Experimental chi translation local MP2

vibeqc.periodic.chi.local_mp2.run_chi_local_mp2 connects an admitted classic physical-pair RI RHF ChiHFReference to the shared translation-aware local-MP2 engine. This is an explicit experimental library route. Chi remains experimental and D93 fitted/post-HF remains not-qualified. Source tests do not establish scientific acceptance, production threshold accuracy or scaling.

The classic RHF/MP2 convergence study separates finite-source algebraic acceptance from physical-support, basis and mesh convergence, with fixed gates and independently measured reference differences.

Reference and usage

Prepare a reference with prepare_chi_hf_reference using the explicit controls in the fitted-support guide, or restore an accepted classic RHF archive as described in restart. The source must be a neutral three-dimensional singlet, use full Coulomb RI with unscreened physical pairs, and carry a complete uniform unshifted character mesh, tight stationarity, integer gapped occupations and its original physical input binding. The adapter never reruns SCF, refits factors or changes supports. This extends the D6-D7 block routes with sealed physical-pair transport. It reuses the same CorrelationSource, CyclicAOOperator, factor-provider, selection, PAO/PNO and iterative solver interfaces. Per-character frozen and active projectors are preserved without introducing D6’s global energy sorting or its full virtual-orbital payload.

from vibeqc.periodic.chi.local_mp2 import run_chi_local_mp2

result = run_chi_local_mp2(
    reference, frozen_core=0,
    tcut_mkn=0.0, tcut_pno=0.0,
    max_iter=250, conv_tol_energy=1e-13, conv_tol_residual=1e-11,
    damping=1.0, max_transport_bytes=256 * 1024**2,
    factor_provider="streamed", max_factor_bytes=64 * 1024**2,
    factor_auxiliary_tile=16, factor_cache_bytes=1024**2,
    compact_storage=True, max_selection_bytes=64 * 1024**2,
    output=output_dir / "local-mp2",
)
raw = result.raw_e_corr_per_cell
pno_estimate = result.pno_correction_per_cell
converged = result.converged

output writes .out, .system, .bibtex and .references through vibeqc.output. Without a stem, active text/structured output channels receive the same result. The manifest records the retained factor source, consumed reference and adapter identities, runtime, actual overlap/Fock/factor transform audits, electron counts, domain and PNO settings, selected spaces, solver controls, convergence and method convention. chi_correlation_record provides the same structured payload to other output consumers.

frozen_core counts lowest explicit occupied spatial orbitals per character. The adapter preserves the frozen and active projectors separately and orders all frozen columns first in the shared source. The engine receives the total torus frozen count, prod(mesh) * frozen_core. Scalar ECP references retain their executed ECP identity, full metadata and distinct physical, ECP-removed, explicit, frozen-explicit and correlated electron counts. ECP cores are already absent. This interface does not claim ECP acceptance or close #530.

UHF, ROHF, SR, KS/hybrid, reduced or shifted meshes, symmetry-reduced references, fractional occupations, metallic gaps, overlap-truncated AO spaces, charged cells and lower dimensions refuse. An old ChiAcceptedReference or historical torus Hamiltonian cannot substitute for this sealed physical-pair reference. Accepted HF restart is reusable; local-MP2 amplitude restart is not implemented.

Scoped new-source acceptance

Full-domain/zero-PNO admission passes for the accepted H2/cc-pVDZ Gamma source and LiH radius-24 (4,1,1) source, with independent LiH frozen 0/1 partitions. Bounded and prepared transport agree exactly in the recorded raw energies, residuals and PAO/PNO ranks; maximum canonical error is 7.55e-15 Ha/cell. H2 uses AO seeds and LiH the explicit cosine option. The convergence record contains runtime pins, controls, residuals and separate corrections. This accepts the finite-source full-space route, not nonzero truncation thresholds, physical convergence or general crystal accuracy. No method fix was needed.

The LiH support follow-up adds full-space admission on seven larger-support sources, preserves the reciprocal-40 factor-recovery refusal, and measures independent domain/PNO errors on the original radius-24 source. PNO cutoffs 1e-6 and 1e-7 fail the 10-microhartree raw target for its all-electron partition, even though separate PNO estimates reduce the corrected errors. No production cutoff is inferred.

Explicit occupied seed frames

The default seed_basis="ao" greedily selects translated families of normalized primitive AOs and applies symmetric Lowdin orthogonalization. An admitted occupied projector need not admit this particular frame: an AO may have no projection onto the occupied space at one character even when it has a large projection at another. A refused frame is not evidence of an invalid HF reference or a failed MP2 iteration.

seed_basis="cosine" explicitly uses real DCT-II mixtures of the normalized primitive AOs, re-normalized in the home-cell overlap metric, as candidate seeds. The same primitive mixing is used at every translated cell. Projection, complete Gram spectra, the strict seed_lindep test, deterministic greedy order, symmetric Lowdin construction and global admission checks are retained. Active and frozen partitions are selected and checked independently. No automatic fallback, rank relaxation, canonical occupied array or change of SCF Fock is introduced. This option can also refuse a common frame.

