sizes, measured error and automatic preparation overhead are in the support-selection benchmark.

This is automatic physical component selection, not a relaxed total-error RI-BUPO profile. Finite fitting/metric, arithmetic, rank stability, relaxation, XC and basis/k error ledgers, useful performance, low-dimensional sources, CCM/chi, source-qualified symmetry, derivatives/stress and remaining acceleration gates stay required by the full 0.18.x goal.

A compact local vq integration calculation also passes after merging incoming BIPOLE lattice-key exports and weighted Fourier moment reuse and refreshing the native runtime. Its S/H/F, density, energy and source certificates match the independently qualified compact state bitwise. The benchmark records both native identities; the earlier diffuse scientific evidence is reused without duplicate calculations.

Nested periodic RI metric-factor truncation bounds

Source 522b81f9651db8e382d328b313d92ecbc4e28e8b adds optional combined coupling and nested stored-factor bounds to the existing Gamma J-only accuracy selector. The selected factor, shared finite-source producer, fixed density family and all five resource caps retain their existing contracts. A finer reference cutoff adds positive modes from the same stored eigensystem; this does not certify an ideal inverse or an unfitted Coulomb operator.

Twenty-two focused cases pass: independent finer-rank RI references for complex indefinite densities, Decimal90 positive contractions, empty and zero-rank limits, partial reference spaces, invalid-cutoff and unmet-target refusals, all five resource caps and complete HF/KS output compatibility. 265 shared producer/RI/support-selection regressions and 468 changelog and citation checks pass. The earlier unrelated changelog-format issue is resolved on incoming main.

Local vq acceptance runs three converged calculations: full and truncated RHF, and truncated UHF. Independent Gaussian/libint/Fourier finite sources, NumPy factors and SciPy SCF check the selected and reference states. Coupling-reference Fock/energy differences are below 5.0e-15/1.12e-13; independent densities agree within 4.81e-10. The nonzero metric differences are covered, though the bounds remain very conservative. QVF and shared Fock exports agree, and manual selected-source control states agree bitwise. No matched ORCA/CRYSTAL custom-domain reference is available.

The metric-bound benchmark records runtime identity, measured errors, bounds, timing and limitations. Finite fitting-basis/domain, eigensolver, arithmetic, rank-stability and relaxation terms remain open, as do useful automatic truncation and all other unqualified rows of the approved MANTA 0.18.x matrix.

Full-Coulomb periodic RI fitting enclosure

Source 9bfd02610edfacb6974b6f254c1d05acbb5d2199 adds an explicit immutable certificate comparing the selected stored RI map with full zero-average Coulomb. It reuses the existing RI and BUPO builders; the BUPO reference must carry both infinite Ewald-domain and omitted AO-image bounds. A complete real Hermitian probe basis spans the fixed weighted density family. No exact Hilbert projection or variational fitting sign is assumed for separately truncated sources.

Sixteen focused checks and 118 shared RI/BUPO regressions pass. Local vq acceptance converges RHF and UHF and compares their final fixed-density J and Coulomb energy with independent full Gaussian Fourier sums. Reciprocal cubes 36/40 converge within 1.34e-15/2.67e-15; sampled Fourier transforms agree with shifted-contour quadrature. Independent finite-source HF Fock/energy checks pass at 8e-11 and SciPy SCF density error is below 3.23e-10. QVF/shared Fock and bitwise checked/plain J controls pass. Strict source identity caught a validation-fixture reciprocal-frame rounding mismatch; using the native reciprocal lattice fixes it without weakening the guard. No matched ORCA/CRYSTAL custom-domain reference is available.

Observed J/energy errors up to 0.001335/0.017233 Eh are enclosed by 46.038/23018.970 Eh. These large bounds establish the enclosure, not useful automatic accuracy. The fitting-bound benchmark records exact source/native identities, inputs, timing and limitations. The certificate includes selected fit, rank, coupling and domain discrepancies together; do not add those earlier component bounds again. Floating arithmetic, rank stability and density relaxation are excluded. Automatic complete-job attachment, useful auxiliary/domain selection and the remaining full MANTA 0.18.x capability matrix remain unfinished.

Shared BUPO electronic reference preparation

Source 0a4dde646b159d6eace78da3a1b06a551cd67209 extracts the original cumulatively admitted electronic source construction from the HF preparation consumer. RI fitting receives the same immutable full-domain/full-image source directly, together with the budget remaining after its preparation. Native mesh/source identities are preserved and no exchange, nuclear or SCF policy enters this factory.

Fourteen new and 32 existing focused cases pass. Local vq acceptance converges RI RHF/UHF and BUPO RHF. Independent Gaussian/Fourier and SciPy SCF references pass, with unchanged RI fitting errors/bounds. BUPO Fock, energy and density differences are below 8.89e-15, 2.74e-14 and 9.12e-11. The established compensated ordered-Fourier exchange reference resolves an initial unbuffered-contraction mismatch without changing tolerances. No matched ORCA/CRYSTAL custom-domain reference is available.

The preparation benchmark records source/runtime identity, resources and measured costs. No new accuracy proof is introduced. Full-job RI fitting admission still needs shared Gamma ownership, pre-SCF canonical density bounds, fixed targets and joint count-only admission. Useful automatic selection and all unqualified original matrix rows remain required.

Complete periodic RI fitting admission

Source 71c9c45fce409d03dc42412012f7128f0139f25c attaches the shared full-Coulomb fitting certificate to the actual Gamma RI producer before RHF/UHF and pure/global/range KS SCF. Count-only joint plans include the shared reference, all probes, canonical density analysis and later fixed-family validation. Fitted K, XC, physical Fock identities and symmetry authority are unchanged.

Twenty-one new checks pass, and the shared regression’s exchange-only range-KS citation guard is fixed. Local vq acceptance converges all six methods with bitwise plain/certified states and source identities. HF independent full Fourier errors are enclosed, and finite-source Fock, energy and density comparisons pass. KS uses unchanged-source controls and reuses existing independent regression evidence. No matched local ORCA/CRYSTAL custom-domain reference is available.

The complete fitting benchmark records runtime identity, measured errors, bounds and overhead. The J bounds near 18.883 and energy bounds near 1053.4 Eh are still conservative. Targets are deliberately loose; this proves pre-SCF enforcement for an explicit shared reference, not useful automatic accuracy selection or a relaxed-state energy guarantee. Arithmetic/rank/relaxation and the complete unqualified MANTA 0.18.x capability matrix remain required.

