Modern physics has offered many frameworks toward a Grand Unified Theory (GUT), yet an interpretational gap remains between General Relativity and Quantum Mechanics. Here we reformulate the universe as a single large informational rendering system, the “Universe OS.” Interpreting mass m as a 4π spherical patch that specifies 3D space (the UI), we recast kinetic energy, Einstein's energy relation, and the potentials of quantum field theory as optimization costs of information rendering. We survey expressions for resistance, kinetic energy, the volume restoration equation, the effective potential and the hierarchy problem, attending to the geometric quantities common to them.
What the second edition shows: The core of this paper is that the expressions of mechanics, electromagnetism, gravity and relativity share a single geometric quantity — the total solid angle of 3D space, ∫_(S²)dΩ = 4π — and that this sharing originates in the fact that the geometry of 3D space forces the inverse-square law (the n=2 uniqueness theorem of Paper 01). Electromagnetism and gravity already belong to this solid-angle family; taking m=4π makes mechanics join them through the same constant (Conclusion, §5.1). This is unification of the same kind as Maxwell's gathering of E and B into a single tensor: the physical content is unchanged, but the structure becomes visible.
Withdrawals in the second edition: The first edition positioned this paper as “presenting a grand unified equation”; that claim is withdrawn, on three counts. (i) The “The ONE” ratio (16π²)/(16π²)=1 is an algebraic identity, not a mechanism resolving the hierarchy problem (§3.2). (ii) The “Yamagishi Zero-Tension Sync Equation” presented in the first edition subtracts an antiderivative from its own integrand and is not mathematically well defined as it stands (Section 4). (iii) This paper juxtaposes known equations in a common vocabulary and, containing neither new predictions nor derivations from existing theory, is not a unified theory (Conclusion). However, (iii) does not negate the sharing of a geometric quantity stated above; the two must not be conflated (§5.2). The second edition is positioned as an overview.
(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 algebraic relations presented are transformations of known expressions; the aim is to propose a geometric reading of them. No claim contradicting established theory is made.
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). Physical Law as a Description Language of the Universe OS [Paper 13]. Zenodo.
DOI: 10.5281/zenodo.21404917
ORCID: 0009-0006-8587-3450