MANTA: optional integral and Coulomb/Fock engine

Status: staged implementation, 2026-10-10. Current experimental molecular and finite-source periodic HF/KS interfaces are documented in the MANTA manual. The wider capabilities on this page remain implementation and acceptance targets. No default change or performance advantage is claimed.

The maintainer-approved bounded 0.18 release qualifies existing controls; it does not require this entire research matrix. See the release-control guide for the frozen examples, acceptance evidence and exclusions. Remaining capabilities here retain their implementation obligations beyond that release.

The full implementation work map indexes development tracker #617 and its claimable packages, reusing the existing Fock, parity, correlation and real-Gamma issues. It covers the entire matrix alongside libint.

MANTA is the working name for a native, optional Gaussian integral provider and associated contraction kernels. It coexists with libint. Users select the integral provider independently of the Coulomb algorithm and exchange approximation. BUPO-J accelerates Coulomb construction; it does not supply K.

The design has three parts:

• This page: integration, interfaces, capability gates, ownership and routing.

• Scientific contracts: equations, literature mapping, molecular BUPO, periodic extension, CCM identities and symmetry.

• Implementation and acceptance: ordered increments, numerical references, resource gates and performance measurements.

The periodic KS checkpoint now includes physical RKS/UKS, bounded cutoff source generation and a separately admitted 3D atomic quadrature source. Joint grid/domain/SCF admission and selected public RKS/UKS jobs are available, including immutable evaluated snapshots, complete source receipts and lossless QVF spin densities. A jointly admitted frozen-density grid assessment now compares XC energy and every spin/k potential against a caller-selected reference grid. It reports differences, not a continuum error bound or an automatic accuracy certificate. An explicit-source global LDA/GGA hybrid adapter now combines semilocal XC with scaled full-Coulomb exchange and an explicit zero-mode convention. Hybrid cutoff domains reuse the shared HF G/Q and physical pair source and separately admit XC images. A joint atomic grid/domain/hybrid-SCF factory retains every source owner through confirmation. Selected public hybrid jobs now preserve the exchange convention, scaled component energies and exact evaluated spin density through standard output and QVF. Explicit-source range-separated LDA/GGA RKS/UKS now resolves the full signed Coulomb/erfc component list, including distinct ranges, finite screened zero modes and a separately selected long-range singular correction. Shared cutoff/grid factories now admit all range-separated components together with their retained sources and confirmation builds. Selected public range-separated jobs now preserve complete signed kernel receipts, actual/requested zero-mode handling and the evaluated QVF spin density. An explicitly partial hybrid grid diagnostic now compares semilocal energies and potentials at one frozen density, retaining the required exchange descriptor and jointly admitted grid owners. Energy/potential accuracy profiles remain open. This checkpoint does not qualify the remaining periodic fitted/BUPO, low-dimensional, CCM/chi, symmetry, derivative/stress or acceleration rows below.

P3 primitive substitution now also includes jointly admitted raw erfc GDF metrics and shared-q three-center blocks. The native MANTA evaluator uses the existing GDF sphere/capsule image and screening selectors, with distinct component identities and measured work. Independent analytic sums, libint blocks, complex trial responses and high-angular radial/Fourier witnesses qualify this short-range source. Complete finite Coulomb SR/LR blocks now also combine MANTA auxiliary/AO-pair Fourier panels with the existing GDF jellium kernel. Independent converged bare-Coulomb sums check splitting and zero-mode assembly. Immutable shell tiles now feed a fixed complex positive projector and streamed retained-mode Gamma J/transfer K consumer. Independent Gaussian and libint references, energy derivatives, gauge transport, rank rejection and joint resource admission qualify this component boundary. A whole-mesh spin Fock consumer now composes the fixed Gamma and ordered transfer sources. Explicit-source fitted UHF reuses the physical S/T/V/nuclear producers and bounded spin solver, with independently checked correction, evaluated-density and terminal-confirmation gates. A jointly admitted RI UHF cutoff factory now generates pair-complete AO images and certified Gamma/off-diagonal reciprocal spheres, preserving the fitted ket-minus-bra convention and fixed projector owners. Selected scientific calls record complete fit and domain provenance through the standard output layer. Public UHF jobs now admit explicit RI J and RI K with a resolved auxiliary basis and independent fitting controls, retaining evaluated spin densities through standard output and QVF. A shared RI HF source now also feeds the actual bounded RHF leaf with spin-summed closure and energy gates. Explicit/cutoff scientific calls and public RHF jobs preserve the restricted evaluated density, fixed fit and source receipt. Independent restricted references, retained-space/gauge tests and landed FockBuild crossings qualify this finite subset. Fitted KS acceptance follows below, including bounded physical range fitting. Source-specific symmetry qualification remains required. The whole-mesh RI consumer now also admits fixed independent J/K targets. RI-J owns only the Gamma source and skips all exchange-transfer metrics; RI-K preserves every required transfer and skips the Coulomb contraction. Selected component/source identities and shared Fock/gauge tests establish this component boundary without enabling reduction. Jointly admitted mixed exact/RI RHF and UHF now compose either selected fitting target with the complementary direct reciprocal producer. Explicit sources, generated cutoffs and public jobs preserve the selected K transfer convention, both component receipts, fixed fitting projectors and same-density method energy. Independent SCF, capped-state, resource, gauge, QVF and shared Fock checks qualify this finite subset. BIPOLE parity and source-specific symmetry remain separate gates.