This changes only the seed matrix in the existing projected-seed construction of Riplinger and Neese, Sec. II B1, with the finite-character transform of Nejad et al., Sec. II, Eqs. (2)-(10). It is an experimental deterministic frame, not optimized Wannier localization or a production localization default. Mixed seeds can alter domains and PNO truncation errors; compare them separately from the full-space raw limit. Provenance records the basis recipe and selected cosine indices; active_seed_aos and frozen_seed_aos are empty for mixtures, so cosine indices are never presented as individual AO labels. Compact preparation adds 8*(5*b*b+2*b) bytes to its controlled payload reservation for a primitive basis of size b. The existing exclusions from that reservation remain in force.

Exact finite-source transport

The overlap and Fock home-row blocks are computed directly as

\[B_D = N^{-1}\sum_k e^{-ikD} A(k),\qquad A_{R,T}=B_{T-R}.\]

All displacements remain. The adapter supplies CyclicAOOperator objects and checks reality, cyclic symmetry, positive overlap symbols and forward recovery of every original Bloch matrix. It does not build square supercell AO overlap or Fock matrices. The actual SCF Fock, including its BvK exchange zero-mode term, enters the amplitude equations unchanged. The retained Coulomb factors supply occupied-virtual numerators; the overlap-only zero-mode constant has zero occupied-virtual matrix elements. Canonical comparisons must keep the same SCF Fock, equivalent to keep_exxdiv=True in references that expose that choice. No historical torus source or finite-size correction is substituted.

Complex Bloch orbitals are admitted only through a verified real-space transformation. With unitary Fourier-folded occupied coefficients Z, the real span [Re Z, Im Z] must have exactly the original occupied rank and unit nonzero metric-Gram eigenvalues. Compact preparation evaluates its complete spectrum through character blocks, described below. The normalized real-span projector must reproduce the original complex metric projector at every AO entry and displacement. Active and frozen spaces are checked independently, including at self-inverse characters. Arbitrary orbital phases and character ordering are allowed; a complex projector is not. The preceding canonical reference’s complete metric, stationarity and physical-source admission is unchanged. Conventional D9-D12 adapters keep their complete eigenspace replay.

The default factor_provider="streamed" borrows the immutable retained Bloch operator. factor_provider="dense" explicitly selects the existing native home-auxiliary transform as a small-system oracle. There is no automatic fallback. Both must recover every retained complex AO factor entry within 1e-10 absolute tolerance, including canonical auxiliary null modes. Real and symmetric admission uses the same tolerance. Incompatible auxiliary gauges refuse; no retained rank, support or source identity changes.

The read-only factor-fidelity payload reports this fixed-gauge defect separately from complete within-transfer Coulomb-block conjugation. A small operator defect does not override entry admission. The reciprocal-40 investigation localizes an archived LiH refusal to retained-eigenspace forward accuracy near the metric cutoff; its original factors remain refused.

For N cells, define the unitary orbital transform and the retained factor convention by

\[c_{k\mu p}=N^{-1/2}\sum_R e^{-ikR}C_{R\mu p},\qquad B_{tP,R\mu,S\nu}=N^{-2}\sum_{ij} e^{ik_i(R-t)-ik_j(S-t)}L_{ij,P\mu\nu}.\]

The two inverse AO transforms each supply \(1/N\). Contracting with two orbital columns supplies \(\sqrt N\) from each AO sum, leaving

\[X_{q,Plr}=N^{-1}\sum_{k_j-k_i=q} c_{i,l}^{\dagger}L_{ij,P}c_{j,r},\qquad B^{\rm MO}_{tP,lr}=\sum_q e^{iqt}X_{q,Plr}.\]

Character orthogonality gives \(\sum_t e^{i(q+q')t}=N\delta_{q',-q}\). For the admitted real pair inputs, \(X_{-q}=X_q^*\), so the actual pair kernel is

\[(ia|jb)=N\sum_{qP}X_{q,Pia}X^*_{q,Pjb}.\]

The conjugation is on the second pair factor. This is also the canonical retained-operator convention \(L_{ia}L_{bj}^{\dagger}\) after expanding the orbital coefficients. No extra per-cell energy division occurs in the provider; the shared solver applies its existing orbit weights and division by N. Nonorthogonal AO bases require no added overlap in this covariant coefficient contraction. Complex orbital inputs to mo_transform retain the left-coefficient conjugation and explicit auxiliary-cell sum.