Kernel-capped constant-pair image envelopes

Source 8fda8ceb874499b6502b90874bf41df48ba280a6 tightens the shared BUPO/RI reference image mass producer while preserving its global kernel constant. Plain s-s primitive exponents use t=min(1,A/(a+b)); other derivations remain intact. Eight new and 77 affected checks pass, including independent reconstruction of the old mixed-angular enclosure and tighter complete RI targets. Ten existing gradient/Fourier checks pass. Local vq converges six RI methods and BUPO HF; independent Fourier/finite-source/SCF checks and previous-state bitwise comparisons pass. No matched local ORCA/CRYSTAL reference exists. The fitting benchmark records bounds, runtime and costs. The unchanged finite fitting discrepancy now dominates this reference remainder; useful automatic source/auxiliary selection and all other unqualified MANTA capabilities remain required.

Full-Coulomb metric cutoff selection

Source b5a0594eac4cc2320d1a712312f9a1bdb2fa90e0 passes 160 focused checks, including 22 new cases and documentation checks. Local vq accepts six converged RI HF/KS profiles plus a gradual five-trial RHF search. Every candidate uses the same full reference; the selected source is retained for SCF. Independent HF numerical references, explicit selected controls and unchanged-state comparisons pass. The initial KS control-identity failure was resolved by matching cutoff settings, with passing HF evidence reused. No matched local ORCA/CRYSTAL custom-domain reference is available.

The fitting benchmark records the rejected and accepted ranks, bounds, costs and runtime. This implements bounded metric selection, with explicit auxiliary and reference domains. Their automatic selection and all remaining unqualified MANTA capabilities stay required.

Automatic periodic RI reference selection

Source c8a2bb129e07bbd91fe894c1d669bb3e25563849 passes 455 focused checks. Local vq accepts default shared-reference refinement followed by metric refinement for RHF, UHF, RKS, UKS, PBE0 and HSE06. Complete states, source identities and full certificates match explicit selected-reference controls. Prior independent HF numerical evidence is reused after exact source/state/hash checks; new bounds enclose the same full-Coulomb values. No matched local ORCA/CRYSTAL custom-domain reference exists. Fixed-cutoff fitted K and separate component policies retain their contracts; symmetry grants and BIPOLE/CRYSTAL conventions are unchanged.

The reference-search benchmark records measured cost, reference trials and native identity. Count plans reserve a declared cap; actual stages charge cumulative admitted costs, including rejected work. Dry runs claim no accuracy. Automatic physical fitting-domain and auxiliary selection and every unqualified original MANTA capability remain required.

Final accounting source c01c7ace969fc193c17ee84d7c70c179e863e113 adds four passing setup/margin checks and two accepted local vq RHF calculations. Default and larger search margins preserve states/certificates. Complete preparation controls are recorded. Together with reused evidence above, 459 focused checks pass; no additional numerical accuracy scope is claimed.

Automatic physical fitting-domain selection

The shared GDF producer now enlarges the actual RI J pair, auxiliary-image and reciprocal supports under pre-SCF full-Coulomb admission. Complete plans reserve the largest allowed candidate for every SCF call; rejected domain/reference/metric work remains charged. This does not change the bases, kernel convention, complementary physical sources, unified Fock ownership or symmetry permissions. See scientific contract Section 5.25.

The source-qualified local acceptance used six converged RHF/UHF/RKS/UKS/ PBE0/HSE06 calculations, each with three physical domains and two metric trials per domain. Every preceding candidate failed at least one target; the selected pair/auxiliary radii were 6.75/9 bohr, with reciprocal cube two and 124 vectors. All selected-source controls preserve energies, densities, Fock/core/overlap matrices and certificate identities bitwise. The four KS profiles also pass on the runtime containing the incoming shared periodic XC projection reuse. Native sources and complete state exports retain their existing qualifications.

For the two HF fixtures, the full-rank J bound decreases from 0.525835 to 0.106848 and then 0.0153705 Eh; its same-density Coulomb energy bound drops from 145.965 to 26.1934 and then 1.10547 Eh. The configured 0.02/2 targets pass only at the third physical domain. The deliberately coarse starting reciprocal support belongs to a synthetic acceptance fixture; these are not recommended production targets or converged total energies.

State	Observed full-Coulomb J error / Eh	J bound / Eh	Observed Coulomb energy error / Eh	Energy bound / Eh
RHF	0.00132026	0.0153705	0.0189208	1.10547
UHF	0.000909658	0.0153705	0.00816172	1.10547

Independent finite Gaussian/libint M/T arrays and NumPy factors agree with the accepted source. Independent complete HF Fock errors are below 7.0e-15 Eh; SciPy SCF densities agree within 1.53e-9. Independently summed full reciprocal cubes 36/40 agree within 7e-16 Eh in J, after checking Gaussian Fourier panels against shifted-contour quadrature. No matched local ORCA/CRYSTAL custom-domain reference was available. KS uses bitwise selected-source controls and qualified shared-producer/functional tests; the external-reference limitation remains explicit.

The 33 new domain tests, 77 existing fitting-admission tests, 667 affected shared/documentation checks and 50 incoming XC checks pass. Coverage includes all five complete and staged resource caps, rejected work, nested metric resets, first-pass retention, limits, initial-support nesting, shared producer union/integral/action checks and component-contract refusals. One test initially inspected the wrong nested plan and was corrected; scientific tolerances were unchanged.

The two fresh-process benchmark pairs measure roughly 0.763/0.402 seconds for automatic/fixed RHF and 0.718/0.411 seconds for UHF, with peak RSS about 275 MB. This is a bounded selection cost, not a speedup or crossover claim. The benchmark record contains the exact procedure and source/runtime pins. Auxiliary-basis selection, remaining numerical/relaxation ledgers and every other unqualified MANTA 0.18.x capability remain unfinished.

Shared product auxiliary candidates

The shared generator and prepared periodic job adapter in scientific contract Section 5.26 are qualified for the admitted sources. Local source-pinned calculations cover RHF/UHF/RKS/UKS/PBE0/HSE06 with level-zero candidates and two finer level-one HF cases. All eight converge and retain their full-Coulomb certificates. Plain selected-basis controls preserve energy, density, Fock/core/overlap matrices, physical source identity and certificate identity bitwise. Standard output includes generation receipts and the Stoychev2017 citation; QVF validates. The four affected KS profiles also pass on the merged XC scheduling runtime with unchanged energies and certificate identities.