Explicit fitted pure/global LDA/GGA RKS and UKS now reuse the functional solver leaves with independently selected exact/RI J/K. Fixed projectors, all component workspaces and the actual XC energy are jointly admitted. Independent SCF, functional derivatives, capped epochs, truncated fits, AO/auxiliary images and rectangular overlap spaces cross the landed Fock and symmetry transport APIs. Existing direct KS density/snapshot identifiers now separate the evaluated density from interaction selection; saved direct numerics and source identities remain unchanged. Fitted KS cutoff/grid factories now jointly admit certified geometric domains, retained atom-centred quadrature and the actual functional solver. Independent integer spheres, raw-fit SCF, budget boundaries, image transport and shared Fock exports qualify these generated sources. Pure fitting generates no K table; global K keeps its selected exact or fitted orientation and diagonal ownership. Public fitted KS jobs now preserve those native sources and the existing RKS/UKS result types, with complete output admission, owned functional state and evaluated-density QVF in the nuclear AO frame. Independent public SCF, capped states, image gauges, resource and output-lifecycle checks qualify this route. Physical range fitting domain factories and public jobs, periodic BUPO and all unqualified matrix rows remain required. Explicit bounded range fitting is described below.

The current periodic RI-BUPO increment shares call-wide pair charges and auxiliary inputs, and projects summed auxiliary/pair fields once per source panel. It reuses the ordered GDF producer, immutable Gaussian preparation, bounded certified partitions and shared Fock path. It leaves the finite metric, method-owned exchange/XC and source-specific symmetry unchanged. The shared producer now supplies a global ordered pair tree, exact capsule masks, complete auxiliary-image unions and source-owned Bloch-frame factors. An opt-in global pair-tree contraction now consumes these APIs. It aggregates only wholly included, separately Gaussian-certified far blocks and applies paired upward/downward moment actions. Gamma coupling completes conjugate pair orbits only after checking the literal finite support. The approximate source has its own identity; the exact metric and method-owned K/XC remain unchanged. This is a bounded pair-tree by auxiliary-image traversal, with explicit accuracy controls. Per-shell-block error and magnitude ledgers now preserve which contributions reach the same output and carry a Euclidean forward bound into the fixed-metric RI energy/J estimates. They leave the numerical source unchanged. The shared isolated erfc error model now also uses a joint radial derivative envelope and interior absolute moments. This changes accepted partitions and therefore versions approximate coupling identities while preserving the exact metric and reference. Explicit tighter tolerances are measured at fixed density and through complete SCF. Lossless total-degree interaction storage and actual-entry cache charging now reduce high-order partition rebuilds without changing the numerical source. Shared componentwise omission and exact-reference column envelopes now propagate through the actual retained metric factor, keeping the older scalar bounds when tighter and preserving the numerical paired maps. Automatic useful-accuracy profiles, a general production crossover and the remaining P3b/0.18.x matrix are unfinished. See the pair-tree action benchmark and the explicit accuracy measurement.

Optional automatic physical support selection now uses the shared domain and component-bound APIs before RI HF/KS SCF. It chooses AO-pair, nuclear and reciprocal supports within explicit limits, keeps the operator fixed during SCF, and charges every discarded trial. The final method recomputes and verifies its selected source and certificate identities. Compact and tight diffuse component targets are qualified in the support-selection acceptance. The larger diffuse domains remain costly. Whole-method fitting/metric, arithmetic, rank stability and relaxation ledgers and every remaining capability row below remain unfinished.

Optional nested metric-factor truncation bounds now compose with the periodic coupling certificate before RI SCF. They compare selected and finer positive-mode spaces in one stored finite metric eigensystem, reuse the shared source envelopes and keep the selected operator fixed. Complete local HF calculations and independent finite-source references qualify the bounded increment. The nonzero bounds are still conservative. Fitting-basis/source-domain, eigensolver, arithmetic, rank-stability and relaxation accuracy are not covered, and the full automatic RI-BUPO/0.18.x matrix remains unfinished.

An explicit full-Coulomb fitting certificate now compares the unchanged RI operator with the existing full-domain/full-image BUPO reference over a fixed weighted Hermitian density family. It covers the selected fit, rank, coupling and domain discrepancies together, without assuming a variational fitting residual. Converged local RHF/UHF calculations and independent Fourier references qualify the fitting enclosure. Bounds remain very conservative. Complete-job attachment is now qualified below; useful auxiliary/domain selection, floating arithmetic, rank stability, relaxation and all unqualified matrix rows remain required.

The full-domain/full-image electronic reference now has shared native preparation independent of HF exchange and SCF. Existing BUPO HF and RI fitting consume the same immutable producer, with cumulative reservations and remaining-budget propagation. Its acceptance preserves physical source identities. Complete RI HF/KS now reuses that reference and the actual Gamma RI owner for pre-SCF J/energy admission with canonical density families and joint counts. The complete-job acceptance qualifies this optional path. Bounded metric selection and automatic shared BUPO reference preparation/refinement now also pass complete RI HF/KS acceptance with explicit resource caps and unchanged Fock/symmetry authority. The automatic reference acceptance records its scope. Optional bounded physical fitting-domain selection now reuses shared GDF producers and reserves the largest allowed SCF source. A shared bounded primitive-product auxiliary generator now supplies nested candidates with preserved seeds, provenance and complete periodic job costs. Optional bounded selection now tests those candidates against the same full-Coulomb certificate, retaining the first passing physical source. Bounded shared Ewald/BUPO reference batches now preserve scalar fitting certificates while sharing direct kernel and Gaussian-bound evaluations. Approximate BUPO partitions retain explicit scalar fallback. Separate finite-fitting and reference energy enclosures now guide automatic reference readiness, and compact HF profiles pass 1e-6/1e-4 Eh fixed-density J/Coulomb-energy targets through the shared search. The remaining whole-method ledgers and unqualified capabilities are still unfinished; this does not complete the full 0.18.x matrix.

1. Audit and integration decision

The inspected Fock/operator source is revision e2a3947bb617; the shared symmetry reference is 80f9f392651e. These are source-audit anchors, not release or numerical acceptance evidence. The four requested design pages remain at their original paths. The symmetry reference also contains newer GDF transport diagnostics. Its in-progress GDF/IBZ edits are not prerequisites or accepted behavior in this proposal. Reconcile their landed state at implementation time.

