Symmetry parity delivery¶
Priority and current verdict¶
Feature parity comes first, then best measured time-to-solution on declared workloads, then extensions beyond those reference capabilities. CRYSTAL23 is the primary periodic workflow comparator; molecular comparisons use matched ORCA or other justified independent references. No single example establishes all-code parity, and no universal fastest-code claim is testable.
The shared layer has metric-aware Cartesian/pure actions, Seitz/Bloch transport, representative/stabilizer machinery, source-qualified molecular J/K and bounded periodic wedge consumers. These are reusable foundations, not blanket production admission. Geometry, numerical-source equivariance, state invariance and retained subspace covariance remain four separate permissions.
The canonical-orbit molecular increment passed 106 focused checks and four same-source reduced/ordered RHF/UHF calculations on its recorded runtime. Maximum ORCA difference was 1.049e-10 Eh; Fock/energy reconstruction errors were 1.422e-14/2.843e-14 Eh. Full qualification still read 625 tiles. Subsequent MANTA kernel changes require separate integration evidence. See the detailed symmetry status for scope and measured costs.
The non-Abelian ammonia harness reconstructs accurately, but its recorded setup was 14.34834 s and reduced contraction plus reconstruction 0.37066 s, versus 0.17443 s for full contraction. It is experimental algebra, not a production reduced correlation pipeline or a release prerequisite.
Delivery order and existing owners¶
Source certification and finite screening: #635, #623, #748, #753. Bind producer content/program, finite supports, actions, screen policy and metric rank. A combined-action certificate can avoid only proven audit reads; nonzero bounds and bubble hierarchies are separate producer obligations.
Periodic feature parity: #593/#577 with #767 physical-domain representative Fock and #768 IBZ-native SCF. Packed SACO blocks (#834) complete the storage, Fourier/eigensolve/density pipeline; asymmetric XC grids remain an explicit coverage gap. Preserve nonsymmorphic images/phases, momentum, mesh weights, spin/state admission and distinct CCM/chi sources.
Correlation: producer-qualified C3v residuals (#832) and complex-Abelian consumers (#833), with retained/frozen/auxiliary/local-space covariance under #589. Complete residuals and method energies precede generalized group claims.
Derivatives: #578/#637/#773, method-specific response, Pulay, fitting and support terms. Validate gradients at displaced geometries and stress under strain independently; energy evidence cannot close either target.
Efficiency: #638 and #747-#758, measured qualification/transport/kernel/ contraction/reconstruction costs and cache amortization at unchanged source identities. Keep losing crossover cases visible.
Parallel/GPU execution: #639, tensor representations #801, GPU #803, MPI #804 and #818-#826. Distribute accepted representative/block tasks; preserve density epochs, ownership, phase/multiplicity metadata and collective errors. Include transfers, communication, host/device peaks and node/GPU-hours.
All methods consume the shared evaluated Fock contract (#472/#608), MANTA producer seams (#617) and tensor engine (#793). No new competing operator, representation library or backend-specific chemistry implementation is needed. Each coverage row records implemented, experimentally accepted, rejected or missing, and links actual source/runtime and complete vq evidence. Reuse valid results and active owners; no review chains or whole-program release gate.
Literature-to-code interpretation¶
Davidson (10.1063/1.430484), Pitzer (10.1063/1.1680474) and Dupuis-King (10.1002/qua.560110408) motivate representatives, charge-distribution sectors and shell actions. They do not certify the arithmetic or support of a particular finite producer.
Hellmann-Gauss (10.1021/acs.jpca.6c00311), sections 2.3-2.5 and Eqs.9-12, demonstrate closed-shell C3v CCSD. Generalization needs explicit irreducible products, multiplicity spaces, partner gauges, recoupling and finite inverse maps. Reduced-block transposition alone is insufficient.
Kitsaras-Stopkowicz (10.1021/acs.jpca.6c00998) is held as the explicitly labeled arXiv:2602.12457v1 preprint. The journal publication is JPCA 130, 4683-4692 (2026); publisher retrieval returned 403, so equation equivalence between versions remains unverified. Preprint sections II.A-B require conjugate characters and creation/annihilation variance; time reversal is separate.
Melega (10.1021/acs.jpca.5c08579), including geometry SI, connects Abelian sectors, two-step Cholesky and analytic CCSD gradients. Differentiated ERIs are not generally positive semidefinite. Response, metric and support derivatives must accompany reduced integral work. Its real-Abelian CD-CCSD demonstration converges amplitudes, Lambda and Z-vector equations explicitly. The geometry SI comprises four ZMAT text files and one XYZ; preserve format, units and dummy atoms. Changing Cholesky bases can impair optimization smoothness, so displaced-geometry checks must record numerical topology.
MolSym (10.1063/5.0216738), representation/RHF SI, and libmsym (10.1186/s13321-017-0193-3) inform detection and adapted bases; those do not establish numerical-source or electronic-state symmetry. MolSym si1 contains RHF equations/timings; si2 contains representation matrices. Table S1 averages Fock builds over 50 iterations, not complete SCF. libmsym real spherical SALCs and complex-representation restrictions require explicit scope admission.
