This record provides both English and Japanese full versions of the paper: - paper_AC_unified_en.pdf / .md — English version (full translation, 22 chapters) - paper_AC_unified_ja.pdf / .md — Original Japanese version - fig1_three_pillars.svg — Three-pillar structure diagram (shared) Abstract This paper starts from the question: why can light oscillate in an observer's frame when its proper time integral along null geodesics is zero? To address this gap between "light without a clock" and "observed oscillation", we introduce an observation-null matrix-valued connection on a Kerr-null parent geometry that combines observer time t with a null time direction u. Three pillars: (i) The U(1) Maxwell Projection Theorem (Theorem 1) recovers ordinary Maxwell equations on the observer time axis under three limit conditions (commutativity / null-time-direction invariance of the observation connection / purification to the U(1) subgroup). (ii) The Maxwell Residual Generator K_{u,obs} appears in observation space when any of these conditions break. (iii) The Gravitational-Electromagnetic Unified Connection on the direct sum bundle E_grav ⊕ E_em recovers Einstein-Maxwell systems in the diagonal-dominant limit (Proposition 2). Chapter 15 closes the framework with 19 lemmas and the Reinforcement Closure Theorem 15.20. Appendices A–D respectively address: - (A) anticipated review concerns, - (B) editorial consistency for publication, - (C) comparison with existing phase archetypes (Dirac matter wave, Sagnac effect, COW gravitational phase), - (D) a three-stage path from standard null phenomena to the upper observation-null structure with CP projection isomorphism (cf. CP violation paper DOI 10.5281/zenodo.19800883). The paper does not replace Maxwell equations or Einstein-Maxwell systems, but recovers both as special limits of an upper-level matrix-valued connection theory.

Multilingual: This record provides both English (paper_AC_unified_en.{pdf,md}) and Japanese (paper_AC_unified_ja.{pdf,md}) full versions of the paper. The English version is a full translation of the original Japanese manuscript, with the same 22-chapter structure (Chapters 1–15 + Appendices A–D + Chapter 16 outlook + Chapter 17 glossary). Version: Preprint, version 2 (replaces version 1 which contained only the Japanese version). Translation notes: The translation preserves the Hayashi naming convention "where/what/role" (e.g., "adopted parent geometry Kerr-null / observation-null matrix-valued connection / U(1) Maxwell projection theorem") as a type-safe naming framework. Plain-language reader-facing blocks (labeled "In one line" and "This chapter in plain language") are translated in a friendly teacher-tone English style while remaining within academic register. Source repository: https://github.com/khayashi4337/pysic/tree/master/draft/CP_yabure/phase5_maxwell_null