An exact-word, case-insensitive search of tracked repository content found no existing MANTA symbol or product name. Reserve vibeqc.manta and vibeqc::manta for this work; this is a repository naming check, not trademark clearance. The initial implementation is independently written from published algorithms. No ORCA code, paper PDFs, SI archives, or third-party GPU source is to be bundled. Any later dependency or redistribution needs its own license review under the repository rules.

Inspected boundary	Finding and consequence
cpp/include/vibeqc/basis.hpp, cpp/src/basis.cpp	BasisSet owns a libint basis. ShellInfo exports each contraction with normalized coefficients. Pure functions use standard m=-l..l; Cartesian components use descending x, then y. Start with a lossless adapter, not a new parser or renormalization.
integrals.hpp, integrals.cpp, fock.cpp	Existing small-system Eri4D is a dense reference. Keep it for bounded tests; do not make it MANTA’s production data model.
jk_builder.hpp, jk_direct.hpp, jk_direct.cpp	Reuse the existing molecular JKBuilder factory seam. Direct J/K already share quartet traversal. The interface has spin slots, incremental state, runtime thresholds and reset hooks despite historical immutable-builder comments. A const builder is not a frozen solver operator.
df.hpp, df.cpp, density_fitting.py	Raw 2c/3c kernels, metric factorization and fitted contractions have distinct roles. Dense factors and streaming consumers coexist; MANTA must offer tiles and actions rather than require full Eri3D or B storage.
lattice_integrals.cpp, periodic_fock.cpp, lattice_pair_cells.hpp	Multiple numerical image domains exist. Inspect function-level support, not the older Gamma-only header description. Preserve external AO-pair, density-pair and internal interaction domains separately, including exchange’s AC/BD pairing.
periodic_fock_multi_k.py, ewald_composed.py	Whole-mesh J has an existing bounded Fourier route. Do not replace it with a molecular-limit Gamma density assumption. Reuse it as an independently implemented reference when conventions match.
periodic_k_gdf.py, aux_basis.py, periodic_gaussian_fock.hpp	q-dependent metrics, complex factor contractions and native resource plans already exist. The native finite-Gaussian response is not by itself a complete converged periodic Hamiltonian. Retain its source/context and work accounting.
pbc_bipole_fock.py, bipole_domain.py, bipole_dispatch.py	BIPOLE is a method/source family, not a synonym for BUPO. Active erfc/reciprocal and dormant multipole routes have different qualification. MANTA may replace admitted primitive kernels without enabling the dormant source.
periodic/ccm/route.py, periodic/chi/scf.py, periodic_fitted_support.py	Neutral real-Gamma, neutral Bloch, union-and-weight and chi have separate contracts. The same representation theorem applies only after specifying the same Hamiltonian.
solvers/operators.py, hermitian_operator.hpp	Reuse HermitianOperator, FockOperator, metadata, and the strict solver boundary. No new eigensolver API is needed.
symmetry_shared.py, symmetry_ao.py, symmetry_gdf.py in the symmetry reference	Reuse named spaces, compact actions, stabilizers, tensor transport and evidence. passed_probe is not production_reduction_authorized.

The operator workstream’s docs/design/operator_contract.md and docs/design/operator_consumers.md are now integrated on main. MANTA export crossing tests reuse those types. Bounded native kernels retain their admitted storage and numerical leaf; zero-copy semantic adapters remain separate work. The shared symmetry design, symmetry developer reference, and BIPOLE domain contract remain authoritative for their layers. MANTA adds providers beneath them. It does not require a repository-wide Fock rewrite before useful molecular work can land. The initial libint reference adapter validates owned matrices directly; its FockOperator integration gate awaits that independently developed foundation.

2. Architecture

Mermaid source showing the data flow, including the SCF loop:

flowchart TD
    Input[Method and explicit calculation options] --> Source[Immutable numerical source contract]
    Basis[BasisSet and ShellInfo adapter] --> Shells[Immutable shell and pair data]
    Source --> Plan[Bounded execution plan]
    Shells --> Plan
    Sym[Shared group, space, orbit and tensor actions] --> Gate[Method-owned symmetry qualification]
    Source --> Gate
    Gate --> Plan
    Plan --> LI[Libint provider]
    Plan --> MA[MANTA MD provider]
    LI --> Tiles[Ephemeral integral tiles and factorized actions]
    MA --> Tiles
    Tiles --> Dig[Direct J/K, RI, BUPO-J and RI-BUPO-J consumers]
    Density[Immutable whole-density epoch] --> Dig
    Plan --> Dig
    Dig --> Build[Density-dependent method Fock builder]
    Other[Hcore, XC, ECP and method corrections] --> Build
    Build --> Frozen[Fixed FockOperator snapshot]
    Frozen --> Solve[Strict solver]
    Solve --> Occup[Method occupations and next density]
    Occup --> Density
    Build --> Receipt[Build provenance and numerical diagnostics]
    Receipt --> Output[vibeqc.output]

The provider evaluates mathematical kernels. The consumer contracts them. The method owns the Hamiltonian, coefficients, finite support, boundary conditions and energy. The solver sees a fixed linear operator. Symmetry provides representations and a qualified schedule, without choosing a new physical source.

