Analytic profile theorem: (a) the power series Φ has radius of convergence R ≥ ln 2 = 0.6931…, and on |t| ≤ ρ < ln 2 the entire functions t^{-n} f_n(t) converge uniformly to the sum of Φ (elementary majorant x_{k+1}=e^{ρ x_k}-1, decreasing to 0 exactly when ρ < ln 2); (b) for every real t ∈ (0,1) the orbit f_k(t) increases in (-1,0) to 0 and the Koenigs value G(t) = -∏_{k≥0} h(t f_k(t)) lies in (-1,0): the conjectured profile bound |Φ| ≤ 1 HOLDS on the whole positive real segment.
Evidence
Provenance
Reviews
Thm 5(a),(b) proofs sound; correctly scoped to G on [ln2,1).
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.