Re-run of the reproducibility package by the second independent verification run (15 October 2026).

The package was taken from release/source.zip (sha256 4bbec5aa8b6f18297d5fa62ebf0cc29733acace1b52cecfbc2df82844bbf74e8),
extracted into a scratch folder, and every program was run in a copy of that folder (Python 3.13.5, numpy 2.5.2,
scipy 1.18.1, sympy 1.14.0, mpmath 1.3.0).  The outputs of this re-run are in this folder.  "identical": byte-identical
to the recorded file of the package; "identical up to the path": the program prints the path of its input file, which
was ../outputs/<file> here and <file> in the recorded run.

check_note.py                                            identical            check_note_output.txt (27 checks, 0 failed)
original/scripts/verify_cert_independent.py (3 files)    identical up to the path   original/verify_cert_independent.out
original/scripts/regen_check.py (3 files)                identical up to the path   original/regen_check.out
original/scripts/cert_n3_exact.py                        identical            original/cert_n3_exact.out
original/scripts/cert_n3_sym.py                          identical            original/cert_n3_sym.out
original/scripts/exact_system.py 3 4 (screen output)     identical            original/exact_system_d3_n4.out
original/scripts/exact_system.py 3 4 (system_d3_n4.json) identical (cmp)      (not copied: equal to the recorded file)
verification_run_A/vA_prop1_exact.py                     identical            verification_run_A/vA_prop1_exact.out
verification_run_A/vA_certcheck.py . DATA                identical            verification_run_A/vA_certcheck.out
verification_run_A/vA_groebner.py . 4 r23 / . 4 s23      same as rerun_outputs/vA_groebner.out (basis [1] in 0.9 s / 0.0 s)
verification_run_A/vA_probe_lm_drift.py .                the 24 data lines are identical to rerun_outputs/vA_probe_lm_drift.out;
                                                         residual * |h| between 2.61 and 3.03, |h| from 521-1092 to 44069-103504
verification_run_B/own_prop1_exact.py                    identical            verification_run_B/own_prop1_exact.out
verification_run_B/own_cert_check.py (3 files, classes 100; 100,010; 100,111)
                                                         identical to the first 18 lines of the recorded own_cert_check.out

Not re-run: the long numerical searches (gcub.py with 200/400 starts, the node-space and h-space searches of run B, the
sphere searches of run A) and the searches for the identities (cert_exact.py, cert_sparse.py); their recorded logs were
read and every number quoted in Sections 5 and 7 of the note was compared with them.
