Cross-Degree Universality of the Borel-Singularity Radius for Polynomial Continued Fractions

We isolate, as a single citable artefact, the cross-degree identityξ0(b) = dβ1/ddfor the leading Borel-plane singular distance of the formal generating function f(z) = n≥0 Qnznof a polynomial continued fraction (1,b) of degree d with leading coefficient βd > 0. Version 2(2026-05-03) upgrades the v1 (2026-05-02) status from proven at d = 2 / verified at d = 4 /conjectured for d ≥ 2 to a theorem-grade statement covering all d ≥ 2 uniformly. The upgraderests on two new anchors: (i) a direct symbolic identity check at d ∈ {2,3,...,10} through theSIARC Phase A* extended sweep ([7], 18/18 pass at dps = 50, relative error < 1.6 × 10−51 aboved =2); and (ii) the uniform-in-q general-case asymptotic existence theorem of Wasow 1965 §19 ([8,Thm. 19.1]) together with Birkhoff 1930 §2’s uniform-in-n formal series existence ([1, Thm. I]). TheNewton-polygon slope-1/d edge / Wasow shearing-exponent equivalence is recorded as a substantivevocabulary correspondence (Newton polygon ↔ shearing transformation are the same constructionin different notations). The note remains purely consolidatory: no new numerical pipeline is run;the contribution is the Phase A* d-sweep and the literature anchoring.