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Review settlement DP and anchored attaining header #6753

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201 changes: 201 additions & 0 deletions research/settlement-header-word-review/LICENSE
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18 changes: 18 additions & 0 deletions research/settlement-header-word-review/NOTICE
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Settlement/header-word external written review

New external review prepared by ToikY with substantial OpenAI Codex assistance
through separate target-known abstract, source-aware code and metadata roles.
Apache-2.0. Source-aware AI agreement is not human or proof-kernel acceptance.

SHIN09-git authored PR6712 monomial guard settlement, its central theorem,
implementation and original evidence, with substantial OpenAI Codex assistance.
Determinant identities, elementary row operations and debt-partition ideas have
earlier sources. PR6710 supplied retained exact finite-field arithmetic. ToikY
provided the predecessor binary complete-header/all-field pair-sign extension;
Nick Petalas authored the marginal/common-covector pair law. None is recounted
as a new theorem, construction, count or test in this review.

Exact source notices are retained in inputs/NOTICE, inputs/source/6710-NOTICE
and inputs/ROOT-NOTICE. Apache licenses are retained as LICENSE, inputs/LICENSE
and inputs/source/LICENSE. Original attributions and limitations remain intact.
This inert subset is not the original runnable suite; no endorsement is implied.
20 changes: 20 additions & 0 deletions research/settlement-header-word-review/README.md
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# Settlement/header-word source review

This is an external **written** review of SHIN09-git [PR6712](https://github.com/CrocSwap/integer-mult-bounds/pull/6712), frozen at `03caa7f6cb5bd21c834024e9d81f6b43eb325b91`. It covers the central zero-target h−Z settlement/partition argument, the actual constructed row-addition word and the anchored full-prefix/proper-minor implication. The exact statement and limitations are in [REVIEW.md](REVIEW.md).

Separately sealed abstract and source-aware code roles found no material gap within that scope, followed by source/peer reconciliation. This is a qualified written outcome, not a new central theorem or implementation, proof-kernel acceptance, or a fresh replay of existing source checks. Historical predecessor familiarity and source exposure are disclosed in the retained notes/seals. Commit/export/publication/CI status belongs to separate later receipts.

The source valid exact-field/value domain, full-family and anchor hypotheses remain essential. Generic mathematical helpers operate on their stated generated-data domain; they are not an arbitrary hostile certificate-packet parser. The anchored gate replay already exists upstream and was not executed here. The later source binary/ternary/envelope/orbit/pricing classifications are **UNREVIEWED** here; numerical DP outputs remain unreplayed; source eight commands,20faults and finite counts were not rerun.

[Source pins](SOURCE-PINS.json) bind15 exact inert inputs/90418bytes:13 foreign-head objects and2 canonical root license/notice objects. [Canonical provenance](SOURCES.json) has the eight current-main guidance pins plus LICENSE/NOTICE; it makes no claim that foreign pending source objects are canonical ancestors. Source code copies have `.txt` suffixes. This curated subset is not the original47-file runnable suite, and there is no scientific `VERIFY.json` or scientific command in this package.

[TASK.json](TASK.json) retains the complete original formal-interface card and records the narrowed written scope. Its formal/kernel gate remains unmet. [NOTICE](NOTICE), [LICENSE](LICENSE) and the retained source notices preserve credit: SHIN09-git owns the source theorem/code/evidence; classical determinant/elementary-row/debt-partition methods, PR6710 finite-field arithmetic, ToikY's predecessor header/pair-sign extension and Nick Petalas's marginal/common-covector pair law are not new results here. This review uses substantial source-aware OpenAI Codex assistance.

No native or physical invoice, supplier, all-five-assumptions discharge, multiplication theorem, κ/frontier change, adoption or merge follows. Maintainer edits and auto-merge must remain disabled if published; actual settings require a separate live receipt.

## Open next questions

- Formalize the typed exact-field/value domain, allowed operation alphabet, generated word and full-family/anchor implication in a proof kernel.
- Specify and independently audit any hostile-packet parser or physical primitive invoice separately. The current mathematical interface does not provide either contract.

Read the preserved [abstract first draft](RECORD-DERIVATION-DRAFT.md), [code first draft](RECORD-CODE-DRAFT.md), [source cross-binding](RECORD-CROSS-DERIVATION.md) and [exact-version assessment](RECORD-ASSEMBLED-REVIEW.md), with their adjacent seals.
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