An Entropic Perspective on P vs NP: Reformulation via Kolmogorov Complexity

DRAFT version. This is an advanced draft. Major revisions are not excluded. We present a unified framework for the known equivalence between the P vs NP problem and resource-bounded Kolmogorov complexity, framing it as an entropic reformulation. The paper does not prove P != NP; instead it gives a cautious information-theoretic presentation of the witness-entropy gap, distinguishes known equivalences from new terminology, and identifies the remaining uniformity bridge as the central open challenge. CHANGELOG Changes in Version 1.3 (May 2026) Critical: Claim strength reduced: the manuscript is now framed as a presentation and framework paper for known P-vs-NP/Kolmogorov-complexity equivalences, not as an independent separation result. Major: Priority and related-work notes for Orponen--Ko--Schöning--Watanabe, Fortnow, Allender, Hirahara, Liu--Pass, and Santhanam were strengthened throughout the EN/DE text. Major: Advice-Erosion and Search-Flow Conductance were added as heuristic bridge diagnostics; the Bounded-Proof-Family guardrail clarifies that entropy, OGP, advice, or conductance signals only count when carried by a pre-specified bounded proof/solver/witness family. Major: MCSP and proof-complexity bridge routes were sharpened while marking their hypotheses and quantitative losses explicitly. Minor: Hodge/Kolyvagin analogies and numerical evidence language were softened; Post-Zookeeper transfer language was restricted to operational normal-form guidance. DE/EN: English, German, and combined bilingual PDFs were rebuilt from the 2026-05-06 local candidate. Changes in Version 1.2 (March 2026) Major: Instance compression bridge strategy elaborated (Remark rem:compression-bridge): 3-step argument via Fortnow–Santhanam no-sparsification connecting witness-finding to PH collapse Minor: Remaining quantifier-order gap explicitly identified Changes in Version 1.1 (March 2026) Major: Resolution-Width Conjecture connecting proof complexity to entropic hardness Major: Resolution width as thermodynamic observable Minor: Bibkeys unified, AC0 entropy obstruction proposition