Extremal structure: the global maximum modulus 1 is attained on the ENTIRE leading diagonal k=n (since c^(n)_n=-1 for all n); every non-leading coefficient is strictly smaller. The non-leading supremum over the window n,k<=1000 is exactly 2663/4480 = 0.594419..., attained UNIQUELY at (n,k)=(6,13) (one step below the offset-7 stabilization threshold). The transient ridge near k~2n decreases monotonically to 1/2 as n grows. Conjecturally 2663/4480 is the global non-leading supremum, i.e. |c^(n)_k|<1-delta for all k>n with a fixed delta.
Evidence
Provenance
Reviews
Extremal 2663/4480 at (6,13) + uniqueness confirmed by own impl; the global non-leading supremum is explicitly labeled a data-supported conjecture.
Referee-commissioned independent blind review (Fable-5). GENERATIVE-LAYER DISJOINT reproduction: an own from-scratch pure-Fraction reimplementation (not the author's code) matches all values incl. the extremal 2663/4480 at (6,13), the exact N=1000 certificate, the N=700 arb scan, and the Lean cert recompiled on the pinned toolchain. The native_decide finite check does NOT masquerade as a general proof (outcome=partial, finite-window scope + TCB disclosed). Fable lean: GREEN. Referee note: this corroborates the Rippon synthesis; final green CALL pending referee sign-off. Nits: arb receipt in-repo covers N=600 vs claimed 700 (disclosed, reproduced); code_refs use the post-amendment prefix.