Re-runs of 18 October 2026 (one laptop, Python 3.13.5, numpy 2.5.2, scipy 1.18.1, networkx 3.6.1; nice -n 10).
Each program was run from a copy of its folder; outputs were written to new files and compared with the
recorded files of this package.

check_note.py                                         16 s   ALL CHECKS PASSED; output = check_note_output.txt

verification_run_B/
  test_literal.py                                     0.3 s  identical to test_literal.txt
  check_structure.py <new file>                      13 s    jsonl and summary identical to struct_main_R256.*
  check_children.py <new file>                       10 s    jsonl and summary identical to children_R512.*
  test_detect.py                                      0.8 s  identical to test_detect.txt
  window_seq.py                                      18 s    identical to window_seq.txt (Table 1 of the note)
  run_spectral.py                                    56 s    identical to spectral_survey.txt
  chain_check.py                                      1.6 s  identical to lines 1-49 of chain_check.txt
  run_certificate.py 3072 8 1/16                    414 s    identical to certificate_M3072_s8_lam1_16.txt except
                                                             the time field (recorded: 458 s)
  run_certificate.py 1536 8                         114 s    identical to certificate_M1536_s8.txt except the
                                                             time field (recorded: 112 s)

original/
  nonframe_check.py                                   0.1 s  identical to runs/nonframe_check.out
  fiber_gramian.py --b 1/6 --xi 3/10 --N 5 --allpairs 0.4 s  identical to runs/allpairs_b1_6_xi3_10_N5.json
  structure_compare.py 7 30 <8 values of b>          79 s    identical to runs/structure_compare_N7.out

Earlier on the same day the second verification run had re-run all programs of original/ from a copy
(fiber_gramian.py --allpairs for 7 values of b, scan.py conv and scan, nonframe_check.py, structure_compare.py,
flow_check.py, fiber_sparse.py N = 16 for b = 1/6 and 1/5), with outputs identical to the recorded files up to
fields that record running times, and floating-point eigenvalues equal up to 1.2e-16.

Third verification run (the note as written), 18 October 2026, same machine and versions (nice -n 10), from an
extracted copy of source.zip; every output written to a new file and compared with the recorded file:

check_note.py                                         17 s   ALL CHECKS PASSED; identical except the time line
verification_run_B/
  run_certificate.py 3072 8 1/16                    423 s    identical except the time field (128 intervals,
                                                             certified at 1/54 and 1/16; min float DP 0.06971)
  test_literal.py, check_structure.py, check_children.py, test_detect.py, window_seq.py, run_spectral.py
                                                             identical to the recorded files (both .jsonl too)
  chain_check.py                                             identical to lines 1-49 of chain_check.txt
original/
  flow_check.py 8 60 <8 values of b>                366 s    identical to runs/flow_check_N8.out
  scan.py scan ... 8 120 <5 values of b>            477 s    605 lines, identical to runs/scan_N8.jsonl except
                                                             the time field t
  scan.py conv ... 10                               100 s    84 lines, identical to runs/conv.jsonl except time
                                                             fields
  structure_compare.py, nonframe_check.py, fiber_gramian.py --allpairs (b = 1/6, 3/20)
                                                             identical to the recorded files
  fiber_sparse.py --b 1/6 --xi 67/100 --N 16                 lambda_min 0.1284101323655891 (recorded
                                                             0.12841013236558924); same counts
verification_run_A/
  vA_fiber.py direct (5 fibers), random 7 300 1, random 9 120 2; vA_affine.py (4 rows)
                                                             every line occurs verbatim in outputs_vA.jsonl
  vA_sparse.py 1/6 67/100 18,20; vA_tree.py 1/6 67/100 24,...,40
                                                             same counts; smallest eigenvalues equal to the
                                                             recorded ones up to 3e-16
independent_run_2/
  run2_structure.py 20261018                         21 s    111,276 checks, ALL CHECKS PASSED
  run2_spectra.py 40                                 11 s    2,566 checks, ALL CHECKS PASSED
