Committed on 2026-10-26 in its own commit, before any rerun result exists. The failed gate at omega = 727.95134 (RESULTS.md section 6) stays recorded as it is, whatever this rerun finds.
Hypothesis H
Revers's subsection 6.3 omega, printed "\omega=727.95134", is the Saouter-Demichel 2010 value 727.951335792 (his own history table) rounded to five decimals. His S* = -1.002922947193156 was computed at 727.951335792.
Fixed in advance
- Parameters, unchanged from target B: alpha = 6e12, A = 6.85e7, T = 10379600 (N(T) = 22,000,000), sum as in
skewes_terms.lehman_sum(Revers Theorem 3.1, both terms), zeros from Arb at 64 bits, sums at 128 bits. - Decisive evaluation points: omega = 727.951335792 (H's value) and omega = 727.951335426 (Saouter-Trudgian-Demichel 2015's omega_0).
- Control: omega = 727.95134. The rerun's ball there must overlap the recorded S = [-0.99067672 +/- 1.89e-9]. If it does not, the rerun is inconsistent with production B and nothing below is evaluated until that is explained.
- Descriptive grid: 727.951335792 + k * 5e-8 for k = -40 .. 40. Every point is reported. No claim is made at any omega picked from the grid after the data. All 83 points are listed in
omega_grid.json, committed with this file.
The decision rule
Let S(w) be the ball sum over the 2.2e7 zeros at omega = w, and let B = 2.60111e-5, Revers's stated worst-case zero budget (Delta S1 + Delta S2, subsection 6.3).
- H supported iff every point of the ball S(727.951335792) lies within B of S*: |S - S*| + rad(S) <= B.
- H not supported iff that fails. If S(727.951335426) instead meets the same rule, that is recorded as an observation about which omega the printed S* matches. It does not support H, and it was not a hypothesis.
- If neither decisive point meets the rule, the discrepancy is not the rounding, and target B stays "attempt unresolved".
Prediction under H: S(727.951335792) is within B of -1.002922947. Revers's float computation with zeros to 1e-9 typically lands much closer than the worst-case B, so a gap above about 1e-6 would already be surprising under H.
What may be claimed afterwards
- A ball-grade localization, meaning a positive lower bound -1 - S - R at Revers's tabulated eta values, is stated only at a decisive point (727.951335792 or 727.951335426). It holds whether or not H is supported, since the bound does not depend on matching Revers. Its grade is that of target A: a hardened computation on a cited derivation, with completeness on Arb alone and route 2 sampled.
- Grid values are descriptive. A positive bound at a non-decisive grid point is reported as a value, not as a localization claim.
Planted faults, run on the rerun data
- Drop R4 at the decisive points and report the move.
- Replace gamma_1 by gamma_1 + 1e-6 at the decisive points and confirm the ball moves out of its own unfaulted position.
- The grid sum must equal the stored single-omega sums at 727.95134 and 727.952018 on a small shard (
test_skewes_terms.py). A grid shifted by one step must fail that test.