Run 058's crossing polynomials R(p) are exact. Writing R(p) = c·p^ℓ·∏(p − p_j), with ℓ the shortest crossing path and p_j the remaining zeros, the log derivative at the fixed point gives an identity, λ = R′(p*) = ℓ + p*·Σ_j 1/(p* − p_j), so the exponent y = ln λ / ln 9 is a statistic of where the zeros sit. Is it controlled by the few zeros nearest the fixed point, as the Fisher-zero picture says, or spread over all of them? And do the zeros stay within the disc |p − 1| ≤ 1?

Sealed 2026-09-29, before any zero of any crossing polynomial was computed (codifier). Known at sealing: every number in run 058, including each generator's λ and p*, and the exact counts a_k in rg058.json, which no one has factored. Not known: ℓ, any zero, S, or any share. The identity for λ is algebra, not a finding; it is the control.

Why the two bets. (1) In the Fisher-zero picture of a phase transition, the exponent is set by how the zeros nearest the critical point pinch toward the real axis, so a few zeros should carry most of S. Against it: these are small polynomials of degree 76–144, where zeros near p = 0 and p = 1 are numerous and each pulls on p* a little; the sum could be spread. (2) A conjecture of this disc shape for reliability polynomials (Brown–Colbourn) is, as the codifier recalls it, false for graphs in general; whether it holds for these planar generators is open, which is why it is a test and not a formality. Neither attribution is relied on; both are to be checked before any note cites them.

What the outcomes mean. Confirmed on (1): the exponent that ordered all eight lattices is local in the complex plane — a handful of zeros near p* — and run 059's correction terms should be read as moving those zeros. Falsified on (1): the exponent is a global statistic of the zero set, and a theory of it must account for every cut and path size at once. On (2): a disc bound, if it holds, confines where the zeros can go under any change to the room, which bounds how far y can move.

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Scored 2026-09-29 — falsified

Results: R29_crossing_zeros/RESULTS060.md, zeros060.json, stats060.json (commit c5cb5be). cypari2 2.2.4 / PARI 2.17.2 at 250 digits; R(p) rebuilt exactly from rg058.json and matched to its stored power-basis coefficients.

† a conjugate pair straddles the cut; the range gives the whole-pair counts on either side.

What it settles. The disc bound fails on every generator, by a wide margin; whatever confines these zeros, it is not |p − 1| ≤ 1. And ℓ = 8 on all eight — the shortest crossing path is the straight row in every room (the kept boundary ring guarantees one), so λ = 8 + S and the whole difference between rooms' exponents lives in the root sum S.

What clause 1's pass does not mean. The sealed threshold (f₄ ≥ 0.5) was met on seven of eight, but a share above 1 — f₄ up to 1.46 (U), 1.31 (B), f₈ up to 2.9 — means the nearest zeros pull on p* more than the whole sum does, and farther zeros pull back. The partial sums do not settle; the exponent is a cancellation between near and far zeros, not a few zeros carrying it, and the square (f₄ = 0.165) does not even meet the threshold. The Fisher picture in which zeros pinch the fixed point is a statement about large systems; at generation 1 the nearest zero sits 0.24–0.35 from p*, nowhere near pinching. The next: asks whether composition moves them in.

Note on the first pass. Control (i) first failed at ~1e-17 because cypari2's polroots ignores the global precision unless precision= is passed on the call; the compute chat diagnosed it before reading anything into the data. Filed in OPS.md as a failure mode.

Pointers corrected 2026-10-05 (codifier; no sealed field, score or number is changed). The script: line was written with the seal, before the script existed, and read: script: R29_crossing_zeros/ (to be written by the compute chat). It now names what was written and committed: R29_crossing_zeros/zeros060.py, R29_crossing_zeros/analyze060.py. Found by sync_cases.py's record-field check (docs/REPO-AUDIT.md 5.4).