Run from g2_simultaneous after extracting the cumulative bundle; sibling g2_low_schur and g2_weighted_signed provide the original exact witnesses and assembly. Python dependencies: python-flint 0.9.0, numpy, scipy; mpmath for the smallest finite diagnostic margin. PDF generation additionally needs LaTeX and PyMuPDF/Pillow for layout review.
Main verification (does not regenerate or change the frozen witness):
python simultaneous_trial.py --mode verify --normalized --parity even --M 4096 --J 65536 --steps 16 --bits 768
python simultaneous_trial.py --mode verify --normalized --parity even --M 4096 --J 65536 --steps 16 --bits 896
python complete_margin.py 768
python complete_margin.py 896
The reports must say PASS_COMPLETE_HEAD and PASS_COMPLETE_EVEN_RELATIVE_MARGIN. The same exact dyadic witness hash is used in both replays. The latter verifies U < (1-62629/100000)K by interval LDL, not by a floating eigenvalue estimate. The complete remote bound accounts for every mode beyond65536; the inverse majorant uses the previously certified shifted inner factors, whereas the outer energy/residual are unshifted.
joint_remote_gate.py is a supplementary bound with a common remote Gram; it is not needed for the main sign. quantify_head_error.py records ordinary-error estimates for failed trial bounds. The unscaled even and both odd trial reports are exploratory and inconclusive for exact sign. Positive individual directions never replace the simultaneous matrix test.
window_scaling_probe.py --lambda-value 3 (and4,5,6,8) is a DIFFERENT, finite-only pipeline: even heads throughlambda², cuts256/384,4096-bit arithmetic. It is not a complete-tail certificate. Floating diagnostics can lose tiny margins; the lambda8 inverse-metric branch avoids subtracting nearly equal numbers and records a separately verified relative threshold. Earlier exploratory2048-bit/interval-LU attempts were rejected and are discussed in the log, not asserted as certificates.
To replay the two fresh far-cut tables without launching the finite study:
python - <<'PY'
from window_scaling_probe import far_cuts
for bits in [320,384]:
for lam in [3,4,5,6,8]:
print(far_cuts(lam,bits))
PY
These thresholds certify positivity of the stated scalar remote comparison only. They do not certify the intervening inner head. No mu/rho or moment constants have been transferred fromlambda4 to another complete window.
Main result: complete even form atlambda4 positive; oddlambda4 and cofinal G2/RH remain open. See the full manuscript, research log, interval reports and adverse reviews for hypotheses and limitations.