Admission folds one primitive AO pair and an auxiliary tile at a time using character/displacement tiles of width d, with d at most 8 and strictly below N for N greater than one. It retains linear d*N*p slabs, never an additional N*N character table or N*N*p audit tile. Define

\[H_{RjP}=N^{-1}\sum_i e^{ik_iR}L_{ij,P\mu\nu},\qquad B_{RSP}=N^{-1}\sum_j e^{-ik_jS}H_{RjP}.\]

For each target character tile I, every displacement block is reconstructed. The separately transformed reversed AO block supplies \(A_{RSP}=\tfrac12(\operatorname{Re}B_{RSP}+ \operatorname{Re}B^{\nu\mu}_{SRP})\). Every imaginary entry and every real symmetry difference is measured before this average. Recovery then uses

\[W_{ISP}=\sum_R e^{-ik_IR}A_{RSP},\qquad \widehat L_{IJP}=\sum_S e^{ik_JS}W_{ISP}.\]

Every retained entry of \(\widehat L-L\) is checked, including every null-space component. The inverse sums run over the complete i axis followed by the complete j axis. The forward R sum accumulates in original displacement order; the S reduction spans its full axis. Tiling changes storage and recomputation, not normalization, conjugation, the real transpose average or any tolerance. All norms are maximum absolute entries in their original representation. Reconstructing B again for each I costs extra work; it is not a speed claim.

The one-entry immutable phase cache holds only a bounded rectangle and is bound to the sealed source identity, character order and mesh. Pair and MO contractions use the same generator, including complex left conjugation and the auxiliary-cell phase product. The phase translation law still visits every character, origin and cyclic shift, including self-inverse cells. The sealed provider’s constructive covariance follows from this checked phase action and the complete factor recovery. factor_audit="all-origins" on the shared engine still checks actual pair contractions at every origin. No sampled energy replaces a source audit.

These transformations follow Nejad et al. (2025), Sec. II, Eqs. (2)-(6), doi:10.1063/5.0290816. The existing shared engine uses its projector/Lowdin occupied frames and Mulliken atom domains, not the paper’s optimized Wannier/OSV/local-fitting procedure. Its occupied coupling residual follows Sec. V, Eqs. (42)-(44). PNO densities and cross-pair metric transport retain Riplinger and Neese (2013), Sec. II B3, Eqs. (23)-(25), and II C, Eq. (30), doi:10.1063/1.4773581. The D1-D5 design explains their density normalization differences and even-mesh pair multiplicities.

Approximations, convergence and memory

tcut_mkn and tcut_pno are independent. Zero means full AO domains and no PNO truncation. Positive domain cutoffs use absolute Mulliken populations; positive PNO cutoffs use the shared pno_norm="mp2" density. lindep and seed_lindep retain the shared PAO rank and occupied seed conditioning controls. For a canonical-limit comparison, also verify that each full-domain PAO rank equals the total explicit virtual dimension and converge lindep if needed. Zero domain/PNO cutoffs do not override numerical conditioning cutoffs. No pairs or occupied Fock couplings are screened. Domains that are empty, or PNO spaces that violate a self-inverse pair stabilizer, refuse explicitly.

raw_e_corr_per_cell is the iterated raw pair energy. The separately reported pno_correction_per_cell is the semicanonical discarded-PNO estimate inside the selected domains. It does not repair missing domains or occupied-Fock coupling. e_corr_per_cell and e_total_per_cell include that named estimate. There is no domain correction. The raw residual and energy change are tested on the same amplitude state. Reaching max_iter returns converged=False, including in artifacts; a correction cannot turn it into convergence.

Each metric/Fock stores N*b*b real numbers for b AOs per primitive cell. The streamed provider removes the additional 8*a*(N*b)**2 byte home-factor array and its immutable snapshot. The retained Bloch source still stores 16*N*N*a*b*b bytes and is borrowed without copying. Dense oracle preparation retains the original allocations and is outside the new factor budget. compact_storage=True (the chi default) retains only selected occupied home columns, with C[R mu,T i] = C[(R-T) mu,0 i]. Active and frozen frames remain separate. Home columns are constructed directly from the cyclic symmetric Lowdin matrix function. Complete source-partition, metric and translation audits use verified cyclic displacement blocks at the existing 1e-10 maximum-entry tolerance; unverified inputs retain streamed column checks. Selection and pair spaces share the same immutable home buffers. No coefficient or occupied tail is screened.

