Verification run 2 (AI-assisted, 2026-10-03): re-run of the packaged scripts

Source: an extracted copy of the source archive as packaged before this run
  (source.zip, 51128 bytes, sha256 d664d81e8768b17fd47b2b6c357b6e2fea7dff4825f83c20a1eeab22e6bfc08f).
Environment: Python 3.13.5, sympy 1.14.0, numpy 2.5.2, scipy 1.18.1, mpmath 1.3.0; PYTHONDONTWRITEBYTECODE=1.
Each script was run inside its own folder of the extracted copy and its output was compared with the packaged output.

script                                   exit  last line                                 comparison with the packaged output
lead/lead_checks.py                      0     ALL LEAD CHECKS PASSED                    identical (byte for byte)
finder/verify_sc.py                      0     ALL CHECKS PASSED                         identical except the printed run times (5 lines)
finder/profile_numeric.py                0     ALL NUMERIC CHECKS PASSED                 identical (byte for byte)
independent_run/indep_profile_mp.py      0     ALL PROFILE CHECKS PASSED                 identical (byte for byte)
independent_run/indep_curv_b.py          0     ALL INDEPENDENT SYMBOLIC CHECKS PASSED    identical except the printed run times (3 lines)

Archive hygiene of that copy: 21 entries; no __pycache__, no .DS_Store, no absolute local paths, no e-mail address
other than the author line of main.tex; directories extract with mode 755; every file agrees with release/.

Values that the packaged outputs and the programs of this run have in common:
  F (m = 1) = 0.374182345504   (run 2: 0.374182345504147; rigorous enclosure [0.3741759542, 0.3741887368])
  F (m = 2) = 0.187088345621   (run 2: 0.18708834562096;  rigorous enclosure [0.1870851493, 0.187091542])
  F (m = 4) = 0.093543452033   (run 2: 0.0935434520328014)
  rho_1/|w_1| (m = 1) = 0.478508   (run 2: rigorous enclosure [0.4785, 0.47851635])

After this comparison the print label of the tested formula in independent_run/indep_curv_b.py was changed to
"formula (3)" (header comment, three print statements, name of the helper function; no computation was
changed), and the script was run once more to regenerate its packaged output: exit 0, last line
ALL INDEPENDENT SYMBOLIC CHECKS PASSED, 25 lines ending in True, none in False. The regenerated output differs from
the earlier one only in that label and in the printed run times.
