RERUN_LOG.txt -- re-runs of 11 October 2026 (Python 3.13.5, sympy 1.14.0, python-flint 0.9.0, numpy 2.5.4,
scipy 1.18.1, clarabel 0.11.1, sdpa-multiprecision 0.2.3; macOS, one laptop), made when the note was written,
from a copy of this folder

Part 1.  Output of `sh run_quick.sh` (all exact programs; total time about 12 seconds).
"passed": the program ended with "BOTH CASES: ALL CHECKS PASSED".  "identical": the new output is byte-identical
to the recorded file.  "identical up to times": identical after removing the lines and fields that record running
times.

== checksums of the certificates
certificate_n5_m6.json: OK
certificate_n7_m4.json: OK
== part 1: standard library
-- writing_stage/ (the program of the note)
passed                verify_note.py (BOTH CASES: ALL CHECKS PASSED)
identical             writing_stage/verify_note_output.txt
-- original/ (programs of the first results)
identical             original verify_certificate_n5_m6.out
identical             original verify_certificate_n7_m4.out
identical up to times original check_prior_note.out
-- verification_run_A/
identical up to times A vA_verify_n5_m6.out
identical up to times A vA_verify_n7_m4.out
identical up to times A vA_prior_note.out
== part 2: with sympy, python-flint, numpy, scipy
-- original/
identical             original verify_independent_n5_m6.out
identical             original verify_independent_n7_m4.out
-- verification_run_A/
identical             A vA_sympy_scratch_n5_m6.out
identical             A vA_sympy_scratch_n7_m4.out
identical up to times A vA_extra_n5_m6.out
identical up to times A vA_extra_n7_m4.out
identical             A vA_interval.out
identical             A vA_bkr_identity.out
-- verification_run_B/
identical up to times B verify_exact_B_n5_m6.out
identical up to times B verify_exact_B_n7_m4.out
identical             B check_kriebel.out
== 0 failures or differences, 0 skipped

Part 2.  `sh verification_run_B/programs/rerun_claim.sh`: the 18 recorded runs of the programs in
original/scripts (single-threaded; total time about six and a half minutes).  The driver was run twice, with the
same result; exit codes and seconds of the second run:

    verify_certificate_n5_m6 exit=0 seconds=0
    verify_certificate_n7_m4 exit=0 seconds=0
    verify_independent_n5_m6 exit=0 seconds=1
    verify_independent_n7_m4 exit=0 seconds=1
    check_prior_note exit=0 seconds=0
    make_certificate_n5_m6 exit=0 seconds=1
    make_certificate_n7_m4 exit=0 seconds=0
    explore_overlap_configs exit=0 seconds=2
    explore_five_variables_window exit=0 seconds=1
    explore_six_variables exit=0 seconds=8
    explore_quartic exit=0 seconds=1
    explore_hessian_VT exit=0 seconds=1
    explore_hyperplane_VT exit=0 seconds=9
    explore_hyperplane_VT_more_seed1_step0.2 exit=0 seconds=54
    explore_hyperplane_VT_more_seed2_step0.5 exit=0 seconds=54
    explore_hyperplane_VT_more_seed3_step1.0 exit=0 seconds=26
    explore_thin_layer_gmp exit=0 seconds=68
    explore_recheck_point9_gmp exit=0 seconds=152

Comparison of the new outputs with the recorded files in original/outputs:

    identical              verify_certificate_n5_m6.out, verify_certificate_n7_m4.out
    identical              verify_independent_n5_m6.out, verify_independent_n7_m4.out
    identical up to times  check_prior_note.out   (the recorded file has one more line, with the running time)
    identical up to path   make_certificate_n5_m6.out, make_certificate_n7_m4.out   (last line: name of the file written)
    identical              explore_five_variables_window.out, explore_hessian_VT.out, explore_quartic.out,
                           explore_recheck_point9_gmp.out
    identical up to times  explore_overlap_configs.out, explore_thin_layer_gmp.out, explore_hyperplane_VT.out,
                           explore_hyperplane_VT_more_seed1_step0.2.out, ..._seed2_step0.5.out, ..._seed3_step1.0.out
    differs in digits      explore_six_variables.out: 29 lines with a margin; the same solver status and the same
                           sign in every line; the 19 lines with status "Solved" agree to five digits or more
                           (largest relative difference 7e-06); among the 10 lines with status "AlmostSolved"
                           the largest relative difference is 0.41 (c = 2.54, t = 0.01: -3.27e-08 against the
                           recorded -1.93e-08), the others are below 0.01.  The re-run of verification run B
                           showed the same differences.
    regenerated certificates (make_certificate.py): both byte-identical to certificates/certificate_n5_m6.json and
                           certificates/certificate_n7_m4.json

