v1.2.0 — a standalone note, and four corrections
Released 2026-08-17. Previous: v1.1.1 (2026-08-16). (Correction, made minutes after publishing: the banner, CITATION.cff and this line first read 2026-08-18 — a date copied forward from a drifting round header and never once asked of the clock. Zenodo, which does not take our word for the date, is what caught it. Fixed here and in the repository; the copy inside the archive keeps the wrong date, because the tag now carries a DOI and is not moving. A fact every reader already knows is a fact nobody checks.)
This release adds a fourth manuscript and corrects four statements that were public in v1.1.1. Read the corrections first; they are the part a reader of the old version needs.
What is new: a standalone note
paper/note1.tex — Two speeds at the boundary: zeros of sums of conjugate sections of power series, 11 pp., with a Japanese edition in paper-ja/note1_ja.tex.
The note takes one question out of Part III and states it in the standard language of power series, with no prerequisites from this repository and no citations to the other manuscripts at all. For non-negative reals w_j, with G(z) = Σ_j w_j z^j and G_k its sections, it studies the zeros of
F_k(q) = 1 + G_k(2q) + G_k(2−2q)
— a sum of two sections under substitutions that are complex conjugates along the line Re q = ½. Jentzsch's theorem covers the zeros of a single section, and adding functions can cancel zeros; we found no result covering sums of sections, and the note says exactly where we looked so that one reference can overturn the claim.
The note contains: the reduction (on that line the object is real, so its zeros are sign changes, which cannot be cancelled); a closed form and an existence theorem for constant weights, with the zero set exact in one case; a two-regime rate law for decaying weights; what a proof of the decaying case would have to supply, including the attempts that failed; and one constant that remains unsettled, with the reason it will stay unsettled at computable sizes.
It carries no vocabulary of its own and cites nothing. That was a condition of its approval, and meeting it improved it: a note that cites its parents invites the reader to go and check whether the parents are any good, and this one does not need them.
Corrections to statements that were public in v1.1.1
A DOI makes a version permanent; it does not make it true. Four statements in Part III are corrected here. Each is corrected at its own statement in the manuscript, with the reason, and none has been deleted.
1. rem:pinchformula — the k = 70 table
The measured row read 0.503895, 0.413403, 0.305147, 0.220690, 0.133982, 0.070741, 0.022306. Those values are wrong from the fourth significant digit, with mixed signs and a largest error of 3×10⁻⁴ at c = 2. The replacement is computed by two independent methods — one forming the polynomial and taking every root, one never forming it and locating the nearest zero by the argument principle — which agree to 94–120 significant digits, are stable between 60 and 120 digits of working precision, carry an argument-principle certificate per row, and reproduce a zero the paper proves exact.
We cannot reconstruct what produced the old row. The obvious hypothesis, an off-by-one in k, was tested and refused: the published values match neither k = 69 nor k = 71.
2. rem:nopinchreading — the displayed profile
The remark displayed m_j = ⌊2^j (j+1)^(−2)⌉ and, in the same sentence, the constant it generates, Γ_k → 5.230199559. The displayed formula gives 3.480199559. The missing ingredient is the clamp m_j ≥ 1, which is forced — m_j is half a gap between distinct odd numbers — and which was in the computation and not on the page.
3. rem:rateregimes — the dividing line
The dividing line between the two rates was conjectured to be Σ_j w_j < ∞. That is disproved. The harmonic profile w_j = (j+1)^(−1) is not summable and takes the √(s log k / 2k) rate: k·t₁ runs 11.9, 18.0, 27.3, 37.0, 55.6 at k = 64…1024, growing rather than approaching π/2. The line is w_j → 0.
The mechanism had said so all along: it uses w_k and never uses the sum. When a conjecture and its own mechanism disagree about what the hypothesis is, the mechanism is the one that was derived.
4. rem:rateregimes — a refutation of ours, withdrawn
We recorded the candidate λ_eff → s − ½ as refuted, on the grounds that |λ_eff − (s−½)| stays in [0.34, 0.48] over k ≤ 2048 without shrinking. That band is exactly what the candidate predicts at those k: the approach is −½ + (log log k)/(2 log k) + O(1/log k), and the correction term alone is 0.13966 at k = 1024. The refutation is withdrawn.
A refutation needs a resolution claim. "It did not converge" is evidence only if the hypothesis predicts convergence you could have seen.
Also corrected, without having been wrong
prob:converse was posed asking whether R = 1 forces the pinch at rate π/2k. The rate clause is answered no and has been withdrawn from the problem statement out loud; the existence question is untouched and remains open. And the "doubled ladder" fingerprint now carries its measured scope: the evenly spaced ladder is a constant-weight phenomenon, not a general one — measured gaps run 0.17 to 0.73 in units of π/k once the weights decay.
How these were found, since it bears on the rest
Three of the four were found by building something new and noticing that it contradicted a sentence written elsewhere — not by any of the twenty-one mechanical checks. The fourth was found by a gate: a rule that the phase picture must postdict a known scale before it earned an instrument, which produced a model that then withdrew our own refutation.
The failure ledger in tools/ records all of this, with the general rule extracted from each. It now has 87 folded entries and 14 pending.
Everything else in this release
- Part III: 51 → 54 pp., carrying the four corrections above and the two-regime rate law with its full record.
- Japanese editions track all four manuscripts;
note1_ja.texis new.C13checks that every number in a translation occurs in its source (630 literals) andC19that the skeletons match. - New checks:
C21refuses any file in the tree whose name says it holds credentials. The check announces its own limit — it cannot see a secret that is innocently named. - New scripts and logs:
rate_r200,pinch_r202,trackm_r203,divide_r204,lambda_r206,envelope_r206b,note1tab_r208,rung0_r211, and the referee-pass logsrefpass_r201,refpass_r209. Every number in every manuscript is copied from one of these.
What has not changed
Not peer-reviewed. Every statement still declares its own status where it is stated. The Lean canon is unchanged and still replays through an independent kernel that must first reject three deliberately corrupted modules.