The compact HF seed has three functions. Level zero produces eight functions and retains rank eight; level one produces twelve and retains rank ten at the original 1e-12 metric cutoff. The KS seed contains one exact generated duplicate, giving seven functions at level zero. All profiles select the same 6.75/9 bohr pair/auxiliary radii and reciprocal cube two. The preceding seed-basis HF certificate had J/energy bounds 0.0153705/1.10547 Eh. Level-zero enrichment gives 0.00205124/0.481827 Eh; level one gives 0.00205079/0.481811 Eh. These conservative synthetic-fixture targets are not production accuracy recommendations or converged total energies. Increasing basis size does not imply monotonic observed error.

State and level	Observed full-Coulomb J error / Eh	Observed Coulomb energy error / Eh
RHF, zero	8.57946e-5	8.56740e-4
UHF, zero	6.29797e-5	4.62476e-4
RHF, one	8.57972e-5	8.56730e-4
UHF, one	6.29831e-5	4.62472e-4

Independent finite Gaussian/libint metric/coupling arrays, NumPy factors, full HF Focks and SciPy SCF agree. Maximum Fock error is 1.12e-14 Eh and density error is 2.85e-10. Full reciprocal cubes 36/40 agree within 1.12e-15 Eh in J and 2.67e-15 Eh in energy, after checking Fourier panels against shifted-contour quadrature. All observed errors lie inside the reported fixed-density bounds. No matched local ORCA/CRYSTAL custom-domain reference was available. KS uses bitwise selected-source controls and qualified shared-producer/functional tests; that limitation remains.

The 827 focused generator, periodic job, shared-method and repository checks pass, plus 86 incoming XC checks. Coverage includes exact seed preservation, nested grids, independent angular-product spaces through orbital f, normalized shells, the metadata angular ceiling, overflow, source matching, four generation caps and complete job memory/work charges. Test fixture parity, citation routing/output paths, changelog format and test classification were corrected; no numerical tolerance was relaxed.

Two fresh benchmark processes include generation separately and compare complete prepared/plain-basis jobs. Level-zero RHF costs about 1.57/1.53 s; level one about 2.00/2.03 s. Generator time is below 20 microseconds on these tiny fixtures; periodic source construction and solving dominate. Peak process RSS is about 275 MB. The benchmark record provides exact reproduction and runtime pins. No speedup claim follows. Automatic selection among auxiliary candidates, remaining numerical and relaxation ledgers, and all other unqualified 0.18.x capabilities remain unfinished. Unified Fock, BIPOLE/CRYSTAL and symmetry authority are preserved.

Automatic periodic RI auxiliary selection

Scientific contract Section 5.27 is qualified by eight complete local queue calculations: RHF/UHF/RKS/UKS/PBE0/HSE06 at generated level zero, plus two HF cases selecting level one. Every calculation starts from the seed and resets the original metric at each auxiliary/domain trial. The deliberately rank-zero initial cutoff is refined inside each trial. Both targets must pass on the same canonical density family and shared reference. The first six states select after twelve trials; finer HF cases use eighteen. Fixed selected-source controls reproduce energy, density, Fock/core/overlap, physical source and certificate identities bitwise. QVF validates and standard output records the actual selected basis and generator citation.

The compact HF seed has three functions. Targets 0.005 Eh in J and 0.7 Eh in same-density Coulomb energy select eight functions, rank eight. Tightening the energy target to 0.48182 Eh selects twelve functions, rank ten, at cutoff 1e-12. Their bounds remain 0.00205124/0.481827 and 0.00205079/0.481811 Eh respectively. These conservative synthetic targets exercise the controller; they are not production tolerance recommendations. No monotonic convergence assumption or metric repair is introduced.

Independent finite Gaussian/libint M/T and NumPy RI factors agree directly. The four HF states, fitted J arrays, selected vector arrays and entry bounds match the preceding accepted generator calculations bitwise, with the same RI/reference source identities. That match permits reuse of their independent SciPy SCF, full-Fock and Fourier cube 36/40 witnesses. Observed full-Coulomb errors remain 6.30e-5 to 8.58e-5 Eh in J and 4.62e-4 to 8.57e-4 Eh in Coulomb energy, within the reported bounds. No matched local ORCA/CRYSTAL custom-domain reference was available. KS uses bitwise selected-source controls and the qualified shared-functional tests; this limitation remains.

The 913 focused/shared/repository checks pass, including 31 new selection checks and 90 incoming torus/adjoint checks. Coverage includes fixed fitting supports without domain search, retained seed or generated owner, finer candidates, metric resets, immutable captured controls, source mismatch, shared integral parity, sequence lifetimes, all five cumulative search and complete capacity caps, limit refusals and component-contract refusals. No scientific tolerance was relaxed. Incoming release bookkeeping preserves the numerical source; runtime/source pins and job outputs are retained in the private acceptance record.

The updated benchmark compares automatic selection with the identical fixed selected source and reference in two fresh processes, with preparation reported separately. It measures controller overhead, not a speedup. Reproduction and numerical results include source/runtime pins. Unified Fock composition, BIPOLE/CRYSTAL conventions and symmetry authority are preserved. Arithmetic, rank stability, relaxation, useful whole-method accuracy and the remaining 0.18.x matrix are still unfinished.

Reference energy enclosures and tighter periodic RI profiles

Scientific contract Section 5.28 is qualified by eight complete local queue calculations. RHF/UHF/RKS/UKS/PBE0/HSE06 use J/energy targets 0.001/0.05 Eh and permit no reference refinement. All six retain the initial shared BUPO reference because its entrywise energy enclosure passes the fraction test; the former L1*maximum-J estimate would refuse these same controls. The actual fitted source still has to pass both combined targets. This prevents unnecessary reference growth without weakening scientific acceptance.

Two tighter HF profiles use J/energy targets 1e-6/1e-4 Eh, automatically refining the shared reference and selecting the generated auxiliary basis and physical fitting domains. The search retains the same fixed canonical density family throughout. Pair/auxiliary fitting radii stop at 6.75/9 bohr; the reciprocal cube can grow to four. These controls qualify compact synthetic fixtures, not a general production default or whole-method bound.

State	Profile	Observed full-Coulomb J error / Eh	J bound / Eh	Observed Coulomb energy error / Eh	Energy bound / Eh
RHF	reference-energy	5.27954e-07	0.000209896	4.1168e-06	0.0148146
UHF	reference-energy	3.61145e-07	0.000209896	1.94592e-06	0.0148146
RHF	tight	1.1979e-09	5.08334e-07	1.98388e-08	2.3501e-05
UHF	tight	2.57568e-09	5.08334e-07	7.46476e-09	2.3501e-05

Every selected-source control reproduces energy, density, Fock/core/overlap, physical source and certificate identities bitwise; QVF validates. Direct independent finite Gaussian/libint M/T and NumPy factors agree. Complete HF Focks differ by at most 3.09e-14 Eh and independent SciPy SCF densities by at most 2.85e-10. Full reciprocal cubes 36/40 agree within 4.72e-16 Eh in J and 4.44e-15 Eh in energy, after a shifted-contour check of Gaussian Fourier panels. Observed finite-fitting and reference energy discrepancies separately lie inside the new component bounds. No matched local ORCA/CRYSTAL custom-domain reference was available. KS uses bitwise selected-source controls and qualified shared-functional regressions; the external-reference limitation remains explicit.