2.1 Existing and proposed interfaces

The following C++ declarations are proposed internal interfaces, not new exported ABI promises. Names other than the explicitly identified existing types do not exist yet. Use spans/views appropriate to the project’s C++ standard; do not add a language-version dependency just for this sketch.

namespace vibeqc::manta {
struct ShellChannel {
    ShellId id;
    int l;
    Representation representation;       // Cartesian or real pure
    ExponentView exponents;
    CoefficientMatrixView contractions;  // primitive x radial channel
    Vec3 origin_bohr;
    NormalizationId normalization;
    AOIndexMap output_order;
};
struct KernelRequest {
    KernelKind kind;                     // S, T, V, moments, FT, Coulomb
    CenterArity arity;                   // 2c, 3c, 4c
    RangeKernel radial;                  // full, erf, erfc; omega in bohr^-1
    DerivativeSpec derivative;
    ShellImageTuple shells;              // exact integer images, no wrapping loss
    ScalarKind scalar;
};
struct IntegralTileView {
    TensorLayout layout;                 // axes, strides, conjugations, AO order
    ConstBuffer values;                  // valid only until next evaluate call
    PermutationDescriptor permutations; // no hidden degeneracy factors
};
class IntegralProvider {
public:
    virtual CapabilityResult supports(const KernelRequest&) const = 0;
    virtual WorkspaceRequirement workspace(const KernelRequest&) const = 0;
    virtual IntegralTileView evaluate(const KernelRequest&, Workspace&) const = 0;
};
class IntegralConsumer {
public:
    virtual DensityEnvelope envelope(const BatchDescriptor&) const = 0;
    virtual void digest(const IntegralTileView&, TargetPanelSet&) = 0;
};
struct BuildRequest {
    NumericalSourceHandle source;
    DensityEpochView density;            // all spin/k blocks, immutable during call
    TargetRequests targets;              // independent J, K, response right sides
    AccuracyBudget accuracy;
    ResourceBudget resources;
    ExecutionPolicy execution;
};
BuildPlan prepare(const BuildRequest&, const IntegralProvider&);
BuildResult execute(const BuildPlan&, const BuildRequest&, WorkspacePool&);
} // proposed internal namespace

BuildResult owns immutable output panels or a frozen linear action plus a BuildReceipt. A method then assembles Hcore, J/K and XC and creates the existing FockOperator. A frozen action captures the density epoch, supports, coefficients and numerical plan by immutable ownership. It must not consult a live SCF builder, incremental cache, changing threshold or current density. Generation counters alone cannot fix mutable captures. A cancelled or failed build returns no usable partial snapshot.

Initial molecular integration is a new JKBuilder implementation wrapping this interface, preserving existing build_J, build_K, paired-spin, slot, reset and range-separated behavior. Multi-k gets a separate whole-mesh adapter, not repeated calls to the molecular one-density API. Consumer batches can include Hermitian indefinite density differences and, in a separately declared response mode, non-Hermitian transition densities. Positive occupations are not an integral-engine precondition.

The factorized MD consumer API additionally accepts contract_pair_density, apply_hermite_coulomb, and project_pair_potential operations. These may bypass explicit integral tiles for J. A libint provider can supply the same semantic action by digesting shell tiles. K uses distinct crossed contractions. Small reference materializers have explicit dimension/byte caps and are never an implicit implementation of an action.

2.2 Numerical source and provenance

A proposed NumericalSourceContract contains:

• geometry, cell, dimensionality, orbital/auxiliary basis and normalization IDs;

• physical method/source ID, finite domain membership and weights, screening and retained-space policy IDs, kernel coefficients and units;

• full k mesh and weights, Bloch/FT conventions, integer image maps and q wraps;

• Hartree gauge, net charge/background, surface boundary, nuclear self terms, and exchange singularity convention, all as separate fields;

• RI metric, auxiliary basis, retained projector/rank, solve tolerance, and any compensation/charge constraint;

• basis-pair support, interaction partition, bubble hierarchy, expansion-order policy and qualified symmetry-plan identity;

• schema/algorithm revisions and actual backend build identities.

Content identities bind actual numerical inputs and supports. A descriptive string or source revision is useful provenance but does not authenticate a tensor. Reuse the finite-Gaussian native context/receipt model where practical. The shared symmetry OperatorContract is a compact declared projection of this richer record; it is not replaced. Existing solver OperatorMetadata retains basis, generation, spin and k-point annotations. Initially keep the larger receipt beside the operator in the method result; adding a receipt ID to public metadata is a separately reviewed additive change.

Cache identity is layered: geometry/basis for primitive data; plus kernel and images for integral tiles; plus metric/cutoff/projector for fit data; plus partition/order/symmetry for execution plans; plus all density blocks and spin slots for incremental state. Changes invalidate the affected layer and its dependents. Keep neither density caches nor factorization policy in solvers.

The current molecular C++ producer seam is IntegralProvider in manta.hpp, implemented by MantaProvider and LibintProvider: source_identity(), kernel_request(), and borrowed evaluate/evaluate_batch tiles. Build receipts separate source and density identities. A null TileView.values denotes screening or underflow, not a certified zero. This interface does not yet supply a general rigorous shell-quartet omission certificate covering density policy, auxiliary truncation and finite support. The molecular extent and BUPO error ledgers have their own narrower contracts; they cannot be relabeled as that certificate. A bounded exhaustive finite-source symmetry audit may certify whole-orbit omissions for its actual source and per-density matrix norm, including nonunitary Cartesian transport. It must compare with the identical screened source and retain the complete policy identity. Symmetry owns orbit admission and scheduling; MANTA retains ownership of kernel bounds, screening policies and bubble hierarchies. Such an audit does not establish scalable producer certification or periodic KS admission.

2.3 Memory, execution and numerical stability

Production is bounded by an explicit byte/work budget. There is no global four-index tensor, all-q three-index tensor, or all-supercell AO matrix. Even shell-pair lists and Schwarz tables need tiling/spill/replay when their quadratic size exceeds the cap. Logical admission precedes payload scans, copies and output allocations, with checked integer arithmetic.

For a tile, account at least for live E panels, Hermite R panels or slabs, contraction coefficients, integral output if present, packed density/target panels, complex accumulators and compensation, metric solve workspace, cached moments, image/q metadata, callback snapshots and communication buffers. Count per-worker and per-rank replication, Python-owned inputs, snapshot copies, GPU resident and pinned-host storage. Reserve vendor workspace where known; unknown allocator/BLAS overhead gets headroom and measured peak RSS, never an unqualified hard-memory claim. A frozen action still needs admission for solver search vectors and preconditioners.

