Structural_Reclassification_Principle__Isotropic_Deformations_and_the_Unified_Resolution_of_Physical_and_Mathematical_Misclassifications

This paper develops a general structural reclassification principle
for physical and mathematical quantities that have long been treated
as distinct, dynamical, or ontologically independent.

Building on the projection–exclusion grammar established in v1.0
and 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 physics
and mathematics arise from systematic misclassification between
invariant 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 cancellation
and finite adjacency) is shown to be the minimal structure
compatible with observability.

The result is not a modification of physical law,
but a structural clarification of what type of quantity
is being discussed in each context.

This work corresponds to v2.1 of the series and
provides the universal classification layer
that prepares the transition to v3.0,
where update order and irreversibility will be introduced.