canonicalThreshold
plain-language theorem explainer
The canonical materials threshold is the real constant φ − 3/2 in RS-native units. Materials and condensed-matter workers in the RS stack cite it as the fixed cutoff against which domain costs are compared. It is a bare definitional assignment, not a derived inequality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio fixed point of self-similarity.
background
Recognition Science forces a unique dimensionless scale factor $\varphi$ as the self-similar fixed point (forcing step T6). Once the coherence energy $E_{\mathrm{coh}}$ is pinned by the electron mass, every materials cutoff in the stack is required to be a pure function of $\varphi$ with no free parameters.
This module packages structural materials statements under that calibration. A companion domain-cost functional (from the Cost import) measures how far a configuration sits from the recognition minimum; the present constant is the numerical gate those costs are compared against. Sibling lemmas record non-negativity of the cost and positivity of the threshold itself.
proof idea
Definitional abbreviation only: the real is assigned as $\varphi$ minus three-halves. No tactics, no lemmas, no proof obligations.
why it matters
Gives the single numerical gate used by positivity and certificate objects in the same module (threshold positivity and the structural materials certificate). Anchors materials cutoffs to the T6 forcing of $\varphi$, so the stack stays parameter-free after $E_{\mathrm{coh}}$ is set once by the electron mass. Without a named threshold, domain-cost comparisons would re-introduce fitted scales, breaking the structural claim of the module.
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