canonicalThreshold
plain-language theorem explainer
Defines the canonical comparison threshold as φ − 3/2 in RS-native units. Used when certifying that the electron spin quantum number s = 1/2 arises from a D = 2 binary recognition lattice (spinor/Clifford picture). Pure definitional abbreviation; no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity equation.
background
The module derives the electron spin quantum number from configuration dimension: $s = 1/2 = 1/D$ with $D = 2$ for the spinor representation (Clifford algebra supporting SU(2)). In Recognition Science the same $D = 2$ is read as the binary recognition lattice, so $s = 1/2^1$.
The golden ratio $\varphi$ is the unique self-similar fixed point forced by the T6 step of the unified forcing chain. Sibling definitions introduce a nonnegative domain cost on configuration data; the present constant supplies the numerical cut used to compare that cost against the spin-1/2 regime.
Imports are Mathlib, Constants (for $\varphi$), and Cost (for the J-cost infrastructure underlying domainCost).
proof idea
Bare definitional equality: the identifier is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no sorry.
why it matters
Supplies the fixed numerical yardstick against which domain-cost comparisons are made when certifying $s = 1/2$ from ConfigDim. Siblings canonicalThreshold_pos and the SpinQuantumNumCert / cert package consume it to obtain a positive threshold and an inhabited certificate that the spin quantum number matches the D = 2 lattice prediction. Sits inside the broader RS program that forces $\varphi$ (T6), the eight-tick octave (T7), and spatial $D = 3$ (T8), here specialized to the internal spinor dimension $D = 2$.
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