An Arithmetic Stratification of Polynomial Continued Fractions: Program Statement of the SIARC Series (v2.2: Full M-axis V0 Closure Series)

v2.2 (May 2026): Consolidates full M-axis V0 closure series (M4, M7, M8a, M8b) and M6.CC R1; supersedes v2.1 internal staging.

Version difference

The v2.2 revision of the SIARC umbrella program statement extends the v2.0 §Closure Cascade and Bridge Provenance section from 3 milestones to 6 milestones, adding the M-axis V0 ratification cascade triple landed 2026-05-09: M7 V0 (cubic/quartic borderline-anormal A residual; soft-branch ratification at MEDIUM-HIGH; bridge SHA 7f93b9e; SOFT-BRANCH, HARD-BRANCH-PENDING), M8a V0 (catalogue-wide Painlevé-test stratum labeling via the Conte–Musette necessary criterion; 60/60 LABELED uniformly; bridge SHA cb429e1; ALG-TEST-SCALE, STOKES-DICHOTOMY-DELEGATED-TO-M8B), and M8b V0 (numerical foreclosure of the laptop-feasible |S₂| extraction at d=2; cross-provider dual-witness; bridge SHA 74c5630; NUMERICAL-FORECLOSURE, d≥3 caveat carried forward). The v2.0 → v2.2 version sequence skips v2.1 (internal staging only at bridge 883dddf, 2026-05-09) per the operative cascade-132 (fd669d3) PATH_B decision. All mathematical content, conjectures, open problems, and the §Cross-Degree Triple are unchanged from v2.0; v2.2 is a status/provenance addendum, not a content revision.

§2.1 Deposit-time companion-artefact snapshot

Companion artefact state at deposit time (2026-05-11 JST): PCF-2 v1.4 (10.5281/zenodo.20114315, deposited 2026-05-11; cascade-132 Option α Step 1 landed), Channel Theory v1.3 (10.5281/zenodo.19972394, deposited 2026-05-02), T2B v3.0 (10.5281/zenodo.19915689, deposited 2026-04-30), PCF-1 v1.3 (10.5281/zenodo.19937196, deposited 2026-05-01). Picture-chain v1.20+ deposit pending (substrate-prep at bridge b9aa881 2026-05-09; concept-DOI not yet minted); cross-link rows to be spliced via post-publish Zenodo Edit upon picture-chain concept-DOI mint (separate work-stream; cascade-132 Option α Step 3).

§2.5 M1–M12 program-axis coverage (snapshot at Umbrella v2.2 deposit time)

The axis-coverage table follows the SIARC v1 schema locked by slot 160 verdict (siarc-relay-bridge cascade 012736f); status vocabulary and atomic listing are normative. Bridge cascade SHAs are content-addressed persistent identifiers; URLs may decay if the siarc-relay-bridge repository is renamed but SHAs remain recoverable from any clone.

Per-deposit semantics: Umbrella v2.2 absorbs the V0-closure cascade via the v2.2 §Closure Cascade and Bridge Provenance amendment. The 4 V0-closed axes (M4, M7, M8a, M8b) and the M6.CC retirement are program-tier provenance for the Umbrella program statement, not new mathematical content; this is the semantic distinction between Umbrella v2.2 (provenance-tier amendment) and Umbrella v2.3 (forthcoming; mathematical content amendment).