Pair storage reuses the shared PAO recipes V = E_D A - C B, where C is the active/frozen union. The builder compares every reconstructed PAO and rotated PNO coefficient with the dense algebra, then checks the complete metric, occupied exclusion and self-inverse translation stabilizer as before. It retains A, B and domain indices, reconstructing one pair at a time for factor contractions. Native preparation receives neither a dense selected occupied frame nor a dense pair-AO pool. Active and frozen home columns have independent cell-major indexing. It checks every occupied Gram and translation entry, then streams occupied columns for recipe validation and stable pair links. Its stable selected-column branch reconstructs one source pair at a time and includes that rectangle in its existing workspace bound. Recipe/source hashes bind prepared transport reuse without reconstructing AO bases during iteration or provenance recording.

Use compact_storage=False for the dense coefficient oracle, independently of factor_provider. Shared generic translation APIs retain their opt-in compact_storage=True interface. np.asarray(selection.occupied) explicitly reconstructs a detached complete matrix. spaces.pair_coefficients[row] returns a detached pair matrix; neither output is cached in compact mode. The AO-reference solver requires explicit dense coefficient storage.

coefficient_storage reports retained selected/recipe/pair-AO bytes, dense equivalents and the measured complete pair reconstruction defect. The count covers the pair build; the automatic compact selection shares its selected buffers. The bounded storage ladder also counts the dense selection’s separate snapshots. This is a retained storage reduction, not a peak-memory cap. PAO/PNO projected matrices, occupied Fock, amplitudes and prepared transport links remain dense. Complete selected frames and their shared SC/FC arrays are absent on the compact chi path. The PAO builder caches only cyclic metric-applied home columns; it evaluates the current pair Fock through the original four-term expression, retaining both occupied/virtual cross terms, including admitted Fock asymmetry. Full domains can produce projected matrices with the full AO dimension. All-displacement actions and the factor round-trip audit still perform substantial work. The existing shared compact orbital-audit and reconstruction-recipe implementations for other adapters remain unchanged.

Cyclic occupied preparation

Let \(U_{Rk}=e^{ikR}/\sqrt N\) and \(Q(k)\) be one admitted occupied metric projector, with m bands per cell. For the chosen home AO indices J, let \(E_J\) select those columns and \(D_{jj}=\sqrt{S_{0j,0j}}\). The translated normalized seeds have symbol

\[B(k)=Q(k)E_JD^{-1},\qquad G(k)=B(k)^\dagger S(k)B(k).\]

The dense seed Gram is unitarily similar to the direct sum of all \(G(k)\). Hermitianization commutes with that transform. Its smallest and largest eigenvalues are therefore the global extrema across every character block, with no factor of N. The existing admission remains strictly \(\lambda_{\min}>\mathrm{seed\_lindep}\lambda_{\max}\). Greedy candidate order, minimum-eigenvalue score and the tolerance-sized tie envelope are unchanged. Finite-precision \(Q^\dagger S Q\) is retained; idempotence is never used to replace it with \(S Q\).

For \(G(k)=V_k\Lambda_kV_k^\dagger\), form its unique symmetric inverse root \(H(k)=V_k\Lambda_k^{-1/2}V_k^\dagger\) using the complete spectrum. No eigenvector phase, ordering within a degeneracy or additional cutoff selects a gauge. The selected home columns are

\[C_{R\mu,0i}=N^{-1}\sum_k e^{ikR}[B(k)H(k)]_{\mu i}, \qquad C_{R\mu,Ti}=C_{(R-T)\mu,0i}.\]

There are two unitary transforms, hence \(1/N\) rather than \(1/\sqrt N\). The inverse transform checks every imaginary home entry before taking its real part. At self-inverse characters the symbols are real; their complete real matrix function is retained, including degenerate bands. Active and frozen partitions are selected separately. compact_storage=False keeps the explicit dense selector and real-span oracle; no budget failure chooses it.

The chi source real-span audit also has an exact character decomposition. For a partition’s original Bloch columns c, its block is \(A_k=[c_k,c_{-k}^*]/\sqrt2\). The corresponding metric block is \(M_k=[S_kc_k,(S_{-k}c_{-k})^*]/\sqrt2\); keeping this expression preserves admitted source asymmetry instead of assuming it vanishes. At self-inverse characters use \([\Re c_k,\Im c_k]\) and \([\Re(S_kc_k),\Im(S_kc_k)]\) explicitly. The union of the Hermitianized \(A_k^\dagger M_k\) spectra is the original real-span Gram spectrum. Every block must have m unit and m zero eigenvalues at 1e-10, with no new rank cutoff. A conjugate pair is reconstructed as a complete real/imaginary column pair; self-inverse characters use the entire real block. Small coefficient-space recipes are local to this call and included in its symbol charge. Verified complete character representations evaluate these audits through small real-character and cyclic displacement blocks. Unverified tables retain the exhaustive real-column replay.

