IndisputableMonolith.Verification.Exclusivity.NontrivialityShim
Shim module that packages nontriviality hypotheses for the exclusivity verification stack. It sits on the shared physics-framework definitions and supplies the minimal non-vacuity interface so NoAlternatives and necessity arguments do not import each other. Researchers tracing the uniqueness chain cite it when they need the standing assumption that the framework is not the empty theory. Structure is definitional and interface-only; no deep proof work lives here.
claimA thin interface layer asserting that a physics framework $F$ is nontrivial: it admits at least one admissible model (or equivalent non-vacuity condition) used by exclusivity and necessity arguments, built on the shared framework definitions.
background
Exclusivity verification aims to show that Recognition Science has no viable alternative frameworks once the forcing chain and cost axioms are fixed. That argument splits into "no alternatives" results and necessity results; those two directions must not import each other.
The upstream Framework module supplies only the shared physics-framework definitions for both sides: "This module contains shared definitions used by both NoAlternatives and the necessity proofs. This breaks circular dependencies by providing only the core framework definitions."
NontrivialityShim sits on that shared base. It isolates the standing non-vacuity requirement (the framework is not the empty theory, admits an admissible model, or an equivalent Prop) so exclusivity lemmas can assume nontriviality without dragging in the full necessity or NoAlternatives development.
proof idea
This is a shim and interface module, not a theorem module. It imports Mathlib and the shared Framework definitions, then exposes nontriviality as a lightweight Prop or hypothesis bundle. Expect abbreviations, hypothesis interfaces, or thin wrappers rather than multi-step tactic proofs. Any lemma here is at most a one-line re-export or packaging of a Framework-level condition.
why it matters in Recognition Science
Exclusivity is only meaningful for nontrivial frameworks: without a non-vacuity gate, uniqueness collapses to a statement about the empty theory. This module keeps that gate separate from both NoAlternatives and the necessity proofs, preserving the acyclic import graph started by Framework.
No downstream used_by edges are recorded on the page yet, so its consumers are the exclusivity verification developments that import the shim rather than a named parent theorem in the graph. In the broader RS picture it supports the uniqueness side of the forcing story (T0–T8 and the Recognition Composition Law) by ensuring those uniqueness claims are stated only for frameworks that actually carry physics content.
scope and limits
- Does not prove exclusivity or NoAlternatives; only packages nontriviality.
- Does not derive nontriviality from the forcing chain T0–T8.
- Does not define the full physics framework; that lives in Framework.
- Does not discharge necessity proofs or close any sorry in sibling modules.
- Does not assert empirical claims about the Standard Model or measured constants.