Worker-local scratch is leased for the duration of a tile. Tile views never escape digestion; consumers must copy into a charged owner if retaining data. Immutable shell/pair metadata can be shared. Accumulate into owned target tiles, then reduce in a specified order; avoid unbounded thread-local full Fock matrices. MPI target ownership and exchange reductions are explicit. Nested BLAS/OpenMP oversubscription is disabled by plan. Disk spill is an explicit scratch policy with byte limits, not an assumption of free memory.

The baseline uses FP64/complex128 throughout. Boys-function evaluation selects stable small-argument series, moderate-argument evaluation and asymptotic large-argument seeds with stable recurrence direction. Test relative and absolute errors over order and argument; do not use upward recurrence near zero blindly. Track contraction cancellation, diffuse/coincident centers, near-dependent metrics, scaled high-order moments and compensated sums. The erfc branch needs a stable small-difference evaluation rather than subtracting nearly equal full and erf results. Mixed precision and GPU batching are later, separately qualified optimizations.

3. Capability matrix

E means an existing provider/consumer path, with its current method guards; it does not mean every combination has passed independent acceptance. P1 through P6 refer to the staged plan. C means conditional on a source proof, and - means that algorithm does not provide that operation. The MANTA columns retain the approved acceptance targets. Implemented finite subsets and their limits are recorded in the checkpoint above and the manual; a stage label does not mean that its entire row is qualified. Limits are queried by kernel, derivative and representation, not advertised as one universal maximum l: md_capability(request) answers by kernel, center count and derivative order with separate orbital-axis and auxiliary-axis limits, one_electron_capability(request) covers the one-electron operations, md_producer_capability(request) covers the kernel-free Fourier, moment and extent producers, and the fitting, derivative, four-center, Fourier, moment and extent planners derive their admission from those queries. Unqualified parts of every row remain required work.

Kernel/consumer	libint-based reference	MANTA planned	Important boundary
Molecular S/T/nuclear, cross-basis S, moments	E	P1	ECP remains its own provider; origin conventions explicit
2c Coulomb metric and 3c Coulomb coupling	E	P1	RI is a consumer, not a different 3c physical integral
4c Coulomb and direct J/K	E	P1	Direct shell digestion; capped dense reference only
erf/erfc 2c/3c/4c kernels	E by entry point	P1, route admission P3/P4	Kernel existence does not imply every fitted hybrid is supported
Molecular exact J / exact K	E	P1	Screening-controlled analytic finite-basis integrals
Molecular RI-J / RI-K	E	P1/P2	Auxiliary and metric approximation recorded; no implicit RI-K
Molecular BUPO-J / RI-BUPO-J	New consumer may use libint near field	P2	Approximate J; independent exact/RI/COSX K selection
Gamma and multi-k exact/RI J/K	E with route-specific domains/gauges	P3	Complex whole-mesh semantics even for a Gamma-first rollout
Periodic BUPO-J / RI-BUPO-J	New periodic consumer can use libint near field	P3	Proposed periodic extension; lattice, gauge and charge gates
Nuclear gradients / cell stress	E by method	P6	Each derivative is qualified separately for the selected energy

Numerical source	Exact Coulomb J with MANTA	RI-J with MANTA	BUPO-J / RI-BUPO-J	K and representation constraints
Molecule / isolated finite cluster	P1	P1	P2 / P2	Exact K P1; RI-K separately; no periodic background
3D periodic Gamma	P3	P3	P3 / P3	Gamma is a Bloch source, not D(R)=D(0) delta(R,0)
3D periodic multi-k, shifted meshes	P3	P3	P3 / P3	All ket k points and q channels enter K; J uses whole-mesh density
1D/2D periodic	P3 substage	P3 substage	C at P3 / C at P3	Dimensional Green functions and boundary conditions required; no 3D-vacuum substitution
BIPOLE active physical or historical source	P3 kernel adapter	Existing source-specific fit only	C, separately named source	Preserve selected erfc/reciprocal partition and AC/BD exchange support; no dormant multipole activation
CCM union-and-weight / WSSC four-center	P4, same weighted contractions	C, only a specified compatible fitted source	C / C	union12 and alternative weights remain distinct; J/K need not derive from a variational energy
CCM neutral neutral-bloch	C, requires a defined unfitted parent	P4, existing neutral fitted source	C / P4	Preserve fitted Hamiltonian, compensation and exchange seam; complete mesh
CCM neutral real-gamma	Same qualification as neutral Bloch	P4	C / P4	Block-circulant action, no required explicit supercell matrix; equivalence only to the same neutral source
chi four_center finite-character source	P4	C, explicit fit changes approximation	C / C	Preserve finite residue/image weights and source guards
chi ri and finite fitted source	C, compare only to matching parent	P4	C / P4	q-dependent fit/projector and compensation remain part of identity
chi rijcosx	C, changes K approximation if selected	P4 J	C / P4 J	Existing COSX K retains grid/fit/source guards; BUPO supplies no K
Low-dimensional CCM sources	C at P4	C at P4	C / C	Preserve each low-dimensional source; chi 1D/2D refusal remains until separately derived
SECCM / MSINDO-CCM / PM6 / OMx / DFTB / GFN2	- for replacing model ERIs	-	C for an explicitly equivalent long-range electrostatic subterm	Retain parameterized Hamiltonians, charge/self terms and model kernels; sharing the scheduler does not turn these into ab initio HF

The conditional entries are genuine prerequisites, not omissions from scope. P4 must either supply the named same-source implementation or document a mathematical obstruction and an explicit refusal. A method with quartet weights that do not factor into pair-source weights cannot automatically use a single BUPO aggregate density. Correlation needs separately requested 3c/4c or selected MO tiles; a fast J action is not a general post-HF integral provider.