The 364 focused checks pass: 159 fitting/reference/domain/auxiliary regressions, eight complete new profiles, 93 repository/documentation checks and 104 incoming XC torus/adjoint checks. Coverage includes complex indefinite densities, zero entries/weights, quadratic energy scaling, resource caps, first-pass retention, unchanged fixed-state behavior and shared-source limits. No scientific tolerance was relaxed. Incoming XC residue-index reuse is included in the pinned calculation runtime.

Benchmark reproduction and timings record controller costs. Expensive tight-calculation timings are reused from the scientific acceptance runs; no duplicate calculation is needed merely for timing. Unified Fock, BIPOLE/CRYSTAL and symmetry authority are preserved. Fixed-density Coulomb fitting acceptance does not cover integral arithmetic, rank stability, density relaxation or the remaining MANTA 0.18.x matrix.

Bounded periodic reference batches

Six reference-energy profiles (RHF, UHF, RKS, UKS, PBE0 and HSE06) and two tighter HF profiles pass complete local calculations with both batch-eight and scalar reference evaluation. All 16 states converge and each pair has bitwise equal energy, density, Fock, core/overlap, source and certificate identities. Tight J/energy targets remain 1e-6/1e-4 Eh; no tolerance changes. The HF states, fitted J arrays, reciprocal inventory and entrywise bounds also match the previous independently validated reference-energy evidence bitwise. Its Gaussian/libint, NumPy/SciPy and Fourier36/40 comparisons are therefore reused. No matched local ORCA/CRYSTAL custom-domain reference was available; KS retains the complete scalar controls and shared-functional qualification limitation.

The 31 new checks cover C/F-contiguous batches, complex indefinite angular inputs, zero weights and reciprocal inventory, exact scalar physical/bound receipts, explicit approximate-partition fallback, invalid inputs, all five resource caps and off-diagonal probe pairs crossing batch boundaries. Actual shared kernel/domain counts fall while conservative cold reservations remain charged. Full-source identities and symmetry permissions are intact. See scientific contract Section 5.29 and the paired benchmark. Source 1e78b4651f0bddc44a42c01640506f2524a22ee6 qualifies this bounded increment; arithmetic, rank stability, relaxation and remaining MANTA matrix rows are still unfinished.

Integrated shared XC spin-field reuse is also checked on source 5326cccb9ac7e6e221c4fec2a645722b6f304f90, native SHA256 86847691bfa78359f5a0de752c9b31c37af6a6cfb626fb01d25d18363d505a5e. Four affected MANTA KS profiles each pass scalar and batch-eight complete calculations, preserving the prior energies and certificate identities. The 137 focused torus checks pass, with four existing expected empty-spin GGA/MGGA potential-parity failures. These additional calculations qualify integration; the timing table retains the original paired scientific measurements. An incoming native periodic RKS READ-state fixture still fails the AO-image density-domain closure guard; that separate driver is not qualified by these MANTA runs.

Reference component bounds and directed refinement

Source 603c44ebc749ed859447d239975adc89a947dfe2 qualifies separate finite BUPO, real/reciprocal-domain and pair-image J/energy enclosures over the same fixed density family. Independent Gaussian domain increments cover nonzero real and reciprocal errors for scalar and angular bases. A finite approximate BUPO action is compared with direct Ewald; batch/scalar bounds, zero-weight families, quadratic energy scaling, explicit limits and fixed-source controls pass. Existing metric, domain and auxiliary resource admission remains enforced.

Thirty complete local calculations pass: six soft HF/KS and two tight HF profiles each use selective, joint and selected-source controls, plus three directed-domain profiles and their fixed controls. All are converged. Paired physical states are bitwise equal; fixed controls also reproduce certificate identities. Tight combined J/energy targets stay 1e-6/1e-4 Eh. Changed reference domains have independently assessed certificates, not assumed identity with the former joint path.

Independent Gaussian/libint, NumPy/SciPy and Fourier36/40 HF evidence is reused only after matching physical state, fitted J and reciprocal inventory. New bounds enclose the saved discrepancies. No matched local ORCA/CRYSTAL custom-domain reference is available. Complete KS selected-source controls retain the shared-functional qualification limitation. Approximation-directed complete searches are not claimed by these direct-partition profiles.

See scientific contract Section 5.30 and the component benchmark. Arithmetic, rank stability, relaxation and all remaining MANTA capability rows stay unfinished. Unified Fock, BIPOLE/CRYSTAL and symmetry authority remain unchanged; this is not a relaxed total-energy guarantee.

Stored metric spectrum and rank enclosure

Source a070f8860811789fd07fcc48f814ff2ee585fec2 adds a shared outward-rounded residual and orthogonality audit of actual periodic RI metrics. Independent Decimal 2-by-2 eigenvalues across 300 orders of magnitude, complex clustered metrics, Hermitian perturbations, cutoff ambiguity, deficient eigenvectors and resource-admission checks exercise the bound and its refusal conditions.

Sixteen complete local calculations pass: RHF, UHF, pure RKS/UKS, global and range-separated KS, plus tight RHF/UHF, each with a fixed selected-source control. The 8 exported metric certificates all qualify their spectrum and rank. Physical states, sources and full-Coulomb certificates match the controls bitwise. Four HF states/J arrays match prior independent Gaussian, libint, NumPy/SciPy and Fourier36/40 references exactly. No matched local ORCA/CRYSTAL custom-domain reference is available; KS retains the fixed-source and shared-functional comparison limitation.

See the spectral benchmark for measured bounds, timings and scope. The diagnostic leaves factors, unified Fock, BIPOLE/CRYSTAL conventions and symmetry authority unchanged. It does not certify integral/factor/Fock arithmetic or relaxed SCF energy. Automatic rank-aware selection and all other unfinished capability rows remain.

