Cross-Degree Universality of the Borel-Singularity Radius for Polynomial Continued Fractions — v2.1

D2-NOTE v2.1 (2026-05-03) — Theorem 4.1 with closed citationchain. This is the v2.1 release of the D2-NOTE on Newton-polygonuniversality, replacing v2 (concept 19996689 / version 19996690,6pp) with a structurally equivalent but citation-completemanuscript (9pp). The v2.1 release closes the Borel-summabilitycitation gap identified in 5-reviewer peer review of v2(composite mean 4.6/10, REVISE_BEFORE_SUBMIT × 4 of 5). Theorem 4.1 (xi_0-univ): xi_0(b) = d / beta_d^(1/d) at alld >= 2. The proof composes: - Newton-polygon Lemma 3.1: explicit derivation of the indicial polynomial chi_d(c) = 1 + (-1)^(d+1) (beta_d/d^d) c^d at the slope-1/d edge of the Newton polygon of L_d at z = 0, for all d >= 2 uniformly - Wasow §19 (Theorem 19.1, equation 19.3): sectorial asymptotic existence at fractional rank q = (d+2)/2, with §19.3 ramification handling half-integer q - Birkhoff 1930 §2 Theorem I: formal-series existence at irregular singular points - Birkhoff-Trjitzinsky 1933 §§4-6: Borel-summability machinery for irregular linear difference equations at irregular singular points (this anchor was missing in v2 and is the substantive v2.1 addition) - Loday-Richaud 2016 ch. 2 / Costin 2008 ch. 5 (Tier-3): additional Borel-summability framework references Closes G1 (general-d xi_0 universality) at all d >= 2 withno residual flag, structurally lifting G2 (xi_0 at d=3 directverification, previously closed at d=3 empirically by Prompt012) to all d >= 2. M2 (general-d xi_0 proof in print) isfully done; SIARC-MASTER-V0 (M9) gating reduces from{M2, M4, M6} to {M4, M6} unconditionally. Empirical record: siarc-relay-bridge sessions2026-05-03/Q20-CONJ33A-PROOF-UPGRADE,2026-05-03/Q20A-PHASE-C-RESUME (commit 1642b24), and2026-05-03/D2-NOTE-V2-1-WASOW-FULL-CLOSURE (UPGRADE_V2_1_FULLverdict). Peer-review provenance: sessions/2026-05-03/D2-NOTE-V2-PEER-REVIEW/ (5-reviewer consolidation, composite mean 4.6/10). This v2.1 supersedes v2; v2 remains accessible at versionDOI 10.5281/zenodo.19996690 for archival completeness. AI Disclosure: this work used GitHub Copilot (Microsoft) andAnthropic Claude for code generation, numerical verification,and manuscript drafting. After using these tools, the authorreviewed and edited the content as needed and takes fullresponsibility for the content of this article. S154 Compliance Addendum (added 2026-05-13 via Zenodo Edit; per slot 154 verdict bridge HEAD 4761392 / slot 186 runbook) This record was deposited 2026-05-04, before the S154 compliance amendment overlay was introduced (slot 154 verdict 2026-05-10; slot 186 runbook 2026-05-11). The following clarifications are added retrospectively for governance-trail completeness: Mathematical-content vs formalization tooling-state firewall (per discrepancy D-153-3). The results in this note concern the Borel-singularity radius for polynomial continued fractions and lie wholly within the M1-M9 mathematical-content axis. They make no claims about the state of any Lean-4 formalization of these results; the M10 formalization tooling-state axis is documented separately at github.com/papanokechi/wallis-pcf-lean4 with a SCOPE.md document declaring an OPTIONAL UPLIFT pathway and a 2026-08-02 report deadline. M8b sub-leading Stokes constant caveat. This note's universality claims pertain to the Borel-singularity radius (a topological / analytic-continuation invariant) and not to sub-leading Stokes constants. The M8b sub-leading constant analysis carries a PERMANENT_RESIDUAL caveat documented in bridge session T1-SYNTH-M8B-RATIFICATION-CASCADE-ABSORPTION-130R; readers interested in Stokes-constant universality should consult that source rather than this note. Reproduction note. This is a 6-page summary/announcement note; the underlying computations are reproduced in companion artefacts: PCF-1 v1.3 (10.5281/zenodo.19937196), PCF-2 v1.4 (10.5281/zenodo.20114315), and Umbrella v2.2 (10.5281/zenodo.20114861). EBR radius upgrade (added 2026-06-06; per companion EBR preprint 10.5281/zenodo.20564080) The general-d Borel-singularity radius ξ₀ = d/β_d^(1/d) of Theorem 4.1 is, for families satisfying the positivity hypothesis b(n) > 0 for all n ≥ 1, now established unconditionally for the physical generating-function object G(s) = Σ Q_n s^n/(dn)!, superseding the cited-conditional composition (Wasow §19 and Birkhoff–Trjitzinsky) on which Theorem 4.1 originally rested. The proof routes through the holonomic structure of G rather than the sectorial-asymptotics citation chain: G is D-finite, its order-2d annihilator has leading coefficient a_{2d}(s) = d^d s^{2d}(d^d − β_d s) with finite roots only at s = 0 (apparent) and s = R = ξ₀^d, and positivity (Pringsheim) places the dominant singularity at s = +R with none closer. See the companion EBR preprint 10.5281/zenodo.20564080, §3. Grade and scope (load-bearing): the upgrade holds for positivity-hypothesis families, for the physical generating-function object (not the WKB fluctuation object, which carries the distinct scale 2ξ₀). The general-d argument is a closed-form symbolic computation with exact/numeric verification to degree 6 and machine-checked (Lean 4 / Mathlib, clean axiom cone) algebraic layer at degrees 2–5; it is not a proof quantified over the symbolic degree in a proof assistant. The radius result here makes no claim about the local singularity amplitude. This addendum is additive: no theorem, numerical value, or conjecture of the original record is retracted. The original sectorial-citation framing remains as a dated record; the EBR preprint supplies the self-contained replacement proof of the radius for the positive-b case.