Directed Computer-Assisted Certification of a Local Order-10 Operator-Chain Corridor on the Real Interval 5 ≤ s ≤ 14.25 via a Fixed Uniform b₁ Remainder Coefficient, Proof-Preserving Critical-Block Adaptation, and Panel-Aligned Derivative-Group Enclosures

Abstract

Abstract This preprint update presents a directed computer-assisted certification of strict positivity and corridor inequalities for a constructed order-10 real-parameter operator chain on the local interval 5 <= s <= 14.25. Version v1.1 extends the published v1.0 certificate from s = 11.55 to s = 14.25 through 27 additional degree-10 macroparents. The terminal ledger contains 92 historical directed cells and 32 macroparents, giving 124 proof-authoritative continuum parents with maximum endpoint gap zero. A fixed conservative coefficient K_unif = 9.0963237756432186892851014418197902 x 10^-88 is retained without increase, refit, or local replacement over the finite 32-slab range [11.05, 14.25]. Continuation is achieved through directed adaptation of the critical b1 panel width. From slab 10 onward, the noncritical same-slab blocks b0, b2, and b3 are inherited byte-identically and hash-verified while only b1 is recomputed. From slab 16 onward, the remainder engine uses panel-aligned derivative-group enclosures. Slabs 31 and 32 add fast dual accumulation cross-validated against the legacy engine. On the terminal slab [14.15, 14.25], the inherited width h1 = 0.000009 passes two of four conservative Fixed-K gates. The narrowest directed width boundary is h1,max = 0.000008816353715570646... Recomputing only b1 at h1 = 0.000008 restores all four gates. Across the full finite chain, 128/128 final Fixed-K substitutions are positive. All four finite local coefficient sequences satisfy K1 >= ... >= K32. Certified scope Within the stated analytic-computational framework, the accompanying directed certificates establish for every real s in [5, 14.25]: - Q_(10,10)^+(s) > 0;- Q_(10,8)^-(s) > 0;- W_10(s) > 0;- 8 W_10(s) < s b_10(s) W_11(s) < 10 W_10(s). Explicit claim boundary This record does not claim or establish a proof of the Riemann Hypothesis, PF-infinity, global q-monotonicity, global Order-Defect-Cone closure, pointwise K monotonicity, a global coefficient-decay law, or automatic continuation beyond s = 14.25. The PRF-02.17A slab-extension series is terminally closed at PRF-02.17AI. The interval [14.25, 14.35] was not tested or authorized. Reproducibility and provenance The reproducibility package preserves the v1.0 core byte-for-byte and adds 27 frozen update archives from PRF-02.17I through PRF-02.17AI. Direct package audit reports all ZIP CRC checks passing, 5047/5047 internal SHA-256 manifest entries passing, a 124-row positive terminal ledger, and maximum endpoint gap zero. Version-specific v1.1 DOI: 10.5281/zenodo.21713814Record-family DOI: 10.5281/zenodo.21667111Published v1.0 DOI: 10.5281/zenodo.21667112