Bounded reference phases and greedy reuse

Compact reference preparation generates positive-phase rectangles of at most N*d entries on demand, with no retained phase cache. Inverse transforms tile displacements and retain the complete character reduction; forward recovery tiles characters and retains the complete displacement reduction. Both use the original conjugations and normalization. Every overlap/Fock entry and occupied-projector displacement remains audited. Exhaustive threshold replay requests one phase row at a time. Immutable source, mesh and character-order bindings prevent reuse across references; generic supplied tables still need verification and otherwise retain exhaustive replay. The explicitly selected dense factor oracle may construct its complete table under its separate scope.

For each active or frozen selection independently, define

\[H(k)=D^{-1}Q(k)^\dagger S(k)Q(k)D^{-1}.\]

Every candidate Gram is the principal submatrix H(k)[J,J]. One primitive N*b*b cache therefore replaces repeated candidate contractions. This is an algebraic rearrangement of the existing projected-seed criterion, not idempotence substitution or screening. All candidate spectra and their global extrema remain evaluated in the original order. A conservative roundoff guard replays the entire original greedy step near strict rank admission or the tie envelope. The winning conditioning score and final symmetric Lowdin gauge use the original selected-column contraction. This preserves the original arithmetic where it determines a boundary decision; no tolerance is loosened. The cache is bound to projector, metric, mesh and partition identities and is released on return or failure. It is never a translated-seed Gram.

greedy_gram_work records primitive builds, candidate eigenspectra, original contractions, boundary replays and released bytes independently for each partition. Reference-phase provenance records tile, generated entries, zero cache/table bytes and its immutable binding. Gamma pays extra setup/cache cost; ambiguous candidates can require both cached evaluation and replay. The primitive cache remains quadratic in primitive AO count, and retained source factors, downstream amplitudes and transport remain separate costs. These changes preserve experimental scope and do not expand the bounded 0.18 release gate; production periodic DLPNO remains deferred under #557.

Complete cyclic audit norms

For a selected partition X with immutable home columns \(h_X[R]\), define \(c_X(k)=\sum_R e^{-ikR}h_X[R]\). The complete Gram and projector symbols are

\[g_{XY}(k)=c_X(k)^\dagger S(k)c_Y(k),\qquad p_X(k)=c_X(k)c_X(k)^\dagger S(k).\]

Their home-row blocks are \(N^{-1}\sum_k e^{-ikD}g_{XY}(k)\) and \(N^{-1}\sum_k e^{-ikD}p_X(k)\). Every displacement D is reconstructed. Subtract the identity only at D=0 for a same-partition Gram; the cross Gram has no identity subtraction. The largest real entry over all D is exactly the original complete selected-orbital norm. Compare each projector block with its own frozen or active source block before taking that same maximum. The right factor is S, not its adjoint, preserving admitted metric asymmetry. Neither symbol maxima, Frobenius norms nor a sample of D=0 is substituted.

The source real-span frame uses a different orbital basis. For a conjugate pair, its real columns are \(\sqrt2[\Re(U_kF_k),\Im(U_kF_k)]\). With \(g=F_k^\dagger M_k\), the original real Gram is \([\Re g,\Im g;-\Im g,\Re g]\). Its norm is the maximum of the real and imaginary entries separately, not the complex magnitude of g. Self-inverse characters retain the complete real block. Both the original metric-frame action and the admitted real S action are checked. Distinct character pairs are orthogonal by the verified complete character table. The normalized-span projector uses \(F_kM_k^\dagger\) and is compared with \(c_k(S_kc_k)^\dagger\) at every AO entry and displacement, including its imaginary component. Conjugate partners use the same recipe; degenerate subspaces are never split.

Only exact immutable column recipes and cyclic operators with matching mesh, cell-major ordering and source bindings receive structural reductions. Character tables are checked against their actual mesh coordinates and phases. For these representations every origin is a displacement permutation; generator checks on all home entries therefore cover every complete column. Generic dense/custom inputs retain the exhaustive streamed checks. A result within a conservative floating-point guard of the admission threshold replays the original arithmetic; the guard does not alter the acceptance tolerance.