Optional fitting rank-margin admission

Source fa746e2f2791aaa42f4a546c21fdea3ad1dafbc3 qualifies strict stored-Gamma rank margins in fixed and bounded metric/domain/auxiliary fitting admission. Focused checks cover empty/partial/full retained spaces, exact threshold boundaries, invalid controls, None versus zero, independent reference readiness and pre-SCF exhaustion. The Section 5.31 numerical proof and its accepted Decimal and perturbation witnesses are reused without changing the eigensolver audit.

Twenty-six complete local calculations pass. Five searches advance solely because the initial rank request fails despite passing J/energy bounds; metric, domain and auxiliary transitions retain the actual first passing owner. Their fixed controls match energy/state/source/full-Coulomb certificate bitwise. Eight earlier soft/tight HF/KS profiles also pass with a 1e-10 rank request and selected controls, retaining prior energies. Four HF states/J arrays match accepted independent Gaussian/libint, NumPy/SciPy and Fourier references exactly. Four unattainable searches refuse before SCF. No matched ORCA/CRYSTAL custom-domain reference is available; KS retains its fixed-source and shared-functional comparison limitation.

See the rank-admission benchmark. Unified Fock, BIPOLE/CRYSTAL conventions and symmetry authority are unchanged. This is an enforced declared norm margin for Gamma J, not an automatically estimated integral error, all-q or relaxed total-energy guarantee. The remaining original MANTA capability rows stay unfinished.

Stored factor inverse enclosure

Source f7e3c00b47adf1cb34bc88264b9f8d70e796ad03 qualifies the Section 5.33 stored-factor inverse diagnostic through sixteen complete local calculations and independent Decimal inverse witnesses. Shared Fock/rank/fitting resource checks pass; full/truncated/empty spaces, complex clusters, arbitrary factor perturbations, overflow and pre-payload admission are covered.

All eight selected metric certificates qualify. Selected controls remain bitwise identical in energy, density, Fock matrix and physical identities. Four HF profiles reuse accepted independent Gaussian/libint, NumPy/SciPy and Fourier references after exact state/J/inventory comparison. No matched ORCA/CRYSTAL custom-domain reference is available; KS retains its fixed-source comparison limitation. The bound measures an absolute inverse-operator error, and does not change the separate full-Coulomb roundoff exclusion. See the inverse benchmark. Integral and Fock-action arithmetic, relaxed energy and the remaining MANTA capability matrix still require implementation and acceptance.

Coupling-projected metric action admission

Source 79564c6b1be9ad6ccfd67b40de5acc81b8395ce9 qualifies optional numerical metric J/energy targets on explicit coupling tiles. The finite residual proof in Section 5.34 is checked against independent 100-digit Decimal calculations, full/truncated/empty spaces, complex columns, factor perturbations, density scaling, all resource caps and fixed-source state controls. The selected suite passes 755 checks; no full CI is required for this development landing.

Twenty-eight complete local calculations and four pre-SCF refusals pass. Eight earlier soft/tight profiles meet matching fitting and numerical metric targets. Four HF states/J/inventories match the accepted independent Gaussian, libint, NumPy/SciPy and Fourier references exactly. Five action-driven searches and one nonzero ordered-multipole case retain the actual passing owner and match controls bitwise. No matched ORCA/CRYSTAL custom-domain reference is available; KS retains its fixed-source comparison limitation. See the metric-action benchmark.

Compressed/global moment and pair-tree action arithmetic remains unqualified for this additional policy. Integral and actual Fock-contraction roundoff, relaxed energy and the original remaining capability matrix remain open. Unified Fock, physical BIPOLE/CRYSTAL conventions and symmetry permissions are preserved; the full-Coulomb receipt still excludes roundoff.

Joint density-family metric admission

Source 093642f86a2f98637adc04b5a30c133614222e98 uses a verified dual support bound for total and per-entry density limits. Independent 100-digit primal allocation checks cover ties, nearly equal capacities, zero limits, large and small scales, permutations and public resource boundaries. The focused metric and periodic admission checks are reused after a source-preserving rebase. Six complete local RHF/UHF/RKS calculations with fixed-source controls pass on the integrated runtime. HF reuses the accepted independent reference arrays; no matched ORCA/CRYSTAL custom-domain reference is available, and RKS remains a fixed-source comparison. See the joint-density benchmark. This qualifies tighter bounds within the existing explicit-coupling scope; it does not qualify compressed actions or the remaining full MANTA matrix.

Compressed metric-action admission

Source d0e485994ebb37e2eb382a544f696c07f9fedc35 adds producer-owned outward column norms for ordered compressed hierarchy and global-panel sources. 331 successful focused/shared checks cover independent 100-digit Decimal metric action, complex and signed-angular materialized-column witnesses, fixed-source controls, all five resource caps and existing Fock interfaces. Eighteen complete local queued calculations and six strict-target refusals pass. Source/native pins are preserved; previous acceptance is reused only for unchanged components. No matched ORCA/CRYSTAL custom-domain reference is available. See the compressed metric benchmark. The accepted complete profiles use unreduced symmetry and loose transition targets. This does not authorize new symmetry reductions or qualify pair-tree bounds, integral/contraction roundoff, relaxed SCF energy or production whole-method accuracy. Full MANTA remains unfinished.

Composed stored-input paired arithmetic

Source 0c8d17c4 composes the accepted forward, fixed-factor metric and adjoint enclosures into paired J and energy bounds at the actual stored weighted input. The fitting owner reuses its source-qualified column norm; no new numerical route, source sweep or dense coupling tensor is introduced. 243 focused checks and six complete local queued RHF/UHF/UKS calculations with three strict refusals pass. See the paired arithmetic benchmark and scientific contract Section 5.38 for scope, references and limitations. Weighted-input and stored-source construction, final J/K/Fock assembly, relaxed-SCF accuracy and the remaining capability matrix are unfinished. Full-Coulomb roundoff remains excluded; this does not change the pre-SCF inverse target, shared Fock/eigensolver, BIPOLE/CRYSTAL or symmetry authority.

Paired arithmetic from stored spin densities

Source e30df649 extends paired J/energy bounds to exact spin summation and multiplication by the stored k weights. Per-entry input errors feed the existing coupling interval graph, including Gamma completion, then the shared fixed-factor metric composition. Explicit scope flags distinguish the extended comparison. Exact rational and same-source controls qualify 390 distinct checks after correcting first-use cache accounting in a new fixture. Six complete local queued RHF/UHF/UKS calculations and three strict refusals pass. See the weighted-input benchmark and contract Section 5.39. Physical outputs stay bitwise, with no new source sweep or dense coupling tensor. Final J/K/Fock assembly, density/source construction and relaxed-SCF accuracy remain excluded; full-Coulomb roundoff and the remaining capability matrix are still unfinished.