Initial acceptance targets pure and Cartesian orbital shells through l=6 and auxiliary shells through l=7 for scalar kernels, after an s/p milestone. These are proposed tested limits, not claims inherited from SHARK. Shared compact AO symmetry currently stops at l=6; l=7 auxiliary transport needs its own action or an unreduced path. Derivatives need additional internal angular orders and their own tested bounds. Requests beyond an actual provider capability use explicit fallback or fail before SCF.

4. Configuration and fallback

Proposed keyword-only options, subject to additive API review:

# Proposal, not executable in the current release.
engine = IntegralEngineOptions(
    backend="manta",                 # libint remains the default
    fallback="error",                # or explicit "libint_same_source"
    contraction="auto",             # segmented / general / partial_general
    memory_mib=2048,
)
coulomb = CoulombBuildOptions(
    algorithm="ri_bupo",             # exact / ri / bupo / ri_bupo
    auxiliary_basis="def2-svp-jk",
    accuracy_profile="strict",       # expanded numeric settings are reported
    incremental=True,
    full_rebuild_interval=10,
)
exchange = ExchangeBuildOptions(algorithm="exact")  # none / exact / ri / cosx
# run_job(..., integral_engine=engine, coulomb=coulomb, exchange=exchange)

strict is a proposed profile whose numerical settings must be calibrated by the acceptance suite. It is not an established error certificate. Expose resolved primitive/shell/density screening, extent/tail tolerances, per-level orders, near/far criterion, metric/rank/solve tolerance and periodic real/G cutoffs, rather than conceal them behind one accuracy adjective.

Existing density_fit, scf_mode, jk_method, CCM variant and exchange keywords retain historical behavior when new options are absent. When both forms are supplied, resolve equivalent choices or reject conflicts. A method selector continues to choose a physical source; it cannot be inferred from backend="manta". Functional resolution owns exchange fractions and range parameters. Reject a nonzero exact-exchange requirement paired with none.

Resolve all required kernels before expensive setup. backend="libint" never executes MANTA. backend="manta", fallback="error" never executes libint primitive kernels, although the initial basis adapter still uses libint basis infrastructure. With libint_same_source, fallback may replace unsupported kernel tiles while preserving normalization, support, kernel, accuracy and memory contract. Report it as mixed execution. The same source must remain available for energy and derivatives. Never substitute exact J for requested RI-J, RI-K for exact K, a different CCM source, or a looser periodic domain as an invisible fallback.

A BUPO failure can restart the entire J build using its unreduced exact counterpart, or exact RI counterpart for RI-BUPO, only under a separately explicit algorithm-fallback policy. It must remain the same finite numerical source and meet the memory budget. Discard partial accumulators and reseed incremental state. Numerical NaNs, normalization defects or inconsistent source IDs are errors, not fallback opportunities. symmetry="auto" may choose the unreduced schedule for the same source; required reduction refuses if unqualified. No fallback is allowed to allocate a forbidden dense tensor.

Output is produced through vibeqc.output, with a proposed structured engine_provenance result field and compatible QVF vendor metadata. Include requested/resolved providers for 1e/2c/3c/4c/J/K, fallback reasons and actual tile counts, kernel/range parameters, contraction strategy, source/plan/fit IDs, precision, symmetry subgroup and qualification, approximation budgets, incremental/full-build residuals, stage timings and memory/work receipts. The final accepted-density build determines the final record. Citation entries for SHARK, BUPO and periodic methods must be added to output/citations/database.toml when their implementations become selectable. Bibliographic provenance does not imply bitwise equivalence to ORCA.

5. Ownership and dependencies

Workstream	Owns	Consumes / must not duplicate
MANTA integral work	Shell adapter, MD/Boys/radial kernels, moments/FT, workspace and tile provider, libint adapter parity	Existing basis normalization, AO order, native build and privacy policy
Fock/operator work	Molecular factory adapters, immutable snapshots, SCF lifecycle, spin/occupation/DIIS integration	Existing JKBuilder, strict FockOperator and native solve boundary; no density-dependent solver callback
Coulomb/DF work	Direct digestion, metric solves, BUPO partitions, adjoint consistency, incremental error accounting	Provider tiles/actions; no change of Hamiltonian hidden inside an algorithm choice
Periodic/BIPOLE work	Green functions, real/G and image domains, q=0, exchange seam, charge ledger, dimensional policies	Existing source resolvers and bounded FT/GDF primitives; BUPO does not own periodic conventions
CCM/chi work	Source-specific weights, finite characters, fit/compensation and correlation identity	MANTA primitives and shared transport; no cross-source relabeling
Shared symmetry work	Group/Seitz algebra, shell/auxiliary actions, orbit/stabilizer and tensor transport	Method evidence and actual retained projectors; no automatic production permission
Output work	Stable provenance schema, human summaries, QVF and citations	Receipts from the actual executed path; no guessed backends
Validation work	Independent same-convention witnesses and benchmark attribution	Both unreduced providers and each method’s physical acceptance gates

Dependency order is shell/source contracts -> unreduced kernels and consumers -> BUPO and periodic/CCM adapters -> qualified symmetry -> derivatives and accelerators. Symmetry representation development can continue independently; production skipping depends on source qualification. No changes to the ongoing operator or symmetry implementation are included in this design increment.

The physical range fitting component increment adds dense/streamed erfc and erf sources with explicit physical omega and zero-mode ownership, plus fixed-q RI consumers that keep Gamma separate from finite-zero subtraction. Existing Coulomb defaults retain their numerical states and identities. Complete Gamma SCF diagnostics check the components together; the complete bounded explicit method now follows below, together with domain factories and public jobs. See the physical range component boundary in the scientific contract and its focused validation record; no symmetry or BIPOLE parity is inferred.