Part 3.  `python3 recheck_q4.py` in verification_run_B/programs (no output of this program had been recorded; the
numbers agree with those quoted from it in the report of verification run B).  The new output is
verification_run_B/outputs/recheck_q4.rerun_at_writing.out: margins of the sum as found -6.7e-07, -2.8e-06,
-6.5e-07 and after balancing the variables +1.2e-08, +1.2e-08, +3.9e-09 (c = threshold - 1e-5, threshold - 1e-3,
13/4), all with solver status "AlmostSolved".  The multiprecision values for the same point are in
writing_stage/gmp_q4_flagged_output.txt.

Part 4.  Verification run 2 (11 October 2026; the run on the final text of the note; the same machine and
package versions).

(a) Before its corrections: the archive of the package was extracted and `sh run_quick.sh` was run: checksums OK,
verify_note.py passed, 19 comparisons "identical" or "identical up to times", 0 failures or differences, 0 skipped
(independent_run_2/outputs/run_quick_from_extracted_archive_run2.log).  `python3 gmp_q4_flagged.py` in
writing_stage/ (63 seconds): output identical to writing_stage/gmp_q4_flagged_output.txt up to the running times
(independent_run_2/outputs/gmp_q4_flagged_rerun_run2.out).

(b) After its corrections.  Two checks were added to verify_note.py (README, "Changes to programs"); the recorded
output writing_stage/verify_note_output.txt was renewed (four more lines; all other lines unchanged), and the
eight kinds of altered certificates are rejected as before.  The programs of run 2 were added to run_quick.sh.
Output of `sh run_quick.sh`, run from a copy of this folder (about half a minute).  "passed": the last line of
the new output is the expected one.

== checksums of the certificates
certificate_n5_m6.json: OK
certificate_n7_m4.json: OK
== part 1: standard library
-- writing_stage/ (the program of the note)
passed                verify_note.py (BOTH CASES: ALL CHECKS PASSED)
identical             writing_stage/verify_note_output.txt
-- original/ (programs of the first results)
identical             original verify_certificate_n5_m6.out
identical             original verify_certificate_n7_m4.out
identical up to times original check_prior_note.out
-- verification_run_A/
identical up to times A vA_verify_n5_m6.out
identical up to times A vA_verify_n7_m4.out
identical up to times A vA_prior_note.out
-- independent_run_2/ (verification run 2, on the final text)
passed                2 r2_verify.py (RUN 2 EXACT VERIFIER: BOTH CASES PASS)
identical             2 r2_verify.out
identical             2 r2_controls.out
identical             2 r2_prior_preprint.out
identical             2 r2_count.out
passed                2 r2_flagged_q4.py (the flagged point lies in the cone)
== part 2: with sympy, python-flint, numpy, scipy
-- original/
identical             original verify_independent_n5_m6.out
identical             original verify_independent_n7_m4.out
-- verification_run_A/
identical             A vA_sympy_scratch_n5_m6.out
identical             A vA_sympy_scratch_n7_m4.out
identical up to times A vA_extra_n5_m6.out
identical up to times A vA_extra_n7_m4.out
identical             A vA_interval.out
identical             A vA_bkr_identity.out
-- verification_run_B/
identical up to times B verify_exact_B_n5_m6.out
identical up to times B verify_exact_B_n7_m4.out
identical             B check_kriebel.out
-- independent_run_2/
passed                2 r2_family.py (RUN 2 FAMILY CHECKS: ALL PASS)
passed                2 r2_gershgorin.py (RUN 2 GERSHGORIN CERTIFICATES: ALL PASS)
== 0 failures or differences, 0 skipped

With an interpreter that has NumPy but neither SymPy nor python-flint the same script reports 0 failures or
differences and 5 skipped.
