Re-run log, OWR-1274-007 (2026-10-22). All programs were run from a copy of this package outside the package
folder, with Python 3.13.5 (NumPy 2.5.2, SymPy 1.14.0) on macOS (Apple silicon), nice -n 10. Each new output was
compared with the recorded one; "same" means identical up to fields that record running times ("sec": ..., "(...s)").

check_note.py
  python3 -I check_note.py                                   exit 0, about 1 s   60 checks, 0 failed (recorded: check_note_output.txt)

original/scripts (outputs written into a copy of original/outputs/)
  s1_quaternion_identities.py                                exit 0, < 1 s       s1_output.txt identical; s1_padic_matrices.json identical
  s2_coding_check.py 14                                      exit 0, 1 s         s2_output.txt identical
  s2_negative_control.py 6                                   exit 0, < 1 s       s2_negative_control.txt identical
  s3_closure_bellaterra.py 7                                 exit 0, < 1 s       s3_output.txt identical; s3_orders.json identical
  s4_invariants.py 6                                         exit 0, 1 s         s4_output.txt identical
  s5_level_orders.py 12                                      exit 0, 10 s        s5_output_12.txt same; s5_level_orders_12.json identical
  s6_tau_multipliers.py                                      exit 0, < 1 s       s6_output.txt identical
  s7_crosschecks.py                                          exit 0, 7 s         s7_output.txt identical
  s8_hand_invariants.py                                      exit 0, < 1 s       s8_output.txt identical
  not re-run: s5_level_orders.py 14 Aleshin (about 15 minutes; recorded s5_output_14_aleshin.txt; its numbers
  agree with out_layered_aleshin_14.txt of verification run B, computed by a different program)

independent_runs/run_A
  OWR-1274-007_A_check1.py                                   exit 0, 1 s         same as OWR-1274-007_A_check1.out
  OWR-1274-007_A_check2.py                                   exit 0, 5 s         same as OWR-1274-007_A_check2.out
  OWR-1274-007_A_check3.py                                   exit 0, 5 s         same as OWR-1274-007_A_check3.out

independent_runs/run_B (run in a copy of programs/, python -B -I)
  vb_moebius.py 16                                           exit 0, < 1 s       same as out_moebius.txt; vb_moebius_matrices.json identical
  vb_moebius.py 8 neg                                        exit 0, < 1 s       same as out_moebius_neg.txt; vb_moebius_matrices_neg.json identical
  vb_tau.py 22                                               exit 0, 3 s         same as out_tau.txt
  vb_qinv.py 7                                               exit 0, < 1 s       identical to out_qinv.txt
  vb_matrix.py 7                                             exit 0, 13 s        same as out_matrix_k7.txt
  vb_congruence.py 64                                        exit 0, 142 s       same as out_congruence_k64.txt
  vb_negcontrols.py                                          exit 0, 3 s         same as out_negcontrols.txt
  vb_levels.py moebius 9 18                                  exit 0, 79 s        same as out_levels_moebius_9_18.txt
  vb_levels.py automaton 9 18 bartholdi_right                exit 0, 20 s        same as out_levels_bellaterra_9_18.txt
  vb_levels.py automaton 1 11 bartholdi_left                 exit 0, 3 s         same as out_levels_aleshin_1_11.txt
  vb_brute.py bartholdi_right 7 sympy                        exit 0, < 1 s       same as out_brute_bellaterra_n7.txt
  vb_brute.py bartholdi_right 8                              exit 0, 1 s         same as out_brute_bellaterra_n8.txt
  vb_brute.py bartholdi_left 6 sympy                         exit 0, 1 s         same as out_brute_aleshin_n6.txt
  vb_brute.py bartholdi_left 7                               exit 0, 18 s        same as out_brute_aleshin_n7.txt
  vb_automata.py bartholdi_right 20 19                       exit 0, 27 s        same as out_layered_bellaterra_19_20.txt
  vb_automata.py bartholdi_left 13 9                         exit 0, 108 s       same as out_layered_aleshin_9_13.txt
  not re-run: vb_automata.py bartholdi_left 14 14 (recorded 1330 s, out_layered_aleshin_14.txt)
  out_lemma7.txt has no program in the package (see independent_runs/README.md)

Re-run by independent verification run 2 (2026-10-22), from an extracted copy of source.zip (the archive
before the final revision), with the same Python environment, `-I -B` (run B: `-B -I` in a copy of programs/),
nice -n 10; new outputs written to a separate folder and compared with the recorded ones (timing fields masked).

check_note.py                                                 exit 0, 1 s         identical (60 checks, 0 failed)
original/scripts: s1, s2 14, s2_negative_control 6, s3 7, s4 6, s5 12, s5 9, s6, s7, s8
                                                              all exit 0          identical (s5 12: same); the four json files identical
independent_runs/run_A: check1, check2, check3                all exit 0          identical
independent_runs/run_B: vb_moebius 16, vb_moebius 8 neg, vb_tau 22, vb_qinv 7, vb_matrix 7, vb_negcontrols,
  vb_levels (moebius 9 18; automaton 9 18 bartholdi_right; automaton 1 11 bartholdi_left), vb_brute (right 7 sympy,
  right 8, left 6 sympy, left 7), vb_automata (right 20 19, left 13 9), vb_congruence 64
                                                              all exit 0          identical or same; both json files identical
original/scripts/s5_level_orders.py 14 Aleshin                exit 0, 892 s       s5_output_14_aleshin.txt same; s5_level_orders_14.json identical
independent_runs/run_B: vb_automata.py bartholdi_left 14 14   exit 0, 1355 s      same as out_layered_aleshin_14.txt
  (log2 |G(A)_14| = 1393, layer ranks 1, 1, 2, 3, 3, 4, 7, 13, 23, 45, 87, 174, 344, 686 in both)
The programs of independent_run_2/ were run from a copy of their folder in the same way and reproduce their
recorded outputs byte for byte (parts 1-6; part 7 up to running times).