Evaluated HF/KS assembly arithmetic

Source d5364817 adds a shared stored-component Fock/energy audit inside the existing native HF/KS adapters. It covers weighted traces, final callback reconstruction and Hermitian projection, including iteration-capped states, and composes accepted paired Coulomb arithmetic once. Exact rational and complete-method controls pass within 803 focused/shared checks. Eighteen local queued selected/control calculations and three strict refusals pass; physical states, energy and source identities remain bitwise unchanged. See the assembly benchmark and scientific contract Section 5.40. Source/K/XC/correction construction, density generation, non-paired execution and relaxed-SCF accuracy remain excluded. The full capability matrix and whole-method arithmetic budget remain unfinished; shared Fock/eigensolver, PBC and symmetry authority is unchanged.

Direct periodic exchange arithmetic

Source c7f61c14 adds an optional interval audit to the existing reciprocal B^dagger D B exchange producer at stored Bloch panels and reciprocal factors. Per-entry errors propagate through actual method exchange fractions and density traces once, alongside the accepted paired Coulomb and evaluated assembly bounds. Fifty exact-rational raw cases and signed method composition checks pass within 894 focused/shared scientific checks. Twenty-six local queued selected/control calculations and three strict refusals pass with bitwise physical states and source identities. See the direct exchange benchmark and contract Section 5.41. Fourier/kernel-factor construction, fitted/retained/ fused K arithmetic, XC/correction construction and relaxed-SCF accuracy remain excluded. Shared Fock/eigensolver, PBC/BIPOLE/CRYSTAL and symmetry authority is unchanged; full-Coulomb roundoff and the remaining capability matrix stay open.

Stored exchange zero-mode correction arithmetic

Source 19a8cd49 adds the shared interval SDS/scalar audit to the actual BvK correction in admitted paired RI HF/KS. Twenty-six local queued selected/control calculations and three strict refusals pass with bitwise physical states and source identities. The 862 focused/shared scientific checks include independent exact-rational four-index expansion, signed/zero scales, non-Hermitian raw inputs, cancellation, subnormal products, perturbed witnesses and correction error propagation into energy/Fock exactly once. Resource boundaries, malformed input, strict-zero-mode exclusions and converged/capped methods pass. See the correction benchmark and contract Section 5.42. The reference holds S, D, Madelung and exchange scale fixed. Their physical construction, retained/fused RI/XC, rank and relaxed-SCF errors remain outside it. This does not close #624 or the full matrix, change shared Fock/eigensolver or PBC/BIPOLE/symmetry policy, or expand #557.

Retained-mode periodic RI arithmetic

Source 63a80bf1 audits retained F^dagger T, weighted J/energy and fused q-channel K at stored factor/tile inputs without changing physical sweeps. Complete HF/KS consume the retained J/energy bounds through the shared assembly ledger, separately from paired-route bounds. Local queued acceptance passes 26 selected/control calculations, four raw q-channel calculations and three strict refusals; 1094 focused/shared scientific checks pass, with 52 affected checks repeated after resource accounting corrections. Two prior automatic reference budget refusals remain tracked in #643 and are not claimed as passed. See the retained arithmetic benchmark and contract Section 5.43. Complete fitted-K cross-q aggregation, input/factor construction, rank, XC and relaxed-SCF accuracy remain outside this increment. Shared Fock/eigensolver, PBC/BIPOLE/CRYSTAL, symmetry and #557 scope are unchanged; #624 and the full matrix remain unfinished.

Whole-mesh fitted exchange arithmetic

Source 9e3a8c9a propagates existing q-channel K radii through ordered-q accumulation and signed HF/global/range KS assembly. Local queued validation passes 32 selected/control calculations and six exact-rational whole-mesh cases. There are 1428 distinct scientific and 27 documentation/citation checks; independent energy/Fock differences are below 1.12e-13 Eh/4.85e-15 and physical controls are bitwise identical. See contract Section 5.44 and the fitted exchange benchmark. Input/factor construction, rank, XC and relaxed-SCF errors remain separate; #643 budget refusals remain unresolved. #624 and the full #617 matrix stay open. Shared producer/Fock/eigensolver, PBC/BIPOLE/CRYSTAL, symmetry admission and bounded #557 scope are unchanged.

Full-Coulomb fitted exchange component certificate

Source 7107d2e7 qualifies a fixed-family full-Coulomb fitted-K component bound using shared RI/reciprocal producers and existing image/domain tails. Two complete local queued RHF/UHF calculations, four raw family cases and four strict refusals pass; 539 final-native scientific and 28 documentation/ citation checks pass. See contract Section 5.45 and the exchange fitting benchmark. A supplementary case at 7e5f6760 verifies an actually truncated metric; the complete HF evidence is reused with unchanged product source and native. The bounds remain very conservative. Automatic method attachment and useful reference/auxiliary selection, physical range/XC bounds and source/rank/SCF errors remain #623/#625/#626/#627. This does not close the full #617 matrix, change shared state or symmetry admission, resolve #643, or enlarge #557.

Exchange-certificate preconstruction admission

Source c89aef19 qualifies count-only certificate capacity through the existing pair, RI and exchange-tail plans (contract Section 5.46). All 45 affected checks and two complete local queued RHF/UHF cases pass. The earlier numerical certificates, energies and source identities are bitwise preserved; see the capacity benchmark. Reference preparation and retained J storage are charged before construction; RI setup remains the method caller’s responsibility. Automatic method attachment and useful accuracy remain open under #626/#627; the full matrix is unfinished.

Pre-SCF RI HF fitted exchange admission

Source 2dfbd54d attaches the shared full-Coulomb K component certificate to periodic RI RHF/UHF before SCF, with canonical density-family checks and joint J/K reservations. Eight converged and four partial-rank stopped selected/control calculations plus two strict refusals pass through local vq; 184 scientific checks pass, with six accounting checks repeated on the final runtime. See contract Section 5.47 and the admission benchmark. Raw component targets remain very loose; executed-response arithmetic and source/BvK/rank/SCF errors stay separate. KS attachment, physical range/XC and useful selection remain #626/#627. This does not close the full #617 matrix or expand bounded #557. Shared Fock/eigensolver, PBC/BIPOLE/CRYSTAL and symmetry contracts are preserved.

