Complex Multiplication as a Transcendence Predicate for Degree-2 Polynomial Continued Fractions
papanokechi papanokechi · Zenodo (CERN European Organization for Nuclear Research) · 2026
Version 1.6 (2026-05-30) — V_quad surface-type correction, complete. The isomonodromic deformation of the V_quad family (Delta = -11) is corrected from Painleve III(D6) to a non-classical Painleve V transcendent on the Sakai surface of type D5^(1) (W(A3^(1)), delta = -1/2 != 0, so not a Painleve III reduction), per the companion paper "A non-classical Painleve V transcendent from a quadratic polynomial continued fraction: surface classification and resurgent Stokes data" (Zenodo DOI 10.5281/zenodo.20455090). This corrects the abstract, Conjecture A part (iv), and the body section "V_quad as the Explicit Prototype", so the surface-type determination is consistent throughout. No other theorem, conjecture, or numerical result is changed: the Delta>0 / Delta0 F(2,4) Trans-stratum families is corrected from "admit elementary closed forms" to its supported sense: PSLQ-detectability against the working bilinear-pi / special-value basis (220 digits, integer bound 10^10). Detectability against a fixed basis is a positive heuristic signal, not an exhibited elementary closed form; the analytic class is left open. A targeted closed-form search on the cleanest non-degenerate Delta=+1 representative QL09 (b_n = (n+1)(2n+1), a_n = 5n) fails to exhibit an elementary closed form to >= 360 decimal places, and the negative persists under the canonical alternative numerators over the same b_n (the obstruction is a property of the quadratic-b structure, not the numerator). No theorem, conjecture, or numerical result is retracted: Conjecture A is unchanged (its dichotomy is a statement about detection outcomes; part (i) asserts only the Delta= 13 matching digits across all six Delta<0 families. Conjecture A part (iv) is restated as channel-scoped: V_quad is the unique sporadic instance with an explicit Painleve determination in the connection-coefficient / Stokes-constant ODE channel; the channel structure of the other five families remains open. Two new open problems are stated. The 0/6 result in the L(t) and Borel channels is presented as a strengthening of the conjecture, not a refutation: it sharpens the channel-specificity of the Painleve question and motivates a forthcoming "Channel theory" outline as the structural prerequisite for the SIARC Master Conjecture.