Certified obstruction: Φ(-1/2) ∈ [-1.1590440509550799, -1.1590440509550797] < -1 (note |−1/2| < ln 2 ≤ R, so this is the sum of the series itself). By the maximum principle, M(r) := max_{|t|=r} |Φ| ≥ 1.159 for EVERY r ∈ [1/2, R). Hence the Cauchy/sup-norm estimate |A_j| ≤ M(r) r^{-j} cannot prove statement (I) even in the limit r ↑ R: an Abel-type argument (M(r)→1) is ruled out — M(r) stays bounded away from 1. The |A_j| ≤ 1 phenomenon is strictly a cancellation phenomenon, not an L^∞ one, at the profile level (sharpening round-1's Route-B failure analysis into a rigorous statement).
Evidence
Provenance
Reviews
Tail-bound proof + arb certificate sound; independent mpmath Phi(-1/2)=-1.159 inside claimed interval; max-principle consequence valid.
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.