Physical range K is now available across the explicit full mesh, with a mandatory separate Coulomb J source and unchanged reversal/projector audits. Shifted two-k SCF diagnostics exercise the complete composition. The explicit PeriodicRIRangeSeparatedKSOptions method now jointly admits separate J, each physical K source, XC, metric setup, all solver calls and confirmation. It retains the canonical Coulomb-plus-erfc functional decomposition and applies the long-range singular correction once. Independent reference SCFs, signed and mixed ranges, exact resource caps, shared Fock snapshots and image transport qualify this finite source. Cutoff/grid factories now reuse the existing geometry and quadrature producers with joint physical range method admission. Each kernel retains its fixed fitting owners; geometry does not supply its finite zero or singular correction. Generated/explicit/selected states and independent SCFs qualify these factories. Public fitted range-KS jobs now preserve each physical source and complete evaluated method state through standard logs, manifests and QVF, with joint native and output admission. Independent finite-source SCFs and lossless density round trips qualify this public boundary. Automatic accuracy profiles, source-specific symmetry and the remaining matrix stay open.

The automatic coupling selector now uses a declared AO density envelope and the shared producer’s evaluated omission/magnitude bounds to select a fixed Gamma RI-J source before SCF. It preserves the finite metric and retained factor, rejects densities outside the envelope, and records the selected tolerance through existing HF/KS output. Independent K/XC and shared Fock ownership are unchanged. This implements only coupling-tolerance allocation; whole-method useful-accuracy profiles, source-qualified symmetry, lower dimensional boundaries, remaining method adapters, derivatives/stress and production acceleration remain open in the capability matrix.

Automatic RI coupling selection can now derive its density envelope from the same canonical overlap and occupied-space constraints as the bounded HF/KS solver. The shared numerical helper supplies all-k bounds without choosing a density or changing physical sources. This removes a manual AO norm input for supported complete methods; whole-method error and performance acceptance remain separate requirements in the full capability matrix.

Automatic periodic RI selection now retains the shared overlap helper’s entrywise weighted-density envelope as well as its total norm limit. The existing coupling producer owns positive reference-action and omission envelopes, including Gamma orbit transport and exact residuals. The selector propagates them through the actual retained factor and probes the same paired adjoint. No density-dependent source selection, duplicate physical kernel or new symmetry permission is introduced. Full-method accuracy and production performance remain requirements of the full capability matrix.

Measured trial curves identify a narrow certified approximate partition between failed energy bounds and exact finite-coupling fallback. The selector now probes above its linear target estimate, with bounded strictly decreasing requests and evaluated-certificate acceptance. It continues to use the shared producer and fixes the source before SCF; this is an allocation heuristic, not a new accuracy guarantee or symmetry permission.

Complete periodic RI image-accuracy ledger

Optional PeriodicOneElectronAccuracyOptions now composes the shared full AO-image S/T producer with the shared canonical-overlap density envelope in RI RHF/UHF, pure KS, global hybrid and physical range-separated methods. Count-only plans admit setup and retained output; three positive targets check maximum S/T entries and a uniform kinetic-energy bound before SCF. Automatic RI coupling selection reuses the same density analysis. A separate completion-cube control tightens the enclosure without changing physical support. Exact J with RI K is supported; non-RI public selection refuses. Source/target/envelope identities and explicit exclusions accompany the separate output ledger. Unified Fock, BIPOLE/CRYSTAL and symmetry permissions are unchanged. Nuclear, two-electron, metric/solve, arithmetic and relaxed state accuracy remain required for automatic whole-method RI-BUPO profiles. See scientific contract Section 5.12 and the RI image-accuracy benchmark.

Uniform occupied-space exchange prerequisite

The shared full-Coulomb exchange producer now combines its Gaussian AO-image and reciprocal majorants with the existing canonical density envelope. One native call bounds every admitted occupied subspace at fixed uniform weights; a typed reuse call shares an existing overlap analysis. Separate matrix, entry-contracted energy and density-norm energy bounds preserve source and envelope identities. No Fock state, physical support or symmetry permission changes. The complete RI full-Coulomb adapter below composes the fixed-BvK correction. Other kernels and automatic whole-method source allocation remain open. See scientific contract Section 5.13 and the occupied-space exchange benchmark.

Complete RI full-Coulomb exchange admission

RI RHF/UHF and RI global hybrids with exact K now admit uniform exchange matrix/energy targets before SCF. They reuse one canonical density envelope across RI coupling, S/T and exchange ledgers. Shared Gaussian exchange and fixed-BvK overlap producers retain the original mesh, physical cutoffs and singular convention. The source reconstruction/audit is shared with S/T. Fitted K, pure KS and physical range kernels refuse the new option. The adapter is optional and does not change numerical states or Fock identities. Remaining nuclear, metric, arithmetic, relaxation and automatic source-selection contributions still prevent a whole-method accuracy claim.

Physical nuclear-domain accuracy prerequisite

The standalone nuclear bound producer now covers the existing RI pair-midpoint spheres, reciprocal omissions and all missing AO images. It reuses the physical selector and source identity, native Gaussian majorants, reciprocal hole sums and the BUPO periodized point kernel. Separate real, reciprocal and AO-image matrices are uniform in k; nuclear repulsion has separate real/reciprocal limits. Completion cubes tighten bounds without changing physical supports. Ordered arms are checked independently. The native API admits all five resource caps before payload copies and exports owned results. See scientific contract Section 5.17.

Complete RI methods now admit optional matrix, attraction-energy and nuclear-repulsion targets before SCF. The adapter shares one canonical density analysis with the existing RI, S/T and exchange accuracy paths, verifies the physical nuclear source identity, and reserves all five caps. It supports RHF/UHF and pure/global/range KS, including exact-J/RI-K. Physical source selection remains required. These component certificates do not complete automatic RI-BUPO accuracy. Fitting/metric, arithmetic, overlap stability and relaxation ledgers, useful performance and all unqualified capability-matrix rows remain open.

