PrimeCoordinateResidualName
plain-language theorem explainer
Four-tag enumeration of residual labels admitted at the D4 finish line of prime-coordinate factorization. Downstream goal-closure code cites it to name which residual is under commitment (historically the prime-coordinate readout). The declaration is a plain inductive type with decidable equality and a printer; there is no proof obligation.
Claim. There is a finite set of residual name tags at the D4 finish line: prime-coordinate readout, character-spectrum readout, physical-period readout, and classical factorization transport. Equality of tags is decidable.
background
Module GoalClosure sits in the Primitive Recognition Calculus factorization stack. It records which residual is still named at the D4 finish line and certifies that the corresponding readout commitment has been discharged by a native-choice transform rather than a weaker benchmark.
A residual here is a named discrepancy between a Recognition-derived quantity and an external target (compare the alpha-genesis residual alphaInv - alpha_inv_CODATA, confined to a certified band). The prime-coordinate path is the original D4 commitment: supplying it means supplying the $\delta$-prime-coordinate transform, not a heuristic stand-in.
Upstream factorization material (prime-coordinate transform) and the broader forcing/self-reference setting fix the vocabulary; this declaration only classifies which residual name is in play.
proof idea
No proof. The declaration is an inductive type with four nullary constructors and derived DecidableEq and Repr. Downstream code selects a constructor (currently the prime-coordinate readout) as the live residual label.
why it matters
Gives a typed vocabulary for residual labels so goal-closure certificates can name exactly which D4 commitment is closed. The sole immediate consumer is currentPrimeCoordinateResidual, which retains the historical default (prime-coordinate readout) and is documented as closed by the native-choice transform deltaPrimeCoordinateTransform_classicalTransport.
In the Recognition stack this is bookkeeping at the factorization finish line, not a new physical law. It keeps the D4 residual commitment unambiguous while the classical factorization transport and related readouts (character spectrum, physical period) remain available as alternate tags. It does not itself touch T5–T8, the RCL, or the alpha band; those enter only through the transforms the commitment points at.
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