A preparation context reuses at most one overlap and two occupied symbol tensors plus sixteen measured scalar defects. Source, overlap, Fock, partition and home-content identities bind reuse. No complete C, SC, FC, AO projector or translated-seed Gram is cached. The context expires on return or exception; rebinding its source or budget clears both symbol and scalar caches. Provenance names the formulation, all measured metric/projector/cross-partition defects, displacement counts, boundary replays and bounded cache counters. Equivalent checks are reported as evaluations, not skipped scientific checks. Source stationarity, factor audits, pair stabilizers and tolerances are unchanged. The native transport boundary retains its independent streamed occupied checks under its separate budget; cached Python measurements do not bypass that boundary.

max_selection_bytes preflights a conservative controlled numerical-payload reservation for compact chi occupied-source realification, cyclic selection and its admission. For N cells, b primitive AOs and m total occupied bands, the recorded byte charges are 256*N*b*b for symbols/transforms/copies, 256*N*b*m for home outputs/snapshots/reconstruction, 96*N*b*b for exhaustive audit tiles, 128*N*(b*b+b*m+m*m) for cyclic audit intermediates, 16*N*(b*b+b*m) for the bounded symbol cache, 128 bytes for scalar measurements, 128*N*d for bounded reference phases with d=min(8,max(1,N//2)), 16*N*b*b for the partition-local primitive candidate-Gram cache, and 384*(2*b)**2 + 128*b for eigensolver inputs/outputs/copies, 128*N*(b+m+3) for indices/phases and 128*np.getbufsize() for NumPy iterator buffers. Each phase preflights before its affected allocations. Cached symbols are included in this charge even when reused by consumers during the same preparation. No cache persists after the preparation returns. The accounted_peak_bytes field is this conservative reservation, not a measured process peak. The unavoidable selected-home output is 8*N*b*m bytes; the two source-projector outputs retain 16*N*b*b bytes.

This cap excludes existing SCF/source arrays, canonical reference admission, LAPACK/FFT/BLAS internal scratch, Python objects, allocator overhead, already returned buffers and downstream domain/PAO/PNO/native transport/solver work. The native transport cap separately charges its home-metric cache and streamed reconstruction buffers; Python and native binding copies are outside the default prepared transport cap. Full-domain projected matrices, occupied Fock, pair amplitudes and the overlap graph can still be quadratic or larger. Canonical adapter momentum metadata also retains an N*N*N conservation index outside this cap. The bounded selector ladder reports both time and storage. No total-memory bound or linear scaling follows.

max_factor_bytes bounds numerical array payload during each serial streamed provider call, including preparation’s factor audit, coefficient conversion and Fourier buffers, auxiliary tiles, temporary products, cached phases, audit-local reuse and returned arrays until return. Calls on the same provider cannot overlap. Returned pair matrices are unavoidable output storage; their size is charged before allocation and reported as max_output_bytes. Once returned, arrays retained by downstream consumers are outside this per-call cap. The provider uses einsum(optimize=False) with explicit output arrays, so it makes no native factor-binding copies or BLAS packing allocations. The ledger reserves eight complex NumPy iterator buffers at the current np.getbufsize() setting.

For auxiliary width p and character/displacement width d, preparation charges 192*N*d*p audit bytes, 128*N*d phase bytes and the iterator allowance. The audit charge covers concurrently live recovery/home slabs, inverse half-transforms, gathered source entries, reversed blocks, products and finite/absolute-value temporaries. The phase charge covers two live blocks and a replacement’s construction plus immutable snapshot. No full table is cached even when the requested cache ceiling is large.

After choosing this same tile plan, preparation may reserve another 16*N*d*p bytes to reuse its first displacement slab. This is the immutable real transpose average, stored only after measuring the original imaginary and symmetry defects. The reservation covers its snapshot alongside the original and its subsequent lifetime alongside the remaining audit work. Reuse requires spare workspace, more than one target tile, and room for both this slab and the largest phase cache block under factor_cache_bytes. It never reduces the chosen tile widths to make a cache fit. The slab belongs to one source, AO pair and auxiliary tile, and is released before moving to the next pair or returning.

With another 16*N*d*p bytes of spare workspace and cache capacity, a second immutable slab retains raw complex reversed-AO values B_nu,mu[S,R] for the first S tile and all R. Later R and target-character tiles reuse these values when measuring symmetry and forming the real transpose average. The raw snapshot is never realified or averaged, so reuse does not assume symmetry or conceal imaginary defects. Every original home slab still undergoes the complete imaginary check. Remaining reverse blocks and home slabs outside the first R tile are recomputed as before.

The baseline audit reservation already covers a d*N*p reverse output and its half-transform. The second extra reservation covers its immutable copy during construction and its retained lifetime alongside the first cache and other audit work. Both slabs plus the largest phase snapshot must fit the cache ceiling. Both are released per AO/auxiliary tile and before return; d remains capped at eight and below N for non-Gamma meshes. Every source entry is still recovered in the original sum order, including null modes. Neither a complete home tensor nor a quadratic audit array returns.

