We present an information-geometric reformulation of the 3D Poincaré Conjecture (Perelman's Theorem). The argument proceeds in three stages. Stage 1: We formulate the Triple Enforcement Principle (Analytic, Dynamical, Topological), showing that n=2 uniqueness drives local curvature uniformization. Stage 2: We prove a quantitative isomorphism between Perelman's W-entropy functional W(g, f, τ) monotonicity (dWdt ≥ 0) and Universe OS memory compression optimization (avoiding n ≠ 2 system crash). Stage 3: We demonstrate that Ricci flow ∂_t g_(ij) = -2 R_(ij) with surgery re-formats spatial rendering using m=4π units, proving why any simply connected closed 3-manifold converges structurally to the round 3-sphere S³.
(scope note) Positioning of this paper: This paper offers a structural interpretation of established physical laws and mathematical theorems. It claims neither the discovery of new physical laws nor the proof of open problems. The 3D Poincaré Conjecture was completely proved by Perelman (2002–2003); this paper proposes an information-geometric rereading of that proof. It contributes nothing to the proof and proposes no alternative to it.
A note on the aim of this work. This is a structural reinterpretation of well-established physics, not a proposal for a new physical law. Every relation shown is a substitution into, or a geometric re-reading of, equations that are already known and that remain unchanged. The aim is a modest one: to make a few recurring geometric structures — in particular the solid angle 4π and the exponent n = 2 — easier to see within a single picture. Where a particular unit convention is adopted (for example G = 4π), this is a choice of notation, not a claim about nature. Nothing here is intended to contradict existing results.
On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated.
Reference
Yamagishi, Y. (2026). Information-Geometric Reformulation of the 3D Poincaré Conjecturevia the n=2 Uniqueness Theorem and Perelman’s Ricci Flow [Paper 7]. Zenodo.
DOI: 10.5281/zenodo.21404387
ORCID: 0009-0006-8587-3450