Rerun of the release package (second independent verification run, 2026-10-02)
source.zip (pre-run-2 version) sha256: a04741436f6b5a88f845ded2a177b4b2df3ba4fc1b7a7bff087768a5ed2345b9
Extracted into a scratch folder; every script run inside its own folder with python3 -W ignore (Python 3.13.5, numpy 2.3.1, scipy 1.16.0).
Each new output was compared byte for byte (diff) with the output stored in the package.

lead/verify_paper.py: output identical
lead/montecarlo.py: output identical
finder/verify_counterexample.py: output identical (real 1.73)
finder/attain.py: output identical (real 3.83)
finder/n3_consistency.py: output identical (real 0.09)
finder/nary_theorem14.py: output identical (real 3.47)
finder/regions_n4plus.py: output identical (real 8.00)
independent/v1_exact_points.py: output identical (real 0.04)
independent/v2_nonattain.py: output identical (real 164.10)
independent/v3_theoremB.py: output identical (real 1.20)
independent/v4_family_volume_attain.py: output identical (real 1.30)
independent/v5_component.py: output identical (real 0.07)

lead/verify_paper.py: 59 PASS lines, 0 FAIL lines; last line: ALL CHECKS PASSED
N_4 expansions regenerated by lead/verify_paper.py and finder/nary_theorem14.py: md5 f7bf684c4f21df6457cfdff532c4bb04 and f7bf684c4f21df6457cfdff532c4bb04 (both equal to the stored copies)

After this run's comment-only corrections (lead/montecarlo.py docstring: Theorem 2.5 -> Theorem 1.1; lead/verify_paper.py
comment: Lemma 2.4 -> Lemma 2.3) both lead programs were run again from a scratch copy: verify_paper_output.txt,
montecarlo_output.txt and N4_poly_lead.txt are byte-identical to the stored files.