For l left and r right columns, contractions retain the existing charges: 64*N*b*(l+r) conversion/Fourier bytes, p*(64*l*r+32*l*b) auxiliary work, and either 48*r*r pair-output/work bytes or 32*N*a*l*r MO-output/work bytes, plus bounded phases and the iterator allowance. Planning tries d from min(8,max(1,N//2)) down to one, choosing the largest fitting p up to factor_auxiliary_tile. Infeasible budgets refuse before workspace allocation. The minimum audit reservation is iterator_allowance + 320*N bytes; a later contraction can still refuse because its output and Fourier buffers need more.

factor_cache_bytes permits one immutable phase block and the two optional audit-local slabs described above. Zero disables caching; an insufficient ceiling or workspace leaves either the first slab alone or complete recomputation, with the same minimum and tile plan. Cache replacement is charged, and a smaller call plan evicts an oversized previous phase entry before allocation. No home factors survive preparation; orbital arrays are never cached. audit_reuse_workspace_bytes records the extra reservation, and audit_reuse_stores / audit_reuse_hits count slab snapshots / subsequent uses. The corresponding audit_reverse_reuse_* fields separately record the raw reversed-AO reservation, stores and hits. cache_bytes reports only the phase block still retained after return. Diagnostics also report the actual tile dimensions, minimum reservation, accounted peak, cache traffic, generated phase entries, repeated inverse blocks/entries, complete recovered entries and all measured defects. The bounded benchmark compares minimum and larger budgets with the former tiled and complete-table oracles.

The cap excludes pre-existing SCF factors, caller coefficients, reference admission and orbital preparation (bounded separately by max_selection_bytes), already returned buffers, downstream PAO/PNO/solver allocations, Python metadata, allocator overhead and process RSS. It is not a total-memory bound. factor_provider_record identifies the preparation; factor_provider_execution additionally reports final cache hits, largest tile/output, accounted peak and contraction imaginary defects. Source hashing borrows contiguous canonical factor buffers rather than copying a full block to bytes.

For the default prepared backend, max_transport_bytes is enforced by the shared native preparation before allocating the prepared transport payload and its accounted workspace. It does not cover SCF, this adapter, PAO/PNO preparation, Python metadata, binding conversion copies of remaining inputs, solver output copies, allocator overhead or total process memory. The adapter’s storage record reports retained array bytes only. No new total-memory guarantee or production-scaling claim is made.

Reproducible Validator handoff

chi_translation_mp2.py prepares H2 or LiH/STO-3G with explicit finite classic supports, or reuses an accepted HF archive through --reference. Stage it through the configured vq service with a runtime containing this increment and the prepared native translation solver. Keep output outside the checkout and inspect existing job identities before submitting. Suggested cases:

--case h2 --mesh 1 --output RESULTS/h2-m1
--case h2 --mesh 3 --output RESULTS/h2-m3
--case lih --mesh 4 --frozen-core 0 --output RESULTS/lih-m4
--reference RESULTS/lih-m4/hf.vqr --frozen-core 1 --output RESULTS/lih-m4-core

The short support and individual AO seeds are diagnostic defaults, not guaranteed admissible LiH references or frames. For the even-mesh LiH fixture, explicitly use --one-electron-cutoff-bohr 12 --seed-basis cosine and retain --seed-basis cosine when reusing its archive. Wider one-electron support defines a different finite Hamiltonian; compare only with a canonical calculation consuming that same archive. A positive metric and an insulating accepted reference are still required. The support option applies only to fresh HF preparation; a reused archive retains its recorded support.

For example, copy the single example script to an external CASE_DIR, select the verified registered runtime interpreter as RUNTIME_PYTHON, and submit:

vq submit --dir CASE_DIR --cpus 4 --mem-mb 8192 --time-limit 01:00:00 -- \
  RUNTIME_PYTHON chi_translation_mp2.py --case h2 --mesh 3 --output results

These resource values are initial reservations, not measured requirements. Use an installed runtime whose source contains the delivery commit recorded on #508. Record its native identity from the result manifest; an older runtime cannot qualify this adapter. A reused archive must also be staged into the case directory. No source checkout or environment copy is needed.

The example runs both factor providers and both coefficient storage modes by default, compares their raw energies, residuals and separately reported PNO corrections, and records their storage ledgers. Select only --factor-providers streamed for sizes beyond the dense oracle’s scope and --coefficient-storage compact to omit dense coefficients. --max-factor-bytes, --factor-auxiliary-tile and --factor-cache-bytes reproduce budget experiments. --max-selection-bytes controls the separate occupied-preparation reservation. Use --transport-backend bounded --coefficient-storage compact and --max-transport-bytes for bounded link cases; reuse the same archived reference for the prepared comparison. Record the SHA-256 of the installed vibeqc.dlpno.translation_bloch_factors module and pass it as --expected-provider-sha256 to refuse a runtime with different source. The coefficient implementation is checked with --expected-storage-sha256 (SHA-256 of vibeqc.dlpno.translation_storage); --expected-core-sha256 checks the loaded native module. --expected-preparation-sha256 checks vibeqc.dlpno.translation_preparation. --expected-implementation-sha256 binds all thirteen occupied-preparation/consumer modules in a deterministic digest; use it with the native hash to identify the containing runtime. The result records these hashes and the actual loaded native identity. A prepared case is not a scientific verdict or evidence that a future managed runtime contains it.

