Independent squares edition 1 — public publication package

Scott Schubr
Existing edition: https://luminaryoddities.com/researcharchive/independent-squares-average-radius-obstructions-linear-codes/v/1
Manuscript: output/pdf/independent_squares_average_radius.pdf

This package corrects attachment contents only. The published manuscript PDF and
its TeX source are retained byte for byte. This is not a new theorem or edition.
The paper retains its attribution, originality qualifications and limitations.
Internal review/assessment records, private context, QA images and nested older
packages are excluded. No new licence or public reuse permission is granted.

Public file hashes.json identifies the public payload. A native integrity
manifest, where included, also binds that inventory; neither hashes itself.
Hashes identify files; they do not establish mathematical truth or refereeing.
Read the manuscript for the proofs. Run reproductions only in a separate new
work directory. Never treat retained numeric outputs as a substitute for replay.
No mathematical replay was performed merely to filter this package.

Compile manuscript/main.tex with its listed LaTeX packages. Use ordinary Python
3.10+ without -O or -OO: assertion-enabled exact checks are required.
Run each mathematical checker with its own absent or empty external directory:
  python -B code/independent_wedge_check.py --output-dir /absolute/new/wedge
  python -B code/independent_frs_check.py --output-dir /absolute/new/frs
  python -B code/universal_converse_check.py --output-dir /absolute/new/converse
  python -B code/unequal_group_check.py --output-dir /absolute/new/unequal
Validate the supplied explicit certificates independently:
  python -B code/validate_frs_certificate.py --certificate examples/q541_explicit_certificate.json --output-dir /absolute/new/validate541
  python -B code/validate_frs_certificate.py --certificate examples/q2161_fixed_rate_certificate.json --output-dir /absolute/new/validate2161
  python -B code/validate_unequal_certificate.py --certificate examples/unequal_group_small_code_certificate.json --output-dir /absolute/new/validateUnequal
The complete mathematical proof sections in proofs/ remain included because the
unchanged checkers bind these files. Stable filenames reflect earlier internal
names; their public copies omit private assessment framing. The old orchestration
wrapper depends on private history and is excluded; the listed direct commands
retain every mathematical checker and explicit input. Finite diagnostics do not
prove universal quantifiers, optimality, worldwide priority or ordinary-list
recovery claims; the manuscript specifies the stronger average-radius scope.
