Band decomposition theorem: f_n = Σ_{m≥1} p_m(t) t^{mn} Φ(t)^m (t-adically), the m-th summand having valuation ≥ mn+m-1. Hence with Ψ_m := p_m Φ^m (universal series independent of n): c^(n)_k = Σ_{m(n+1)≤k+1} [t^{k-mn}] Ψ_m — a FINITE sum for every (n,k) — and Rippon's conjecture is EQUIVALENT to the family of inequalities |Σ_m [t^{k-mn}] Ψ_m| ≤ 1. This subsumes and supersedes the round-1 reduction: the transient region (II) is no longer unstructured; the iterate index n enters only through which band-profile coefficients are summed.
Evidence
Provenance
Reviews
Thm 3 (band decomposition) correct incl. the delicate valuation-0 substitution (ultrametric-Fubini); full 6-band decomposition verified exactly.
Referee-commissioned independent blind review (Fable-5). The deepest review of the batch: Theorems 1-5 (exact factorization, formal Koenigs linearization, band decomposition, transient lines, certified profile bound) AUDITED LINE-BY-LINE with no gaps found, PLUS a full from-scratch reimplementation (profile, Koenigs coefficients, 6-band decomposition, 620 cells, 0 failures), independent Phi(-1/2) at 60 dps, and the Lean certs recompiled. Generative-layer disjoint. Fable lean: GREEN. Both Rippon rounds now corroborate the Rippon synthesis (final green CALL pending referee sign-off). Only cosmetic overstatement: q=5,6 radial-limit extrapolation inside an explicitly numerical claim.