[artuskg]

This update makes PR647 evidence admission require the fixed package inventory and retained original evidence pins. The old authentication path could accept missing evidence when self-declared lists were reduced consistently. The repair rejects those omissions and coherently rehashed replacements of retained proofs, source records and attribution. It preserves the existing mathematical theorem and deterministic mathematical receipt.

Change and mathematical scope

Adds a self-contained alternative paid-copy E8 realization under research/e8-paid-copy-ram-20261013/, with the Pro provider proof preserved verbatim, an independently reconstructed exact checker, complete source attribution, and an attributed cyclic-Fourier corollary. No existing witness, upstream source, workflow or selected-result pointer changes.

At fixed architecture depth one, the positive Gaussian kernel uses h=9, v=120, real rank 8, R=6968 paid helpers, W=7208 and m=27. The full rank histogram has deficit 24, and its exact moment at 1/15000 has more than one rank-mass unit of slack. The charged all-matrix padding/private-memory proof gives C tensor k in O(2^k(k+1)^(14999/15000)) exact complex RAM work. The existing OpenAI exact-width compiler/sector/CRT/chirp machinery then gives the positive cyclic DFT at every length in O(N(log N)^(14999/15000)(loglog N)^(45001/15000)), eventually O(N(log N)^(29999/30000)).

The cyclic result requires one supplied exact canonical root of explicitly selected order below 1024N^3. Extracting other roots, nonzero scalar-preparation divisions, scheduling, packing and the fixed chirp operand's transform are paid. Indexed access and logarithmic integer-word arithmetic have unit cost; complex cells have unrestricted exact values. Architecture depth is fixed independently of N. Root acquisition from rational arithmetic, finite-alphabet sequential tapes, bit multiplication, numerical stability, practical crossover and new Lean certification are outside the claim.

This is not a record supplier or a new Fourier-transfer mechanism. PR225 already documents community transfer and stronger rates; PR256/274 and Sussman's earlier E8 unit also report stronger rates and a much smaller R=783 core. The proposed value is the explicit independent paid-copy construction, dirty/private ownership proof and reproducible depth-one corollary. PR631's bit-side star-reader puncture result has a different decoder/model and is not refuted. Exact pins and the current overlap check are in NOVELTY.md and SOURCE.json.

OpenAI's imported compiler/transfer attribution and Apache license are retained. The contribution discloses substantial OpenAI Pro/Codex assistance, credits Pro for the retained provider construction, and distinguishes the separate fresh Codex adversarial referee. Earlier E8, frame/cover, dirty-response and community transfer contributors retain credit in NOTICE.md.

Integrity validation for this update

The five-file patch was accepted without correction by a separate OpenAI Codex adversarial referee; this is AI-assisted review, not independent human peer review. Both normal and optimized isolated Python passed 103 negative mutations and six positive/boundary controls per mode with identical outcomes. The new author-run suite passed 14 tests, including 49 negative mutations per mode; that suite was not independently executed by the referee. The referee did not run the mathematical verifier or contributor programs.

The updated package has exactly 16 files and 15 manifest entries, with five required proof files, four required source records and 11 retained original byte pins. All 11 retained files are byte-identical; the original README remains an exact prefix, and all 41 original mathematics/CLI callable ASTs remain unchanged. Only README.md, SHA256SUMS.json, the verifier's authentication step and its module docstring/--help description change; integrity.py and test_integrity.py are added. verify.py now runs the PR author's own integrity.py in the same process as part of the reviewed checker; no third-party generator or contributor program is imported.

python3 -I -B research/e8-paid-copy-ram-20261013/test_integrity.py
python3 -I -O -B research/e8-paid-copy-ram-20261013/test_integrity.py

The executed helper/contract must be authenticated by an independently obtained reviewed Git revision or whole-archive digest. Review covered patch SHA-256 29db510b9f8a8b89ed8a58337bbc320f0a7764d322692e310ffb9b8ca421deaa applied to original head 956bb581e7f97328e1b53baa5aca3d2490f2f607, yielding local review commit 3b3fda9c602fbe4b45d02d1ead0b757b3c94f52c and full candidate tree 31f5db42c48e00c2c953d78325dec2db86200746. These author-reported identities must be matched to independently obtained GitHub/reviewer records and the clean bytes actually executed. The publication commit may have different author/time metadata while containing that exact reviewed tree; any changed package content requires renewed review. Coherently rehashed edits to README.md, verify.py, integrity.py and test_integrity.py can all pass local consistency after refreshing SHA256SUMS.json, including a weakened checker or rewritten mathematical receipt generator; the external anchor is essential. The in-package manifest establishes readable ordinary-file inventory and declared consistency under stable-file assumptions; it cannot authenticate its own release, re-prove mathematics or establish historical execution. Secure loading, filesystem race resistance, inaccessible/nonregular entries and directory-topology authentication are outside this repair. Required SOURCE rows and Git blob checks are redundant defence in depth after the immutable SOURCE and retained file pins; the mutation tests reject rewritten SOURCE earlier and do not isolate those later branches. Optimized Python is supported for the new integrity tests; the unchanged mathematical verifier continues to refuse it.

The repair credits PR838's evidence-coverage finding and PR841's proof-pointer digest-membership repair. PR847/865 frontier Make/CI coverage and PR851 bridge-control identities are related separate scopes; no priority or universal integrity claim is made. No selected witness, generator, workflow or upstream file changes. Existing theorem, supplied canonical root, exact-complex-RAM model and open tape/bit/multiplication obligations are unchanged.

The original-head CI record and original mathematical checks below concern 956bb581e7f97328e1b53baa5aca3d2490f2f607. They do not establish CI success for this new commit. No new full repository suite, Lean build or mathematical replay is claimed for this metadata repair.

Original mathematical validation (original public head)

A fresh independent adversarial referee accepted the mathematical theorem in this specified-root exact-complex-RAM model. The packaged checker reproduces all ten of that referee's mathematical result groups exactly; only authentication, CLI/output and the optimized-Python refusal were adapted.

The complete deterministic --check passed at original public head 956bb581e7f97328e1b53baa5aca3d2490f2f607. Checks include all 7208 live symbolic columns in both orientations, 3601 phase projectors, 240 owner routes, the rational strict moment/padding parameters, dirty DAG compensation, primitive-root Newton/Toeplitz identities, ragged sector operators, 4273 working/root lengths, 62284 CRT phase pairs and eleven exact three-transform chirps. Negative mathematical controls and separate corrupt-import/optimized-output controls pass. Package hashes, whitespace and exact fourteen-file scope were checked independently before publication.

python3 -B research/e8-paid-copy-ram-20261013/verify.py --check

Python 3.9+, standard library only. Finite checks corroborate the reviewed universal proofs; they are not a giant transform implementation or a formal theorem proof. No contributor generator, full repository suite or Lean build was executed, and no such pass is claimed. This is a draft research contribution for review, with no new multiplication kappa or priority claim.