Re-run of the programs of the note at its writing -- AMR-099-0065
=================================================================

Date: 14 October 2026.
Machine: Apple M3 Max (arm64), macOS; Python 3.13.5, numpy 2.5.2, mpmath 1.3.0, sympy 1.14.0, networkx 3.6.1,
scipy 1.18.1.  All runs with `python -I`, under `nice -n 10`, at most three programs at a time, from a copy of
`programs/` (as in this package), writing into a fresh folder `rerun/`.

Commands and wall-clock times (exit code 0 for all):
  bracket.py exp up 32 20 40 ../rerun/exp_up            209 s
  bracket_down.py exp 32 20 40 ../rerun/exp_down        206 s
  bracket.py unif up 1 18 40 ../rerun/unif_up           101 s
  bracket_down.py unif 1 18 40 ../rerun/unif_down        56 s
  mc_check.py ../rerun/mc_check.json                     23 s
  mc_check2.py ../rerun/mc_check2.json                   26 s
  assemble.py ../rerun ../rerun/brackets.json            <1 s
  certify_constants.py ../rerun/certify_constants.json    4 s
  bernoulli_atom.py ../rerun/bernoulli_atom.json         <1 s
  explore_float.py unif 8192 1.0 24 mid                   1 s
  explore_float.py exp 32768 16.0 22 mid                  2 s
(see rerun_at_writing/times.txt)

Interval check of the initial exponential grids (new at the writing; first line of the two logs in
rerun_at_writing/):
  bracket.py exp up      : 2^20 values, 0 violations; smallest margin over i >= 1: 1.287e-06 units of 2^-31
                           (i = 462207); at i = 0 the value is exactly 0.
  bracket_down.py exp    : 2^20 values, 0 violations; smallest margin 9.328e-24 (i = 981626).
The second verification run had found the same margins with its own check (verification_run_B/outputs/
check_claim_init2.json).

Comparison with the recorded outputs (python -I compare_outputs.py rerun outputs; rerun_at_writing/compare.txt):
  - brackets.json, certify_constants.json, bernoulli_atom.json, mc_check.json, mc_check2.json, the four
    *_final.npz states, assemble.log, certify_constants.log, bernoulli_atom.log, mc_check.log and the two
    explore_float logs: byte-identical;
  - unif_up.json, exp_up.json, unif_down.json, exp_down.json: identical except the runtime fields "secs"
    (all 41 exact mean fractions identical);
  - unif_up.log, unif_down.log: identical up to running times; exp_up.log, exp_down.log: identical up to running
    times and the added line of the interval check.
  files that differ in content: 0

Certified results reproduced (outputs/brackets.json):
  U[0,1]  : gamma_rec in [0.268785599, 0.268808710]  (upper bound from level 40, lower bound from level 40)
  Exp(1)  : gamma_rec in [0.379282228, 0.379412906]  (upper bound from level 35, lower bound from level 40)
  level-40 first-moment bounds: 0.266475773 (U[0,1], s = 300), 0.37581812 (Exp(1), s = 200)

check_note.py (from reproducibility/; rerun_at_writing/check_note.log): ALL CHECKS PASSED, about 10 s.
