Certified Prediction Improvement under Matched Contact Occupancy and Switching Flux in a Finite-State Model

Preprint. Not peer reviewed.This paper establishes a computer-assisted prediction-improvement bound for a specified 32-state continuous-time Markov model with a hidden binary source, a noisy binary observation, a four-state memory, and a binary contact. A state-dependent contact process is compared with an endogenous state-independent process with exactly the same stationary contact occupancy and switching flux in each direction. Each process uses its own stationary Bayes readout to predict a future binary observation under Brier loss. The gate is fixed once and is not reoptimized across the certified parameter domain.The main certificate covers 0 ≤ ε ≤ 1/2, 0 ≤ θ ≤ 1, and 63/2048 ≤ g ≤ 65/2048. It certifies G ≥ m₄, where m₄ = 50425539063434482373081891813729 / 2¹²⁵ > 0. Thus the state-dependent loss is at most the matched-comparator loss minus m₄θ for θ > 0 in this box; the losses agree at θ = 0. This is a result for the specified model and comparator. It does not assert optimality, a theorem for arbitrary finite predictors, or measured implementation-cost or energy savings.The manuscript PDF and editable manuscript source archive accompany this item. The associated dataset is Verification Evidence for Certified Prediction Improvement under Matched Contact Occupancy and Switching Flux in a Finite-State Model, DOI: 10.6084/m9.figshare.33644053. That item contains the evidence archive and a short standalone evidence map; a copy of the map is also included in the manuscript source archive. The evidence includes the CAP4 records for all 18,126 accepted closed boxes, whose verification was completed in two stages (10,917 plus 7,209), and the separate 256-box CAP2 records for the smaller-band bound in Appendix C. The 27 diagnostic points and sampled checks do not replace the complete coverings. Historical verifier sources are preserved; their original commands are not guaranteed to run unchanged in a new environment. The editable manuscript source requires a separately obtained publisher class and a suitable TeX installation.AI systems made substantial contributions to derivations, implementation, checking, literature work, and drafting, as disclosed in the manuscript. The recorded additional AI implementations and reviews are distinguished from completed external human or institutional reproduction, which is not claimed. No proof-assistant formalization is claimed. Preparation of this release assembled existing research records and did not generate new mathematical certificates or energy measurements.Author-controlled material in this item is licensed under CC BY 4.0, to the extent of the rights held by Satoshi Kawasaki. In the associated evidence dataset, the 23 research Python files identified by exact paths and SHA-256 hashes in CODE_LICENSE_INDEX.json are additionally available under the MIT License, at the recipient's choice (CC-BY-4.0 OR MIT). See the release LICENSE.md for scope and the unchanged third-party terms. This additional MIT option does not apply to the manuscript or all files indiscriminately.