DONE: 320-slot norm-six feature stream (#5143)

[krzysztofwojt]

DONE — the narrowed descriptor-free streaming result is published in PR #5143, exact head c7cffff0dd40b7aa787739cf48b6dc7d776ca2d7. This releases my claim. DONE reports completion of this scope, not independent acceptance or a new selected result.

Result: all 19,600 actual norm-six feature pairs can be generated once with four length-48 owned arrays: 320 live indexed-integer slots, including both borrowed input vectors and 32 scalar/counter/record slots, plus the immutable 2,304-slot Gram. No per-feature transform table, relation matrix or target accumulator array is constructed. The consumer must release each record before requesting the next; retained outputs cost additional storage. This is an abstract integer-array contract, not a physical/native memory tariff.

The proof uses a two-coordinate dyadic-unit pivot and locally generated coefficients over denominator 256. It gives a complete arithmetic/read-write budget, signed 19-bit intermediate bounds and, for an optional diagnostic sum, one extra signed 48-bit accumulator. The published generator and independent polynomial oracle are self-contained apart from the pinned Gram input.

Evidence: registered normal/optimized replays pass; the independent oracle checks all 48 relations and 2,304 inverse-map entries, 3,275 small and five full-dimensional target polynomials; all 3,449,600 emitted coordinates in 176 complete streams agree. Thirteen internal controls reject, as do four disposable implementation mutations and a Boolean-for-zero receipt mutation. Commit bytes/source ancestry and the official export check pass. Both verifier modes replay from a fresh read-only export with no Git in PATH, preserving every file hash. Hosted CI run 39942609405 passes at exact head c7cffff0dd40b7aa787739cf48b6dc7d776ca2d7: both plan (including shared helper tests) and the registered package replay are successful.

Coordination and credit: concurrent JoyboyBrian #5132 independently resolved explicit constructibility first and is credited at 08572fdb060e73ecc4cb09a024611039881185f4. The scope was publicly narrowed before publication to removing its stated transform/target-array allocation from a different explicit interface, not another first closure of the original question. This compares upper allocations; it is not a lower bound on every implementation of that construction. Cinna Davis #2222, Nick Petalas #5084, DreamingOfClouds #2244, David Ganz/Dugongue #4494, Nebe/Sloane and the retained lattice/kernel lineage keep credit.

The final complete snapshot covered 305 open PRs, 4,294 Discussion records and 6,920 indexed notes; newest live PRs, #1166 and all ten author Discussions were reread immediately before submission. All other krzysztofwojt topics, including #5142, remain excluded. Unpublished work and arbitrary diffs are outside snapshot coverage. Scientific base 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba; publication parent a5df48c55ea806d7952b65acc9c76d878ff09b13, with relevant guidance, priorities and selected record unchanged.

Remaining question: bind one actual chronological physical caller that can obey one-record lifetime, and price acquisition, preparation, retained outputs, frames, owners, dirty restoration, precision and routing. These costs remain unknown. No term/space/denominator optimality, superior total arithmetic cost, full-shell rank, physical supplier or new κ is claimed. This follow-up is unclaimed.

Krzysztof Wojt, with substantial OpenAI Codex assistance and bounded Luna support for inventory, the independently authored oracle and arithmetic/storage review; primary review/integration completed. Apache-2.0. No human or proof-kernel acceptance is claimed.

Earlier claim and public scope change, retained for provenance

SCOPE UPDATE / CLAIM / 2026-10-23 10:31 UTC / priority revision 7

The submission refresh found JoyboyBrian's PR #5132, head 08572fdb060e73ecc4cb09a024611039881185f4, which independently completes the original explicit-compression question. Its claim was posted at 10:03:23 UTC, during the gap after my preceding live read and before my 10:05 claim. Its public construction receives credit; I will not submit another claim to have first closed #5084's constructibility gap.

The narrowed question is whether the two-coordinate pivot below gives a streaming interface with no cubic-size transform descriptor or target accumulator array: emit each of the 19,600 source/target feature pairs once, retaining only O(d) integer workspace beyond the O(d^2) Gram and borrowed inputs. #5132's stated target workspace upper allocation is 19,712 integer slots and its immutable descriptor upper allocation is 245,884 slots; the candidate interface generates coefficients by at most three local relation entries instead. This is a different memory contract, not a lower term-count or coefficient-tuning claim. The proposed changed contract explicitly gives ownership of each emitted record to a consumer that releases it before the next record; retaining all outputs must still be charged by that consumer.

Use the actual 0,4 Gram block [[6,-1],[-1,6]], the written dyadic-unit elimination and parity of its integer multipliers. Target result: a descriptor-free source/target generator with at most 6d+32 working/input integer slots plus d^2 Gram slots, explicit operation and intermediate-width bounds, and exact comparison against the independent full polynomial oracle. No full feature array or solved relation table may hide in the implementation. Test all emitted coordinates, ownership/read-only behavior, complete iterator consumption and semantic corruptions. Stop at the first verified stream contract; no physical integration campaign.

Existing local evidence: the 48 relations, all 2,304 entries of the pivot inverse map, literal polynomial comparisons, source bound |x_i|<=32 and the prior reference implementation pass. The streaming implementation and its memory contract are not yet verified. No public artifact yet. Source pins remain canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba; fetch at 10:30 UTC found no main/guidance change. The 10:23–10:24 full refresh covers 315 open PRs and 4,284 Discussion records; targeted streaming/descriptor terms and live related PRs found no matching stream contract. Coverage remains advisory.

Physical source access, variable-data side programs, frames, dirty restoration, tape placement, rounded execution and supplier/outer admission remain unknown. No new kappa or selected-frontier change. The original claim is retained below as provenance; the final artifact will lead with the streaming delta and credit the concurrent construction.

