Abstract

This record provides a public summary of an operational program to test the Gauge Paradox Theory inside Shinichi Mathematics (SM). The approach treats numbers as a language and studies emergence as a relational, gauge-aware effect between channels (e.g., heat → light). We present the conceptual building blocks—state space D=[0,∞)×S1\mathcal{D}=[0,\infty)\times S^1D=[0,∞)×S1, a Z2\mathbb{Z}_2Z2 gauge (Sign-as-Phase), and a radius invariant A2=NA^2=NA2=N—and describe, at a high level, how a “native influence region” would be identified in experimental maps. What this is not. This is not an attempt to overthrow existing scholarship; it is a conceptual and ethical invitation to test specific qualitative predictions. To avoid premature or unsafe deployment, implementation-critical details (exact thresholds, decision inequalities, morphology parameters, and reduction pipelines) are withheld here. Qualitative predictions. (1) A constructive band that drifts monotonically with frequency; (2) monotone temperature scaling of a native influence measure; (3) systematic material dependence (spatial slope / temporal lag); (4) gauge redundancy: absolute sign is unobservable, only relative π\piπ-phase flips matter. Access to methods (on request). Complete preregistered protocols and analysis assets are available to qualified laboratories upon request under an ethical-use agreement. Interested groups are invited to contact the author. Ethical Use Notice. Use is prohibited for weapons development, surveillance targeting, psychological manipulation, coercive control, or discriminatory purposes. Requests will be screened case-by-case with human-rights and privacy considerations.