Dovesi (10.1002/qua.560290608), Zicovich-Wilson-Dovesi, Casassa (10.1007/s00214-006-0119-z), Rusakov (10.1063/1.4821352) and Orlando (10.1063/1.4895113, section II) describe periodic/local and integrated packed symmetry pipelines. The parity target includes storage, Fourier transforms, IBZ blocks and density reconstruction, not only fewer exchange targets.
Dong-Gull, CPC 307, 109401 (2025), connects SACO/IBZ reduction to finite-temperature self-consistent GW and GPU/MPI execution. The inspected preprint is arXiv:2405.09494; journal-version equation reconciliation remains separate. Sections 3.3-3.4, Eqs. (7)-(8) specify the nonsymmorphic factor system. Section 5.2, Algorithms 2-4 and Eqs. (16), (19), (20) motivate momentum-pair scheduling and batched complex contractions. Preserve k-dependent projective composition and separately admitted time reversal. Qualification fixtures need zone-boundary screw/glide cases and full-BZ versus IBZ-plus-block controls. Large-representation simultaneous diagonalization stability, CPU MPI work, host-resident interaction tensors and on-demand device transfers must enter acceptance and cost records. These are requirements for #834/#639, not evidence of an implemented GW route here.
Prompt for the library chat¶
Update the existing symmetry-acceleration survey and catalog with primary papers and SI available since the October 6, 2026 survey through November 3, 2026. Search molecular/periodic symmetry, finite-source screening and BUPO, packed SACO/IBZ pipelines, nonsymmorphic/projective little groups, covariant local correlation, reduced CC/response/derivatives, and distributed/GPU symmetry-resident contractions. Reconcile the five existing anchors: Melega 10.1021/acs.jpca.5c08579 including geometry SI; Hellmann-Gauss 10.1021/acs.jpca.6c00311 with demonstrated C3v scope; Kitsaras-Stopkowicz 10.1021/acs.jpca.6c00998 (currently a labeled preprint); MolSym 10.1063/5.0216738 including representation and RHF SI; libmsym 10.1186/s13321-017-0193-3. Connect Davidson/Pitzer/Dupuis-King/Stanton and Dovesi/Zicovich-Wilson/Casassa/Rusakov/Orlando. Return feedback to the symmetry chat as DOI/version/status → exact sections/equations → mathematical capability → finite-source/state/rank assumptions → implementation contract → independent fixture/reference → demonstrated limitations. Report missing documents explicitly, preserve licensing/catalog provenance, and distinguish a new publication from a newer version of an existing preprint. Include negative results and complete-cost benchmark conditions; do not summarize abstracts alone. The roadmap priorities are parity, measured speed, expansion.
Ready prompts for implementation chats¶
MANTA / source certification
Claim one #635/#623 slice after reading latest notes. Finish the distinct canonical-orbit source integration, then implement its owner-bound combined sign/permutation certificate with wrong-owner/action/support refusals. Keep nonzero finite-source screening under #748/#753 and BUPO hierarchy ownership in MANTA. Compare arbitrary nonsymmetric trial-density J/K and complete vq SCF to full same-source controls and matched ORCA. Report avoided audit/kernel reads and full qualification/transport/reconstruction cost. Preserve fallback.
Fock and tensor engine
Under #608/#801, consume existing symmetry sectors and producer identities in the unified evaluated Fock and tensor representation contracts. Implement one packed/reduced operation without compulsory full AO reconstruction. Preserve density epoch, tensor variance, metric and terminal physical-state identity. Report concrete prerequisites to the symmetry chat; do not introduce another Fock object or invent generic symmetry permission from geometry.
PBC Parity
Continue #767/#768 under #577/#593 using the exact physical pair and Bloch source. Implement one representative/IBZ path with fractional translations, full atom-image integers, reciprocal wraps and star-consistent occupations. Test arbitrary-density source covariance separately from invariant states, odd/even meshes and broken-spin refusal. Compare complete vq SCF with full same-source and matched CRYSTAL controls. Preserve separate CCM/chi sources.
Correlation / retained spaces
Start the C3v reduced residual work package with one producer-attested CCD term and continue to the full residual. Reuse symmetry_products and its finite-Gram inverse. Under #589 certify frozen, occupied/virtual, auxiliary and PAO/PNO/TNO projectors with matrix sewing, including degenerate spaces. Preserve partner/multiplicity gauges and complex variance; measure all reconstruction costs before expanding beyond C3v or enabling defaults.
MPI / GPU
Under #639/#801/#803/#804/#818, choose a measured accepted reduced-operation bottleneck. Distribute or batch representative/block work with unique ownership and explicit leases; retain phases, momentum, partner indices and density epochs. Compare identical-accuracy complete methods across CPU, ranks/devices, including empty partitions and failure handling. Report total time, transfers, communication, memory and node/GPU-hours; keep CPU fallback.