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, REVISEBEFORESUBMIT × 4 of 5). Theorem 4. 1 (xi₀-univ): xi₀ (b) = d / betad^ (1/d) at alld >= 2. The proof composes: - Newton-polygon Lemma 3. 1: explicit derivation of the indicial polynomial chid (c) = 1 + (-1) ^ (d+1) (betad/dᵈ) cᵈ at the slope-1/d edge of the Newton polygon of Ld 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 xi₀ universality) at all d >= 2 withno residual flag, structurally lifting G2 (xi₀ at d=3 directverification, previously closed at d=3 empirically by Prompt012) to all d >= 2. M2 (general-d xi₀ proof in print) isfully done; SIARC-MASTER-V0 (M9) gating reduces fromM2, 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 (UPGRADEV2₁FULLverdict). 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.