The full-space raw solution is compared with independently evaluated same-source canonical MP2 at 2e-9 Ha/cell, with residual 1e-11 and energy change 1e-13 gates; all three are checked and the last energy change is recorded. Tighten these if residual accumulation approaches the energy tolerance. The example varies domain thresholds at zero PNO cutoff, then PNO cutoffs at full domains, recording raw errors, corrections, ranks, iterations and refusals. Threshold errors need not be monotonic.

For a containing-runtime comparison of prepared and bounded transport, keep the accepted archive bytes, source/Fock/factor identities, seed basis and frozen partition fixed. Run each LiH frozen partition independently; a pass with one frozen orbital does not qualify the all-electron partition. Reuse the accepted canonical and independent same-source reference evidence, then check the changed consumer against it. Record the loaded Python and native identities separately from the archive producer. An earlier prepared-backend pass does not qualify a later bounded implementation.

Compare representative amplitudes, residual tensors and iteration traces as well as raw energies and separate PNO estimates. Pair builds, selected active and frozen projectors, ranks and electron counts must agree between backends. Keep the full-space canonical gate separate from domain and PNO errors; truncated rows still need their own convergence verdict. None of these checks permits omitting an occupied-Fock coupling or relaxing a source audit.

Inspect stable_selected_column_links, target_metric_constructions and target_metric_cache_hits to establish whether a case exercises target reuse. A case with zero stable links checks the nonstable path only. Gamma overhead or a small finite-source timing does not establish scaling. Record retained links, the target reservation and the documented transport budget scope; cache_bytes_after_solve=0 is a lifetime check, not a total-process memory measurement. Keep scientific results and immutable runtime receipts on the acceptance issue. This protocol remains outside the 0.18 release gate.

Source checks exercise a nonorthogonal finite model with occupied-Fock coupling, independently evaluated dense canonical MP2, complex Bloch gauges, frozen core, translation covariance and even-mesh self-inverse multiplicities. They also reject source mismatch and unsupported inputs and forbid historical dense reconstruction. These are implementation evidence. Validator must record the actual containing-source/native runtime and matched conventions, reuse qualifying #492/#530 operands, and assess physical support/cell convergence and ORCA/CRYSTAL comparisons separately. No existing scientific job was replaced by this development increment.

On the deterministic nonorthogonal source model, the largest full-space raw error across meshes (1,1,1), (3,1,1), (4,1,1) with one frozen orbital per character, and (2,2,1) was 5.52e-15 Ha/cell. The largest final raw residual was 1.78e-13; the multi-cell cases required eight iterations with nonzero occupied-Fock coupling. These values are algebra checks, not results for H2 or LiH. The separate three-character threshold experiments measured:

Domain cutoff

PNO cutoff

Raw error (Ha/cell)

PNO estimate (Ha/cell)

PAO/PNO rank ranges

0

0

+1.72e-16

-1.14e-18

6 / 6

0.05

0

+4.34e-3

below 1e-18

1-2 / 1-2

0.01

0

+4.34e-3

below 1e-18

1-2 / 1-2

0

1e-4

+1.01e-3

-1.03e-3

6 / 1-3

0

1e-6

+1.90e-6

-1.96e-6

6 / 4-6

All five solves converged below 2e-14 raw residual. The PNO estimates are reported independently and do not enter the full-space raw comparison.

The occupied audits use verified cyclic blocks. Compact reference phases are bounded and greedy primitive-Gram contractions are reused. Pair reconstruction remains dense one pair at a time, and the default prepared overlap graph remains retained; bounded transport can instead reconstruct links during iteration. Repeated inverse-block reconstruction in the complete factor audit belongs to the separate factor work. Optimized localization, calibrated screening, unrestricted equations and local CC remain separate work.

Internal CCSD algebra follow-up

The translation-native restricted CCSD residual evaluator reuses this preparation and bounded transport to evaluate complete native singles/doubles residuals and raw correlation energy at arbitrary amplitudes. It shares the molecular PNO contractions and is not an iterative CCSD method. Its CC workspace accounting and pending scientific acceptance are separate from the MP2 capability recorded here.