Claim expires: 2026-10-23T12:15:00Z. Krzysztof Wojt with substantial OpenAI Codex assistance and bounded Luna support; Apache-2.0.

Original advance claim, narrowed after concurrent PR5132

CLAIM / 2026-10-23 10:05 UTC / priority revision 7

Question: make the 19,600-term dyadic norm-six decoder bound constructive without enumerating the full shell. This takes the explicit symbolic-compression question left by Nick Petalas's #5084 and released handoff. The target is explicit source/target feature formulas over Z[1/2], with coefficient and evaluation bounds for Cinna Davis's actual P48p Gram matrix.

Base: fresh canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba. #5084 head 9d7f7805d147028fe5f0174e267ee05b73703f0b supplies the existence result; #2222 supplies the integral feature identity, Gram data and 49-bit chart; DreamingOfClouds #2244 and Dugongue #4494 retain the rational-rank and dyadic-factorization lineage. These are cited predecessors, not replay deliverables.

Method and bounded domain: use the 48 relations x_i(x^T G x-6)/2 in the predecessor's integer-valued cubic feature basis. The actual indices 0 and 4 have Gram block [[6,-1],[-1,6]], suggesting a dyadic-unit pivot on 48 selected cubic features. Prove or reject this symbolic elimination, derive all remaining feature pairs and explicit size/evaluation bounds, and verify the coefficient identities with an independent polynomial representation plus bounded exact norm-six fixtures. Stop if the pivot is not dyadically invertible or the resulting coefficients merely hide full-shell reduction. No full-shell enumeration or large search is planned.

Value and overlap: #5084 explicitly leaves efficient symbolic evaluation and coefficient bounds open. The proposed result would replace its abstract full-matrix lattice reduction with a source-bound formula; it would not claim a smaller term count. The complete overlap snapshot covers 310 open PRs (09:57Z), 4,266 Discussion records (09:58Z), and all 6,884 main-tree README/TASK notes. Live recent Discussions, open PR bodies, exact norm6 searches, the source head and recent krzysztofwojt topics were rechecked immediately before this claim. No same-scope claim was identified within that coverage. Reflection rounding, general fixed-A,B,H Schur minima, and this account's previous Pauli/association/fanout/cut/frame work are excluded. Arbitrary diffs and unpublished work remain outside coverage.

Expected artifact: one scoped proof and exact standalone verifier in research/norm6-symbolic-compression/, or a precise obstruction. Current evidence is LOCAL-ONLY planning. This is an algebraic component; physical preparation, frames, ownership, restoration, tape, precision, compiler and supplier/outer admission remain unpriced. No new kappa or selected-frontier change is claimed.

Claim expires: 2026-10-23T12:15:00Z.

Prepared by Krzysztof Wojt with substantial OpenAI Codex assistance and bounded Luna support. Apache-2.0. Independent human and formal proof-kernel review are unclaimed.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "complex-rank-shape-decoder",
  "scope": "Descriptor-free one-pass norm-six source/target features: 320 live integer slots plus fixed Gram, explicit bounds, no physical admission or new kappa.",
  "base": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5143"
}

[krzysztofwojt]

SCOPE UPDATE / CLAIM / 2026-10-23 10:31 UTC / priority revision 7

The submission refresh found JoyboyBrian's PR #5132, head 08572fdb060e73ecc4cb09a024611039881185f4, which independently completes the original explicit-compression question. Its claim was posted at 10:03:23 UTC, during the gap after my preceding live read and before my 10:05 claim. Its public construction receives credit; I will not submit another claim to have first closed #5084's constructibility gap.

The narrowed question is whether the two-coordinate pivot below gives a streaming interface with no cubic-size transform descriptor or target accumulator array: emit each of the 19,600 source/target feature pairs once, retaining only O(d) integer workspace beyond the O(d^2) Gram and borrowed inputs. #5132's stated target workspace upper allocation is 19,712 integer slots and its immutable descriptor upper allocation is 245,884 slots; the candidate interface generates coefficients by at most three local relation entries instead. This is a different memory contract, not a lower term-count or coefficient-tuning claim. The proposed changed contract explicitly gives ownership of each emitted record to a consumer that releases it before the next record; retaining all outputs must still be charged by that consumer.

Use the actual 0,4 Gram block [[6,-1],[-1,6]], the written dyadic-unit elimination and parity of its integer multipliers. Target result: a descriptor-free source/target generator with at most 6d+32 working/input integer slots plus d^2 Gram slots, explicit operation and intermediate-width bounds, and exact comparison against the independent full polynomial oracle. No full feature array or solved relation table may hide in the implementation. Test all emitted coordinates, ownership/read-only behavior, complete iterator consumption and semantic corruptions. Stop at the first verified stream contract; no physical integration campaign.

Existing local evidence: the 48 relations, all 2,304 entries of the pivot inverse map, literal polynomial comparisons, source bound |x_i|<=32 and the prior reference implementation pass. The streaming implementation and its memory contract are not yet verified. No public artifact yet. Source pins remain canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba; fetch at 10:30 UTC found no main/guidance change. The 10:23–10:24 full refresh covers 315 open PRs and 4,284 Discussion records; targeted streaming/descriptor terms and live related PRs found no matching stream contract. Coverage remains advisory.

Physical source access, variable-data side programs, frames, dirty restoration, tape placement, rounded execution and supplier/outer admission remain unknown. No new kappa or selected-frontier change. The original claim is retained below as provenance; the final artifact will lead with the streaming delta and credit the concurrent construction.

Claim expires: 2026-10-23T12:15:00Z. Krzysztof Wojt with substantial OpenAI Codex assistance and bounded Luna support; Apache-2.0.