Pre-SCF signed range exchange admission

Source 1c06da0c attaches the signed physical exchange-component bound before RI range-separated RKS/UKS SCF through shared component owners and the canonical spin family. It retains absolute-coefficient outward propagation, finite erfc zero accounting, joint J/K reservations and separate response arithmetic. Twenty-two converged and eight stopped selected/control calculations and two strict refusals pass through local vq; 468 affected scientific checks pass. See contract Section 5.50 and the range admission benchmark. Existing physical states and Coulomb certificates remain bitwise unchanged. Bounds are conservative; useful accuracy, XC, construction/rank/relaxation and all remaining matrix requirements remain open. The shared Fock/eigensolver, PBC/BIPOLE/CRYSTAL and symmetry contracts and bounded #557 scope are preserved.

Grouped Fourier exchange reference bounds

Source da33a7dd adds optional positive Fourier-decay groups to the existing exchange reference producer and RI accuracy controls. The same primitive envelopes are partitioned by exponent, with all cross-group terms and their separate decays bounded. Physical states and the default one-bin certificates are unchanged. Twenty-three converged and eight stopped calculations, three refusals and four independent complex-density remainder cases pass through local vq; 485 scientific checks pass. See contract5.51 and the decay-group benchmark. HSE06 component bounds improve from about55.69/17999.49 to39.36/4392.80, while remaining conservative. Useful whole-method accuracy, XC, source/rank/ relaxation and the full capability matrix remain unfinished. Shared method, solver, PBC/BIPOLE/CRYSTAL, symmetry, #643 and bounded #557 scope are preserved.

The stored-operand metric assembly rank increment (contract 5.55) is accepted at source e1e80ed6, qualified tree 7b42701d: eleven converged public calculations, nineteen qualified channel receipts, exact state/control reuse, Decimal assembly witnesses and strict cutoff/resource refusals. The metric spectrum benchmark records physical supports, measured bounds, independent reference boundary, actual cost and native identity. Construction of the stored operands, inverse response and total relaxed energy remain outside this conditional proof; #623/#625/#617 stay open.

The finite inverse/projector response increment (contract 5.56) is accepted at source 49b10c64, qualified tree 86d31ddc: ten converged public calculations and twenty qualified metric-channel responses, including an explicit partial-rank RHF control. Decimal analytic and independent complex perturbation witnesses cover rank limits, rotation, clusters, moving cutoffs, subnormals and strict/resource refusals. See the metric spectrum benchmark for actual native identity, supports, bounds, cost and reference limits. This does not qualify coupling construction, J/K/energy propagation or total relaxed accuracy; the broader #617 programme remains open.

The conditional metric-source Coulomb action increment (contract 5.57) is accepted at source a7a00f5a, qualified tree bdbe3132: eleven converged public calculations and one strict complete-method refusal through local vq. Three fitted profiles reuse accepted states and independent reference receipts; four selected/control pairs preserve physical states bitwise. The shared inverse-response norm-family producer supplies a source-only contribution, added outward to the stored-factor action audit when explicitly requested. Explicit, compressed and pair-tree coupling producers are reused. All 223 focused source and 104 public/preparation/documentation checks pass; 17 source-action checks also pass inside the calculation job. See the metric-source benchmark for actual native identity, component bounds, physical supports, costs and reference limits. This does not alter the global ledger or establish source operand accuracy, K response, total relaxed energy, bulk CRYSTAL parity or speedup. The broader #617 programme remains open and experimental; shared Fock, PBC/BIPOLE and symmetry contracts are preserved.

The conditional metric-source K response (contract 5.58) is accepted at source 88d8b48d, qualified tree ab2790ba: nine converged public calculations, seven raw component receipts and 21 actual metric channels. Three fitted profiles reuse accepted state/reference receipts; UHF and both PBE0 spin variants match their controls. Seventy-six focused source checks pass; fourteen also run through local vq, including a strict complete-method refusal. Independent 180-digit Decimal metric perturbations cover weights, complex spin densities, rank limits and physical range kernels. See the exchange metric-source benchmark for actual native identity, inputs, component bounds, costs and reference limits. Separate raw targets do not alter the fitting/signed/global ledgers or establish total relaxed accuracy. Shared Fock/PBC/BIPOLE/symmetry contracts remain intact; MANTA and the unfinished #617 programme remain experimental.

The short-range metric Bloch-phase increment (contract 5.59) is accepted at source/qualified tree 2425cd61: six converged complete calculations reuse accepted physical states and references, with 23 qualified metric-owner receipts carrying the phase contribution. The local vq job passes 36 phase/assembly/refusal checks. Independent 800-digit phase and contracted stored-integral witnesses validate the new contribution; primitive integral accuracy remains outside that comparison. Source (91), J/K consumer (30) and public preparation/documentation (104) checks pass. See the phase benchmark for actual native identity, supports, component bounds, costs and reference limits. This narrows the earlier stored-phase premise for the short-range metric only. No total relaxed-energy, automatic useful accuracy, bulk parity or speedup claim is added. MANTA and the unfinished #617 programme remain experimental; shared Fock/PBC/BIPOLE/symmetry contracts are preserved.

Reciprocal metric weight construction (contract 5.60) is accepted at source/qualified tree 313d1e74: six complete calculations reproduce accepted states and references, with 23 qualified metric owners including the new weight contribution. The local vq job passes 78 weight/phase/assembly and strict-refusal checks; separate source (133), J/K (30) and public preparation/documentation (104) checks pass. Independent Decimal exp/rational and contracted stored-Fourier witnesses cover physical kernels, range cancellation, finite-zero terms, underflow and resource boundaries. See the weight benchmark for actual native identity, physical supports, bounds, cost and reference limits. Pi/volume/prefactor, primitive/Fourier/coupling construction, domains and relaxation remain excluded. The broader #617 programme stays open; no total relaxed-accuracy, bulk parity or speedup claim is added.

The lattice reciprocal prefactor increment (contract 5.61) is accepted at source/qualified tree 9f7d54f0: six converged calculations preserve accepted states and references, with 23 qualified metric-owner receipts including pi and exact stored-lattice determinant. The local vq job passes 117 prefactor/weight/phase/assembly/refusal checks; separate source (172), J/K (30) and public preparation/documentation (104) checks pass. Independent AGM pi and Decimal determinants cover physical kernels, zero conventions, skew/orientation/scale/cancellation cases and strict volume/resource refusals. See the prefactor benchmark for actual native identity, supports, component bounds, costs and reference limits. Lattice/vector generation, primitive/Fourier/coupling construction, domains and relaxation remain excluded. Full #617 remains experimental; no total relaxed-accuracy, bulk parity, speedup or release claim is added.

