Non-Box Obstructions for Proper Hat Guessing on Book Graphs

Research Note No.35, unrefereed public preprint v1.0. Ryutaro Yonezu, Yonezu Research Lab. For every k >= 3, a proper relabeling of an established Gadouleau-type non-coverable point-set recursion gives C_k <= M_k + k^2 and HGP(Bk,n) <= M_k + k^2 for every n >= 1, where M_k = 1 + sumᵣ₌₁^k r^r. Complete proper Cartesian boxes have strictly larger obstruction score. The immediate disjoint-coordinate-color construction already gives M_k + k^2 + 1; color sharing improves that baseline by exactly one (43 to 42, 306 to 305, 3440 to 3439 for k=3,4,5). No exact C_3=42, finite page threshold, winning strategy at 42 colors, historical novelty, or priority is claimed. The included proof and offline verifiers preserve candidate v0.3. All three supplied checks passed on Linux/Python 3.12.14. The external AI review reports PROOF/COMPUTATION/REFERENCES PASS, NOVELTY INCONCLUSIVE and RELEASE HOLD. The author subsequently explicitly instructed this qualified public release on 24 October 2026; this is not reviewer release approval or journal/conference peer review. The TU Delft thesis full-text comparison remains incomplete. Windows execution is unconfirmed. Files: English paper PDF and evidence ZIP with source, verification scripts, finite witnesses, audit history and SHA256 manifests. All rights reserved. Research inquiries: yonezaemon1+research@gmail.com. Repository: https://github.com/yonezaemon1-hub/no35-nonbox-obstructions-proper-hat-guessing