INDEPENDENT SQUARES AND AVERAGE-RADIUS OBSTRUCTIONS FOR LINEAR CODES
Scott Schubr -- 19 October 2026 -- Revision 2

This revised private publication candidate incorporates unequal shortening
groups into the same list-recovery
research family. It is a linked follow-up to the earlier eight-point paper;
the earlier published eight-point and restricted sixteen-point results remain
unchanged. Preparing this package does not submit or publish it.

CONTENTS

manuscript/main.tex
  Complete standalone manuscript, including all mathematical proofs and
  primary-source references.
output/pdf/independent_squares_average_radius.pdf
  Compiled manuscript.
proofs/
  Preserved analytical checkpoints supporting the manuscript. These are
  supplementary research records, not additional independent papers.
examples/
  Complete FRS certificates over F_541 and F_2161, plus a small
  unequal-group linear-code certificate over F_3.
code/
  Exact finite-field, subspace and linear-code verification programs and a
  separate validator for each kind of frozen explicit certificate.
reproducibility/
  Portable replay driver and source-bound porting provenance. Historical
  receipts under provenance/ are labeled separately from fresh replay.
assessment/
  Scope, originality comparisons and internal review evidence. Internal AI
  review and computational checking are not external human refereeing.
verification/
  Fresh final replay receipts. Finite checks support, but do not replace,
  the all-field and asymptotic analytical proofs.
MANIFEST.sha256
  Identities of the packaged files; hashes do not establish theorem truth.

REPRODUCE

Use unoptimized Python 3.10 or later. Only the Python standard library is
required. Run from the extracted package directory:

  python reproducibility/reproduce.py --output-dir ../independent-square-replay

The output directory must be outside the sealed package. The driver writes
summary.json, individual stdout/stderr logs, theorem-check receipts, separate
frozen-certificate validation results and meaningful negative-control results.
It rejects Python -O and -OO so that assertion-based checks cannot disappear.
An absolute script path also permits execution from another working directory.
The exact scope and final counts are recorded in assessment/FINAL_REVIEW.txt.

BUILD THE MANUSCRIPT

Compile manuscript/main.tex using a standard LaTeX toolchain that supplies
amsmath, amssymb, amsthm, geometry, booktabs, microtype and hyperref, or use
Tectonic. For example, from the package root:

  tectonic --outdir output/pdf manuscript/main.tex

The compiler's default filename is main.pdf. The distributed reviewed PDF
is named independent_squares_average_radius.pdf. Bibliography entries are
embedded in the TeX source; no network research access is needed to read it.

CLAIM AND LIMITS

The increment is the independent-square profile, its sharp all-field
two-fiber certificate cost, and the resulting average-radius obstruction.
Revision 2 allocates square-axis groups before coloop groups and improves
the finite/general asymptotic converse. The sixteen-message asymptotic
headline and exact FRS witnesses are preserved. The original package and
ZIP remain unchanged; revision history is documented in REVISION_RECORD.json.
Shortening and independent kernel representatives are established methods,
including Yeyuan Chen's folded-linear lower-bound argument. General profile
frameworks and the Boolean-cube comparison also predate this note.

The average-radius conclusion does not refute the ordinary Chen-Zhang
list-recovery conjecture. No same-parameter ordinary-positive versus
average-radius-negative separation is proved. The FRS endpoint and the
universal linear-code consequence are parts of this one contribution.

Originality assessment is bounded by the primary literature examined. The
full text of Chen--Cheraghchi--Si--Zhang's cited 2025 manuscript was not
obtained. Supporting-result overlap remains unresolved, and no priority
over results established there is claimed. This limitation is disclosed
in the manuscript and assessment. No worldwide-first or major-breakthrough
claim is made.

RELEASE STATE

Prepared for Scott's review under his revision-and-reverification
request. No publication permission, Archive delivery, public upload or
submission is inferred from this preparation. Original sources, frozen
packages and prior public editions are preserved.
