REVISION 2: FINAL INTEGRATED ASSESSMENT
19 October 2026 -- private preparation; internal AI review

DISPOSITION

PASS. Incorporate the unequal-group refinement and retain one modest but
publishable specialist note. No remaining mathematical, computational or
presentation blocker was found. Originality remains bounded/provisional,
with the existing unavailable-CCSZ/no-priority disclosure retained.
This is a revision of the same paper, not another independent publication.
No submission, public upload or Archive delivery has been performed.

REVIEWED ARTIFACTS

Title: Independent Squares and Average-Radius Obstructions for Linear Codes
Author: Scott Schubr -- Revision 2
manuscript/main.tex SHA256:
bc924a30c2a88bbad95fd184a7bd39e36c4c76896f03f571733eae11baa83564
output/pdf/independent_squares_average_radius.pdf SHA256:
4220a5a0a265758f697eb0a7f6e1b67a31ba9f1f69947921bb83ffca037d756d
reproducibility/reproduce.py SHA256:
21f953ac292266a0973f1376251e29458d6ced29553cad1d835927cd62d2ee82

Complete proofs are in the manuscript. Preserved checkpoints retain their
historical dates and wording; in particular the refinement checkpoint's
earlier word "optional" describes its original assessment stage. The
revised manuscript now incorporates it as the principal finite converse.

WHAT IMPROVES

For t>=1,c>=0,d=2t+c,M=1+3t+c,C=4t+c and an Fq-linear code of
dimension k>=d in (Fq^s)^n, put u=floor((k-d)/s). There are M distinct
words and at-most-two-symbol input lists with total agreement at least

  2n + min(2n,n+2tu,Cu).

Disjoint groups need only have individual capacity u. Square-axis groups
receive coordinates first, then coloop groups. The proof treats empty
groups, exhausted coordinates, arbitrary characteristic and singleton
tables explicitly. The previous equal-group theorem remains a corollary.

For fixed t,c and rate R, the asymptotic mean-error obstruction is

  1-2/M-min(2,1+2tR,CR)/M,

with a proved O(1/n) remainder uniform in field and folding parameter.
The square-count optimum is only within this specified profile family.
The general power-of-two universal comparison becomes R<2/B_a.
For M32 its upper endpoint increases from82/1575 to4/75. The displayed
exact FRS construction retains the earlier narrower interval; the paper
does not conflate these two consequences.

The sixteen-message asymptotic curve remains
7/8-(5/4)min(R,1/10). Some finite rounding losses can improve even when
c=0. The sharp all-field certificate cost4t+c and the full exact-FRS
construction are preserved. Their393-line manuscript section matches
the authenticated original as normalized text. The complete original
86-file package and original ZIP remain unchanged, as documented in
REVISION_RECORD.json and the separate preservation receipt.

The M8 and M32 finite examples compare this argument's two bounds. They
are explicitly not claims of globally best known converses or new
explicit constructions. Independent proof review caught a stale fixed-rate
u equality; the corrected paragraph invokes the equal-group corollary
with v=floor(n/10). No theorem needed weakening.

SAME PRIOR ASSESSMENT, REPEATED

Validity and rigor: PASS. Independent analytic review checked the full
revision, all new finite/asymptotic endpoints, uniformity, characteristic
two, within-family optimization, numerical comparisons and the distinction
between universal and explicit-FRS intervals. Unchanged certificate/FRS
proof evidence was authenticated rather than relabeled as a new proof.

Originality: the main contribution remains the independent-square profile,
its sharp certificate and coding consequences. Unequal allocation is an
elementary improvement of the same argument, not a new shortening method.
Chen--Zhang, Yeyuan Chen's folded-linear shortening argument, LMS's profile
framework, Li--Shagrithaya, BCDZ and Goyal--Guruswami remain credited.

External novelty: prior20primary-source and8own-source bindings were
authenticated;12fresh primary retrievals and actual Google/Scholar delta
discovery checked the refinement and current close work. No inspected
matched stronger result supersedes the note's strongest contribution.
CCSZ2025 full text remains unobtained. No priority over its results or
worldwide-first clearance is claimed. General ordinary/average distinctions
are established background, not inventions attributed to this note.

Uniqueness: the specific sparse profile, exact all-field cost and exact
standard-FRS endpoints distinguish the work. The allocation refinement
does not establish exclusive ownership of a general technique.

Contribution and value: modest but sufficient for the same specialist
note. The revision removes a known allocation loss, improves coloop
regimes and widens the M32 universal interval. It improves completeness
and quantitative usefulness without changing the overall impact category.

Limitations: ordinary Chen--Zhang remains unrefuted; no same-parameter
ordinary-positive/average-negative separation, optimum among all profiles,
universal cost20 upper bound, decoder, quantum application or major
breakthrough is established. No mandatory further expansion emerged from
the repeated research. Stronger profiles and code-specific projection
ranks remain research directions, not claimed applications.

FRESH VERIFICATION

The full portable replay passed under CPython3.15.0, then independently
under CPython3.12.14 from a different working directory. All baseline
mathematical checkers and their original checks are retained unchanged:
23exhaustive wedge cases,18,585kernels,50,112dependency checks,
7,120larger diagnostic kernels,7FRS cases,30original linear-code cases
and17original exact coefficient comparisons.

New packaged coverage passed:
  2,240 independent dynamic-programming allocation cases;
  60 actual-code constructions over q2,3,5 and vector sizes1,2,3;
  44,956 fixed-M profile comparisons;
  52,954 finite-remainder checks;
  17 exact refined power-of-two comparisons;
  all three frozen certificates regenerated and independently validated;
  18 optimization/certificate-corruption rejection controls.

The independent analytic reviewer also ran a separate implementation:
4,200allocation cases,18,121remainder cases,79,320profile comparisons
and97power-of-two cases through a=100, with endpoint equality checks.
Those counts are separate evidence, not additions to the packaged runner.

The independent code auditor authenticated the baseline, current source
bindings and mathematical implementations, and passed10additional hostile
gates for source mutation, output refusal and malformed certificates.
Deliberately invalid disposable package fixtures are excluded. Clearly
labeled verification/tampered_inputs files are only negative-test inputs.
Finite computation supports the proofs; it does not establish their
universal quantifiers or originality. These are internal AI checks, not
external human refereeing or proof-assistant formal verification.

PRODUCTION AND PRESERVATION

The revised source compiled successfully with the desktop compiler and
Tectonic. All15pages were rendered and visually inspected; no overfull
boxes, missing references or visible clipping remain. The package includes
TeX, full analytical checkpoints, three explicit certificates, portable
standard-library verification, fresh receipts, literature comparisons,
independent review dispositions and a source-bound change record.

The original manuscript, PDF,86-file package and ZIP are preserved.
Revision2 is the preferred private package for this one paper. Public
publication counts and prior published editions are unchanged. Release
permission remains separate from this completed revision assessment.
