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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Structural_Reclassification_Principle__Isotropic_Deformations_and_the_Unified_Resolution_of_Physical_and_Mathematical_Misclassifications

Authors: Iriguchi, Minehiro;

Structural_Reclassification_Principle__Isotropic_Deformations_and_the_Unified_Resolution_of_Physical_and_Mathematical_Misclassifications

Abstract

This paper develops a general structural reclassification principlefor physical and mathematical quantities that have long been treatedas distinct, dynamical, or ontologically independent. Building on the projection–exclusion grammar established in v1.0and the combinatorial uniqueness result of v1.1,and on the observational two-tier separation introduced in v2.0,the present work formalizes a universal distinction between: (1) structure-level invariants, and (2) representation-level or observer-dependent quantities. The framework is developed entirely within the static (isotropic) regime.No physical time, dynamics, or new interaction is introduced.Instead, the work shows that many persistent tensions across physicsand mathematics arise from systematic misclassification betweeninvariant structures and their effective realizations. This reclassification principle is applied uniformly to: – running couplings and renormalization,– bulk–boundary asymmetry,– cosmological tensions,– gravitational interpretation problems,– and mathematical confusions between invariants and representations. A finite structural grammar (Q₄ with first-order cancellationand finite adjacency) is shown to be the minimal structurecompatible with observability. The result is not a modification of physical law,but a structural clarification of what type of quantityis being discussed in each context. This work corresponds to v2.1 of the series andprovides the universal classification layerthat prepares the transition to v3.0,where update order and irreversibility will be introduced.

Keywords

structural reclassification, projection grammar, renormalization reinterpretation, mathematical invariants, observer-dependent quantities, combinatorial structure, isotropic regime, structural minimality, bulk-boundary roles, invariant vs representation, misclassification in physics, order parameters

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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