unique_vacuum_forbids_degenerate_minima
plain-language theorem explainer
A cost function possessing exactly one zero cannot admit two distinct zeros. Physicists examining electroweak vacuum stability within Recognition Science cite this to exclude metastable decay channels. The argument is a direct one-line invocation of the structural uniqueness theorem that converts framework inevitability into a single minimum.
Claim. Let $C:ℝ→ℝ$ be a cost function. If there exists a unique real number $x$ such that $C(x)=0$, then no pair of distinct reals $x,y$ exists with both $C(x)=0$ and $C(y)=0$.
background
The cost function is the J-cost of a recognition event or the derived cost of a multiplicative recognizer comparator on positive ratios. In the QFT.VacuumStability module this encodes the E-002 registry item: whether the electroweak vacuum is stable. The module states that RS inevitability (F-002) forces a unique zero-defect state, so metastability would require multiple consistent minima, which the framework forbids.
proof idea
This is a one-line wrapper that applies the structural theorem rs_vacuum_stability_structural to the supplied cost and uniqueness hypothesis.
why it matters
The declaration completes the structural half of E-002 by showing that uniqueness of the zero-cost vacuum precludes any alternative minimum. It sits downstream of the inevitability result that ties the forcing chain to a single recognizer minimum and supports the claim of absolute vacuum stability. No open scaffolding remains in this declaration.
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