A Newton-polygon formal-level baseline for the Birkhoff-Trjitzinsky exponent on the SIARC polynomial continued-fraction Wallis stratum

A standalone Zenodo note that consolidates the SIARC T1 Phase 2verdict UPGRADEPARTIALFORMALLEVEL (bridge sessionT1-BIRKHOFF-PHASE2-LIFT-LOWER, commit 37c939f, 2026-05-04) into asingle citable artefact: a Newton-polygon formal-level baselinefor the Birkhoff-Trjitzinsky (B-T) asymptotic exponent A on theSIARC polynomial continued-fraction (PCF) Wallis stratum. Triple framing (the note's load-bearing partition): PROVEN (formal level): For the SIARC PCF Wallis recurrence atpolynomial degree d in 2, 8 and any of the three SIARCconventions (alpha-direction, symmetric, delta-direction), thenaive Wimp-Zeilberger Newton-polygon ansatz yields the formalexponent Aₙaive = 2d - degₐ in d-1, d, d+1. This isTheorem 1. 1 of the note. The proof is by direct symbolicbalance analysis on the formal series Qₙ ~ exp (Aₙaive * n^1/2+. . . ) ansatz, derived in Section 2 and closed by per-degreecase analysis in Section 3 across the three conventions. VERIFIED (literature-citation): At d = 2 the formal-levelprediction Aₙaive = 3 (alpha-direction) coincides with theLOWER branch of PCF-1 v1. 3 (DOI 10. 5281/zenodo. 19937196), Section 6 Theorem 5, Vquad family QL01-QL26, verified at 80algebraic digits. The B-T 1933 Sections 7-9 existence andfactorization machinery (Theorem II, Lemma 10, FundamentalTheorem) is verified against the SIARC stratum gates C. 2. 1through C. 2. 4 (non-resonance match, non-degeneracy match, d-rangeapplicability, mu-units consistency) in the bridge Phase Cliterature verification. STRUCTURAL FRAMING (not closure): At d >= 3 the empirical PCF-2v1. 3 (DOI 10. 5281/zenodo. 19963298) record R1. 1 + R1. 3 + Q1yields Afit ~ 2d (50/50 cubic representatives, 60/60 quarticrepresentatives) which lies strictly outside the formal baselined-1, d, d+1. Proposition 1. 2 of the note frames this gap withtwo non-mutually-exclusive structural mechanisms - (i') aborderline-locus condition where the SIARC stratum sits on thedegₐ = 2*degb boundary of the Wimp-Zeilberger normal case, and (ii') a definitional translation under which the empiricalfit-protocol of PCF-2 v1. 3 measures a different exponent thanAₙaive. Distinguishing (i') from (ii') is the open content ofSection 6 Q1. CONJECTURED (Conjecture B4): The note states Conjecture B4 ofPCF-2 v1. 3 (A = 2d for representatives in the SIARC stratum ateach degree d >= 2) verbatim. The note does NOT claim to prove, partially prove, or refute Conjecture B4. The formal-levelbaseline is consistent with - but does not establish - A = 2d. Section 6 Q4 names the sectorial upgrade gap (Wasow Section X. 3Theorem 11. 1, Adams 1928, Turrittin 1955, Immink 1984) thatwould, jointly with the closure of (i') or (ii'), turn theformal-level baseline into a proof of A = 2d on the SIARCstratum. Cross-cited Zenodo deposits and DOIs: - PCF-1 v1. 3. . . . . . . . . . . 10. 5281/zenodo. 19937196- PCF-2 v1. 3. . . . . . . . . . . 10. 5281/zenodo. 19963298- D2-NOTE v2. 1. . . . . . . . . 10. 5281/zenodo. 20015923- CT v1. 3. . . . . . . . . . . . . . 10. 5281/zenodo. 19899996- T2B v3. . . . . . . . . . . . . . . 10. 5281/zenodo. 19915689- umbrella v2. 0. . . . . . . . 10. 5281/zenodo. 19965041 Primary literature anchors: - Birkhoff Immink 1984; Costin 2008; Birkhoff 1930; Loday-Richaud 2016 (related literature). AEAL (Author-Evidence-Aided Logging) schema: 10 entries inclaims. jsonl. Six entries are literature-citation carry-forwardfrom the bridge T1-BIRKHOFF-PHASE2-LIFT-LOWER session (Phase Adeg 2/3/4 baselines, Phase B sweep d in 5, 8, Phase C foursub-gates, Phase D verdict). Two entries are literature-citationanchors to PCF-1 v1. 3 Section 6 Theorem 5 lower branch and PCF-2v1. 3 R1. 1 + R1. 3 + Q1 empirical record. One entry is thecomputation claim recording the three-pass pdflatex + bibtexbuild of btbaselineₙote. pdf (8 pages, 0 unresolved citations). One entry is the reading claim recording the rubber-duck self-review and forbidden-verb hygiene scan, with the four-wayepistemic partition (PROVEN / VERIFIED / STRUCTURAL FRAMING /CONJECTURED) confirmed intact in every section. Related identifiers metadata for Zenodo: - isCitedBy / isContinuationOf / isPartOf: PCF-1 v1. 3 (10. 5281/zenodo. 19937196) PCF-2 v1. 3 (10. 5281/zenodo. 19963298) D2-NOTE v2. 1 (10. 5281/zenodo. 20015923) CT v1. 3 (10. 5281/zenodo. 19899996) T2B v3 (10. 5281/zenodo. 19915689) umbrella v2. 0 (10. 5281/zenodo. 19965041) - isSupplementTo: siarc-relay-bridge sessions/2026-05-03/T1-BIRKHOFF-PHASE2-LIFT-LOWER (commit 37c939f). Build provenance: - pdflatex (MiKTeX 25. 12) ; bibtex (BibTeX 0. 99e), bibliography style 'plain', 15 entries, 0 warnings. - btbaselineₙote. pdf SHA-256 23022f0de77ac8388ed584b2196c0ab995cd8cf18b2dd71efbc0488a0f6e5b7c- btbaselineₙote. tex SHA-256 6746692c517dc25238473e819527c5682465cdc9e1def69d1f6df31c1014d51b- annotatedbibliography. bib SHA-256 589f6e4a0b29de401229d60a6252de15436f355a2fa8b3ac04907779c2de923d Author-AI disclosure: This note was prepared by the author withAI assistance (GitHub Copilot, Microsoft; and Anthropic Claude ina separate session) for code generation, numerical computations, LaTeX drafting, and provenance bookkeeping under the SIARC (Self-Iterating Analytic Relay Chain) protocol. Allload-bearing claims are anchored to AEAL entries with SHA-256provenance to either bridge-session computational artefacts orverbatim literature quotations. The author bears fullresponsibility for the content and the partitioning of claimsacross the four-way epistemic partition. License: CC-BY 4. 0.