Complete RI fitting and selected-metric admission

Optional full-Coulomb J/energy targets now attach to the actual shared Gamma RI producer before complete RHF/UHF and pure/global/range KS SCF. One canonical overlap envelope is shared with existing accuracy paths, while the prepared BUPO reference retains its own admitted electronic source. The combined certificate includes selected fit, rank, coupling and source truncation discrepancies; earlier component bounds are not added again. Count-only plans reserve reference/probe/family work and later builds validate the fixed family. Numerical Fock, exchange, XC, BIPOLE/CRYSTAL conventions and symmetry permissions remain unchanged. See scientific contract Section 5.22 and the complete fitting benchmark. Explicit reference domains, loose bounds, arithmetic/rank/relaxation exclusions and all other unfinished matrix rows prevent an automatic whole-method claim.

Automatic fitting reference contributions

The bounded fitting search now separates finite BUPO approximation, real-domain, reciprocal-domain and pair-image reference enclosures. Its default policy refines the largest available component relative to the requested targets, retaining adequate domains. The optional joint schedule, combined full-Coulomb admission, actual selected RI owner and resource caps remain intact. Scientific contract Section 5.30 and the validation plan record tested scope. This advances automatic fixed-density fitting accuracy; it does not complete arithmetic, rank/relaxation, other energy ledgers or the original capability matrix.

Stored metric spectral enclosure

The shared RI numerical layer now encloses the eigensolver residual and orthogonality of every actual periodic metric. Scientific contract Section 5.31 defines the full-spectrum bound and a strict adaptive-cutoff rank radius. Periodic receipts and complete-job provenance expose qualification flags without changing factors or source identities. This closes the stored-matrix diagnostic portion of eigensolver/rank accounting only. Automatic rank-aware selection, integral and factor/Fock arithmetic, relaxation and the remaining original capability matrix are still open.

Rank-aware periodic fitting selection

An optional strict stored-Gamma metric perturbation margin now participates in final fixed and automatic metric/domain/auxiliary fitting admission. Reference readiness stays separate; the first owner passing rank and J/energy conditions is retained for SCF. Every trial exposes its actual spectrum and rank qualification. Scientific contract Section 5.32 defines the scope. The requested margin is not an automatically estimated integral error. Integral/factor/Fock arithmetic, whole-method relaxed accuracy, production scaling and every remaining original matrix row remain unfinished.

The shared periodic RI metric owner also encloses the actual stored factor product against the exact retained inverse of its stored Hermitian metric. The Section 5.33 certificate reuses the verified spectrum, adds a finite divided-difference error bound and an outward factor-product contraction, and exports scalar terms with the unchanged source/factor identity. This advances factor arithmetic accounting; integral and Fock-action roundoff, relaxed energy and all remaining original capability rows are still open.

Optional metric-action J/energy admission now carries stored-factor error through explicit shared coupling tiles and the fixed density family. It uses finite column residuals and scalar envelopes, with a conservative retained- inverse fallback, and joins existing bounded searches before SCF. Section 5.34 defines the proof. Compressed moment-action arithmetic, integral and Fock roundoff and the full remaining capability matrix are still open.

The metric-action family now uses total and component density limits jointly through an outward dual support bound. The shared family API and periodic aggregate plans include sorting work. This strengthens existing pre-SCF admission without changing the physical RI source, unified Fock arithmetic, BIPOLE/CRYSTAL conventions or symmetry authority. It does not qualify compressed actions or the remaining integral/Fock arithmetic ledger.

Ordered compressed hierarchy and global-panel metric-action admission now compose a producer-owned outward column-norm audit with the shared verified inverse and joint density support (scientific contract Section 5.35). The bound concerns the exact graph of stored moments and residual tiles. Global pair trees now use the same policy with outward descendant-column envelopes and Gamma conjugate completion. Actual contraction roundoff remains open. This does not close the original capability matrix or establish production automatic accuracy.

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-correction arithmetic

The shared assembly audit now encloses BvK correction construction at stored overlap, source density, Madelung coefficient and method scale. Complete RI HF/KS plans reserve its work and scratch, and propagate its entry errors once through the evaluated Fock and energy. No physical operator or shared solver contract changes. Scientific contract Section 5.42 defines the reference; input construction, retained/fused RI, XC and relaxed-SCF accuracy remain open.

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.

Global-hybrid RI KS fitted exchange admission

Source 2dfb076d attaches the existing full-Coulomb K certificate to the actual RI global-hybrid RKS/UKS owner, preserving canonical spin-family validation, source identity and shared Fock/eigensolver semantics. Raw component targets remain separate from physical exchange-coefficient scaling and response arithmetic. Twelve converged and eight stopped selected/control calculations plus two strict refusals pass through local vq; 678 scientific checks pass. See contract Section 5.48 and the KS admission benchmark. The bounds remain loose. Physical range/XC, useful automatic selection and source/rank/relaxation bounds remain open, as do every remaining matrix row, #643 resource failures and the separate bounded #557 candidate work.

Physical range exchange component bounds

Source f1698506 extends the shared exchange-tail and fitted-component bound APIs to erf/erfc, retaining the actual range-specific RI projector. Nonzero range kernels use the existing Coulomb majorant; positive-range erfc accounts explicitly for its finite zero whether retained or omitted. Coulomb defaults and certificate identities remain unchanged. Ten complete local queued calculations, six matching method-source certificates, four additional erf family cases and two strict refusals pass; 488 affected checks pass. See contract Section 5.49 and the range component benchmark. These are raw fixed-family component diagnostics. Automatic signed range KS attachment, XC and useful bounds remain #626/#627; source/rank/relaxation and all remaining matrix requirements stay open. Shared method, solver, PBC and symmetry boundaries and the bounded #557 release scope remain unchanged.

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.