isColorParity
plain-language theorem explainer
Predicate that marks which of the nine ledger parity indices are the three color parities. Anyone citing the 4+3+2 source split of the recognition ledger uses it. The body is a pure case split on the parity-index constructors: true on the three color constructors, false elsewhere.
Claim. For a parity index $p$, the proposition $\mathrm{isColorParity}(p)$ holds if and only if $p \in \{P_C^{(1)}, P_C^{(2)}, P_C^{(3)}\}$, the three independent color-charge sign flips arising from the SU(3) Cartan subalgebra. It fails on the four spacetime parities and the two generation parities.
background
The module formalizes nine independent $\mathbb{Z}2$ parities of the recognition ledger under tick reversal and conjugation: ${P{cp}, P_{B-L}, P_Y, P_T, P_C^{(1)}, P_C^{(2)}, P_C^{(3)}, P_\tau^{(1)}, P_\tau^{(2)}}$.
These split by origin into spacetime (4), color (3), and generation (2). The color triple comes from the three independent color-charge sign flips associated with the SU(3) Cartan generators ($\lambda_3$, $\lambda_8$, and their diagonal product). The ambient type is ParityIndex, an inductive with nine constructors, one per parity.
Sibling classifiers isSpacetimeParity and isGenerationParity play the same role for the other two source blocks. Together they support the claim that every parity belongs to exactly one source category.
proof idea
Definition by exhaustive pattern match on ParityIndex. The three color constructors evaluate to True; every other constructor evaluates to False. No lemmas are invoked; the body is the classifier itself.
why it matters
This classifier is the color leg of the 4+3+2 decomposition that decodes Tesla's "magnificence of the 9" as the exact count of independent $\mathbb{Z}_2$ symmetries on the vacuum page of the ledger (module overview; theory spec lines 1189, 3332-3333).
Its sole direct consumer is parity_trichotomy, which states that every parity index falls in exactly one of the three source categories (spacetime, color, generation). That trichotomy underwrites later results on parity count, independence over $\mathbb{Z}_2$, and the claim that all nine flip under conjugation plus tick reversal. Without a crisp color predicate, the source decomposition cannot be stated as a Lean proposition.
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