Modules Are Not Walls but Limits: A Distinct-Roots Census of Contraction, Deformation and Decoupling, and the Beautiful Temptation of “Stability”.
Physics LOOKS AS THOUGH IT COMES IN MODULES: Newtonian mechanics carries you so far, then the rule seems to change into special relativity, then into quantum theory. This paper answers that appearance with established results, as a LAYER-2 DISTINCT-ROOTS CENSUS. FIRST ANSWER: the modules are not walls but LIMITS, and the boundary always lies where a DIMENSIONLESS NUMBER CROSSES ONE (v/c; GM/rc^2; hbar/S) – a statement independent of units, on which the convention/fact line of 95 bears directly. SECOND ANSWER (the machinery): there are THREE machines joining the modules, and all three are DISTINCT ROOTS. (i) CONTRACTION – Inonu-Wigner (1953): as c goes to infinity the Poincare group contracts to the Galilei group. THIS PUTS A PARENT-CHILD RELATION INTO THE TWO BRANCHES OF PAPER 83 (83 counts the branches; 113 joins them). (ii) DEFORMATION – quantum mechanics is a deformation of classical mechanics in hbar (Moyal 1949; BFFLS 1978; Kontsevich, who proved that every Poisson manifold admits a deformation quantization). Contraction and deformation run in OPPOSITE DIRECTIONS. (iii) DECOUPLING – Wilson’s renormalization group and Appelquist-Carazzone (1975): short-distance detail is cut off from long-distance physics. THIS ANSWERS A DIFFERENT QUESTION – not how the modules connect but WHY PHYSICS CAN BE MODULAR AT ALL; modularity is not a bug but the condition for physics to be possible (connects to 110, 77, 78). There is also a GEOMETRIC ANSWER: through Cartan’s NEWTON-CARTAN THEORY and Ehlers’s frame theory (lambda = 1/c^2), Newtonian gravity too is geometry, and the boundary lies not in “geometry or not” but in WHETHER THE METRIC IS DEGENERATE – Minkowski’s ds^2 (108) splits into a spatial metric and a temporal one-form as c goes to infinity. Papers 92 (Cartan) and 111 (Ehlers, the same Ehlers as EPS) converge here. As a map we place BRONSTEIN’S CUBE (1/c, G, hbar; eight vertices; one empty corner = quantum gravity). AND THE SPINE OF THIS PAPER IS A SINGLE BRAKE: there is a temptation to extend all this into the STABILITY ARGUMENT – constants are deformation parameters, and since rigid algebras should be selected, c, hbar and Lambda cannot vanish (Flato 1982; Faddeev; Vilela Mendes 1994). This paper presents that as a HEURISTIC PRINCIPLE, a criterion of theory selection, and NEVER CALLS IT A DERIVATION OF THE VALUES OF CONSTANTS. The dividing line is the distinction between EXISTENCE and VALUE – a jig Paper 83 already owns (the existence of an invariant speed is forced; its value is settled by experiment). Tested against the four failure modes of Paper 101, the decisive one is the fourth: the argument carries NO DIFFERING PREDICTION as yet, so it is recorded at Layer 2 and NOT promoted to Layer 1. Where Eddington slipped was in trying to derive the VALUE. IMPORTANT (scope): a Layer-2 structural interpretation of established results; no new theorem, no new physics, no prediction. The three machines are NOT unified (they answer different questions). Newton-Cartan is a REFORMULATION and changes no prediction. The empty corner of the cube (quantum gravity) is NOT attempted (admire), and nothing is inferred from the cube having eight vertices (a map, not a theory). Resonance is a signature not a proof (100); no post-hoc adjustment (101). A designer and the Universe OS are Layer-3 non-scientific lenses.
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). Modules Are Not Walls but Limits — A Distinct-Roots Census of Contraction, Deformation and Decoupling, and the Beautiful Temptation of “Stability” — [Paper 113]. Zenodo.
DOI: 10.5281/zenodo.21962996
ORCID: 0009-0006-8587-3450