v1.1.1 — correction release

This is a correction release. v1.1.0 carried false sentences — three about the Lee–Yang ladder of Part III, and one equivalence inside a proposition marked proved. This release says which ones rather than fixing them quietly.

A DOI makes a version permanent; it does not make it true.

What this release makes false

artefact	was	now
Part III, rem:leeyanglacunary	cos(k arctan 2t); rate 3π/2k; ladder (2n+1)π/2k	sin; rate π/2k; ladder θ_n = nπ/k, all integers
the same remark's STATUS	two measured series quoted under one symbol q_1	an erratum naming them as rung 1 and rung 3
prob:converse	rate (2n+1)π/2k, integer set by "the profile's first resonance"	rate π/2k — one ladder, one first rung, no profile-dependent integer
the fingerprint paragraph	"spacing π/k, offset by half", a signature of cos(kθ)	"twice as densely", a signature of sin(kθ)
prop:gqgen item 1	"R ≥ 1 is exactly the statement that Γ(A) is finite" — inside a proposition carrying STATUS proved	R > 1 forces it, R < 1 forbids it, R = 1 decides nothing
rem:nopinchreading	the same claim, in bold	corrected, with a profile of each kind named
.zenodo.json	Part III "45 pp."; version v1.1.0	51 pp.; v1.1.1; erratum in the description
README.md	"Archived release v1.0.0" — stale through the whole life of v1.1.0	v1.1.1, with the DOI caveat in bold under the badge
CITATION.cff	no version, no date-released, no doi at all	all three present

The first error, in one paragraph

On Re q = ½ write z = 1+2it, ρ = |z|, θ = arg z. Then z − 1 = 2it, so Σ_{j=1}^{k−1} z^j = (z^k − z)/(2it), and since ρ sin θ = Im z = 2t:

Γ^(q) = 2 + ρ^k sin(kθ) / (2t)      for a_i = 2^i + 1,  with no approximation
Γ^(q) =     ρ^k sin(kθ) / (2t)      for a_i = 2^i − 1,  an identity

v1.1.0 instead characterised the sum by its largest term, z^j + conj(z)^j = 2ρ^j cos(jθ). That is a modulus-level approximation, and it discards the factor 1/(z−1), whose argument is exactly −π/2.

A quarter turn of phase moves a ladder by half a rung. The half-offset that v1.1.0 wrote up as the discovery was the error itself.

The two measured series in that remark, |q_1−½| = 0.0520, 0.0253, 0.0167 and k·Im q_1 = 4.7736, 4.7457, 4.7299, are both correct measurements of genuine zeros — of the first and the third rung respectively, reported under one symbol. The agreement of the second with 3π/2 was read as confirmation because the search had been aimed where cos predicted a zero and found a real one there.

The second error

prop:gqgen item 1 said the radius of convergence decides whether Γ is finite. It does not decide the boundary case. With w_j ≥ 0, R > 1 forces G(1) < ∞ and R < 1 forbids it, but R = 1 allows either — and both occur among profiles the paper already uses:

profile	w_k^(1/k) at k=1024	R	Γ_k at k=1024
a_i = 2^i + 1	0.99932267	1	1026 (diverges)
m_j = round(2^j (j+1)^-2)	0.98654014	1	5.230199559 (converges)

The surviving direction is the one prop:nopinch actually uses (R > 1), so item 3 and the proposition's use are untouched; what was wrong was the equivalence.

What the corrections gained

Not weaker claims — stronger ones. For a_i = 2^i − 1 the zero set on the critical line is now exact and elementary: q = ½ + (i/2) tan(nπ/k), n = 1, 2, 3, …. All near-½ zeros were confirmed to lie on the line by an argument-principle count on |q−½| = r for r up to 0.25, matching twice the number of on-line sign changes in every case. And the boundary case the proposition folded away turns out to be the one carrying the phenomenon: at R = 1, Σ w_j = ∞ gives pinch rate π/2k while w_j ~ j^-s gives √(s log k / 2k).

Unchanged

The three headline results of Part III (prop:tiltlclt, thm:rigid, thm:transfer) remain unconditional. The main theorem, Part II's unconditional flatness, the coset identity, the character decomposition and the class-number corollary are untouched. prop:nopinch is untouched and its control passes. All twenty mechanical checks pass.

How the errors were found

By running the numerical rung of a proof plan — a script that scanned for sign changes from t = 0 upward and numbered them, rather than searching near where the wrong formula predicted a zero. The adjudication transcribed the paper's own displayed formula literally and summed it term by term; the two routes agreed to 2.8e-29, so the dispute was never about transcription. The second error was then found by a family built to test something else entirely.

A prediction that names a location will be confirmed by any zero near that location, and a dense ladder has one near everywhere. Count the zeros below the hit before calling it the first.

Full erratum: docs/RELEASE_v1.1.1.md. Scripts and logs: lean/pnp/leeyang6_r194, leeyang7_r194, leeyang8b_r194, figures_r194, radius_r197, audit2_r198, audit3_r198.