Auxiliary Fourier construction (contract 5.62) is accepted at qualified source cd9b5002: six converged calculations preserve the accepted states, exact inputs and independent-reference boundary, with 23 qualified metric receipts. The local vq job passes 175 checks; separate source (297) and J/K (30) checks pass. Fifty-eight new checks compare the interval recurrence with an independent 250-digit closed finite moment sum, covering l=0..7, signed and extreme scales, cancellation and strict resource refusals. Public preparation and docs report 103 passes with one unrelated obsolete CONTRIBUTING link-label expectation. See the Fourier construction benchmark for actual source/native identity, supports, component budgets, costs and reference limits. Stored basis/representation/vector generation, SR integrals, AO-pair Fourier/coupling construction, domains and relaxation remain excluded. MANTA remains experimental; no total relaxed-energy, bulk parity, speedup or release claim is added.

Two-center metric integral construction (contract 5.63) is accepted at source cb02db0d: six converged calculations reproduce accepted states and exact inputs, with 23 qualified metric-owner receipts. Local vq passes 237 checks; 94 fitting, 172 metric/spectral and 30 J/K checks pass. Independent alternating radial series and finite derivative sums cover full/erf/erfc through l=7, Cartesian/pure shells, extreme and signed scales, high arguments and strict resource refusals. Existing libint fitting references pass. Public/docs checks and the explicitly excluded stale navigation fixture are recorded in the integral construction benchmark, along with actual source/native identity, supports, component budgets and costs. Raw K energy-component bounds reach 2.354 Eh: acceptance at loose explicit targets does not qualify useful automatic whole-method accuracy. Coupling/basis/vector-data construction, domains/screening and relaxation remain excluded. Full #617 stays active and experimental, without a total relaxed-energy, bulk parity, speedup or release claim.

Positive short-range radial construction (contract 5.64) is accepted at qualified source 87e3fa9b: six converged calculations exactly reproduce the preceding accepted states and inputs, with 23 qualified metric-owner receipts. Local vq passes 247 checks, including ten new cancellation/large-T/panel-boundary witnesses and strict target refusal. Raw K component bounds are 35.68 to 306.56 times tighter, with unchanged physical source/factor/state identities. The positive radial benchmark records native identity, component budgets, cost, independent-reference limits and the known excluded navigation test. The largest raw K energy component remains 0.044642 Eh; this does not qualify automatic total relaxed-energy accuracy. Coupling/data construction, domains/screening and relaxed response remain unfinished. Full #617 stays active and experimental.

Pure representation coefficient construction (contract 5.65) is accepted at qualified source 9e5cd724: six converged complete calculations preserve the accepted inputs and physical states, with 23 qualified metric-owner receipts. Independent rational Legendre and high-precision square-root witnesses cover all supported coefficients and strict resource refusals; existing physical harmonic and integral references are reused. The representation benchmark records actual native identity, component budgets, costs and reference limits. Normalized basis/vector data generation, coupling construction, domains and relaxed response remain excluded. No new symmetry reduction authority or total relaxed-energy accuracy follows. Full #617 remains active and experimental.

Orbital-pair Fourier construction (contract 5.66) is checked at qualified source aa17566e with independent high-precision shifted Gaussian moments and existing real-space quadrature. Six complete periodic methods preserve accepted inputs/supports/states while separate certificates on their actual orbital bases enclose the independent panel witnesses. See measured component costs and boundaries. This diagnostic has not yet been composed into full three-center coupling, SCF or relaxed-energy accuracy admission; existing ledgers and flags remain.

Streamed three-center construction (contract 5.67) is qualified at source 21d5c67b by independent closed polynomial/finite-derivative witnesses, existing libint fitting comparisons and all 222 fitting/derivative tests. Six accepted periodic states retain exact inputs/supports/results while separate unshifted actual-basis shell certificates enclose the independent witnesses. See measured component evidence. Derivative requests now refuse in scalar fitting/construction producers; the dedicated derivative route remains supported. Periodic image/Fourier/ zero-mode composition and action propagation, domains and relaxed accuracy remain unfinished; no existing Fock/symmetry admission is enlarged.

Bounded finite-source metric and coupling admission

Contracts 5.70-5.73 qualify separate finite-source J constraints on the actual Gamma RI owner. The compact Be RHF control retains the same generated eight- function auxiliary basis and physical supports, with joint J/energy bounds 2.0613044587438003e-8 and 1.1078796248453086e-6 Eh. Complete local vq admission passes targets 3e-8/1.5e-6 Eh, while 3e-8/1e-6 Eh refuses before SCF within the same bounded search. The retained numerical state matches prior evidence. The measured acceptance and cost records actual source/native identities, independent-reference limits and previously accepted controls reused by this increment.

This qualifies one fixed weighted-density-family finite fitted J comparison. It does not add unlike full-Coulomb ledgers, enclose occupied/density relaxation or promote the complete P3b matrix. Translation/input generation, infinite domains, full-Coulomb fitting, K, executed arithmetic, basis/BZ/XC/BvK and relaxation remain explicit gaps; no symmetry or bulk-parity permission follows. The other stages and required profiles in this validation plan remain open.

Exact finite metric lattice images

The shared metric proof now encloses exact lattice-times-integer image centers and phases, matching the coupling convention for the selected integer set. Implementation140b95e0/reference repair506e14c7 is accepted through local vq 52f189aae41f: three unchanged complete states and three strict refusals. The larger eight-function control still admits finite J/E targets3e-8/1.5e-6 and refuses energy1e-6. Metric assembly/joint reference identities advance; source, rank, density and Fock identities remain unchanged. See the acceptance and exclusions.

This closes only selected metric image generation. Input/reciprocal generation, image-domain completeness, infinite tails, full-Coulomb fitting, K, executed Fock/energy arithmetic and nonlinear relaxation remain separate. No total relaxed-energy, bulk CRYSTAL parity or speedup claim follows. Reference-aligned whole-method composition and the rest of #617 remain open and experimental.

Evaluated finite Coulomb response

Source1dee3252 composes the immutable finite-source certificate with one retained or paired executed-arithmetic proof at the evaluated stored spin density and weights. Local vq922d68c30af0 passes four unchanged complete states and three strict refusals. The eight-function auxiliary evaluated Coulomb energy bound is1.1078799401486478e-6 Eh. Existing pre-SCF targets remain source-only; the evaluated receipt does not silently extend their semantics. See bounds, costs and independent-reference limits.

This closes the raw J/Coulomb response arithmetic composition for the admitted finite reference. Restricted embedding, final assembly, physical/reference completion and nonlinear relaxation remain separate. The unlike full-Coulomb ledger is unchanged. Full#617 and useful automatic whole-method accuracy stay open and experimental; no total relaxed-energy, parity or speedup claim.