RERUN_LOG.txt -- re-runs of 11 October 2026 (Python 3.13.5, sympy 1.14.0, numpy 2.5.2, scipy 1.18.1,
Apple clang 21.0.0, macOS, one laptop)

Part 1.  Output of `sh run_quick.sh`, run from an extracted copy of the final archive (before this log was
added) by the verification run on the final text; total time 11 minutes 47 seconds, one process.
56 comparisons with recorded outputs and one test of the end line.
"passed": the program ended with "TOTAL failures: 0".  "identical": the new file is byte-identical to the
recorded file.  "identical up to times": identical after removing the fields that record running times (and
the lines "exit 0" of the first recordings of run A).

== writing_stage/ (program written with the note)
passed                check_note.py (TOTAL failures: 0)
identical up to times writing_stage/check_note_output.txt
== original/ (programs with which the results were first obtained)
identical up to times original verify_T.out
identical up to times original verify_grassmann.out
identical up to times original verify_structure.out
identical up to times original verify_n4_per.out
identical up to times original verify_kw.out
identical up to times original exactness_certificates.out
identical up to times original verify_T_independent.out
identical up to times original explore_K5.out
identical up to times original explore_K5_blocks.out
identical up to times original verify_quotient_n1.out
identical up to times original verify_quotient_n2.out
identical up to times original verify_quotient_n3.out
identical up to times original verify_quotient_n4.out
identical up to times original verify_quotient_n5.out
identical up to times original verify_quotient_n6.out
identical up to times original divisibility_test.out (the lines n = 2,...,5)
identical up to times original explore_cofactor2_n4.out
identical up to times original explore_cofactor2_n5.out
identical up to times original explore_cofactor_n5.out
== verification_run_A/
identical up to times A vA_test1_small.out
identical up to times A vA_test3_grass.out
identical up to times A vA_test4_struct.out
identical             A vA_pi_n4.json (the integers pi for n = 4)
identical             A vA_pi_n5.json (the integers pi for n = 5)
identical             A vA_pi_n6.json (the integers pi for n = 6)
identical             A vA_pi_n7.json (the integers pi for n = 7)
identical up to times A vA_test5_theorem_n1.out
identical up to times A vA_test5_theorem_n2.out
identical up to times A vA_test5_theorem_n3.out
identical up to times A vA_test5_theorem_n4.out
identical up to times A vA_test5_theorem_n5.out
identical up to times A vA_test5_theorem_n6.out
identical up to times A vA_test6_lines_n2.out
identical up to times A vA_test6_lines_n3.out
identical up to times A vA_test6_lines_n4.out
identical up to times A vA_test6_lines_n5.out
identical up to times A vA_test7_extra_part2.out
identical up to times A vA_test8_n8_validate.out
identical up to times A vA_test8_n8_run1.out (Table 1, n = 8, det A = 607)
== verification_run_B/
identical up to times B b1_small.out
identical up to times B b2_build.out
identical up to times B b3_k.out
identical up to times B b4_n5_prime.out
identical up to times B b4_n5_singular.out
identical up to times B b5b_kernel.out
identical up to times B b6_tested_n5.out
identical up to times B b7_treeform.out
identical up to times B b7b_rank.out
identical up to times B b8_cross.out
identical up to times B b9_line_n5_s11.out
identical up to times B b10_n7.out
== independent_run_2/ (verification run on the final text)
identical up to times R2 r2_t3_grassmann.out
identical up to times R2 r2_t4_second_proof.out
identical up to times R2 r2_t5_small_n.out
identical up to times R2 r2_t6_exactness_small.out (Table 1, n = 4, 5, 6)
== number of differences: 0

Earlier runs of the script, each with 0 differences: when the note was written, from the archive of the writing
stage (the first four parts; 8 minutes 36 seconds); by the verification run on the final text, from the same
archive and from two intermediate archives with all five parts.

The following two parts were made when the note was written.

Part 2.  The outputs in original/outputs/ are those of a run of all 13 programs of original/ from this folder
layout on 11 October 2026 (the commands are in README.md; the slow ones: verify_quotient.py 7 1 20261011
--nodetT --modp, 684 s; divisibility_test.py 6 12 7, 128 s; explore_cofactor2.py 6 3, 112 s;
explore_cofactor.py 6 3, 355 s).  Comparison with the first recorded outputs of these programs, after removing
running times and the warning lines of sympy:
identical up to times  exactness_certificates.out, explore_K5.out, explore_K5_blocks.out, explore_cofactor_n5.out,
                       explore_cofactor_n6.out, verify_T.out, verify_T_independent.out, verify_grassmann.out,
                       verify_kw.out, verify_n4_per.out, verify_quotient_n1.out ... verify_quotient_n7.out,
                       verify_structure.out                                   (18 files)
changed as intended    divisibility_test.out          (same numbers; the new field "vacuous cases" was added)
changed as intended    explore_cofactor2_n5.out, explore_cofactor2_n6.out
                                                      (same results; the fields on the interpolation points and
                                                       on the 12 check points were added)
corrected              explore_cofactor2_n4.out       (the first output showed degree 4 for det P_2 and det P_3,
                                                       an artefact of an interpolation from 5 points; the
                                                       degrees are 12)

Part 3.  The computations of verification run A for n = 8 were repeated from a copy of its programs:
vA_test8_n8.py validate, vA_test8_n8.py run 1, vA_test8_n8.py run 2, and vA_test8_dfsrows.py with the compiled
vA_dfs.c.  The four outputs (writing_stage/rerun_n8/) are identical up to running times to those in
verification_run_A/outputs/: pivots per stage [3139, 572, 429] and v_p(det T(A)) = 1430 = C_8 for det A = 607
and for det A = -137; 14 rows of T(A) modulo p^3 equal to the exhaustive enumeration.
