current_transform_provenance
plain-language theorem explainer
The active prime-coordinate transform provenance is definitionally the native δ-readout choice (factorization descent). Anyone assembling the factorization goal-closure certificate cites this equality. The proof is pure reflexivity against the current provenance definition.
Claim. The currently selected transform provenance for the prime-coordinate factorization equals the native $\delta$-readout constructor (the choice obtained by prime/factorization descent).
background
In the Primitive Recognition Calculus factorization layer, solving is rephrased as coordinate readout once a residual commitment and a transform provenance are fixed. Transform provenance records which geometric or algebraic route produced the prime-coordinate chart; the native $\delta$-readout option is the descent path that reads factors directly from the residual coordinate.
The module packages a small certificate that the residual is named, exact, closed, and would recover a prime divisor. Upstream, currentPrimeCoordinateTransformProvenance is defined to be exactly that native $\delta$-readout constructor. A separate residual target (signed genesis residual against CODATA) sits nearby in the constants stack but is not needed for this equality.
Local setting: GoalClosure wires named residual commitments to transform provenance so that factor recovery becomes immediate once the readout commitment is supplied.
proof idea
One-line term proof by rfl. The left-hand side is the definition of the current provenance, whose body is already the native $\delta$-readout constructor, so definitional equality closes the goal with no lemmas.
why it matters
This equality is one of the five fields of goal_closure_certificate, which builds a GoalClosureCertificate recording residual naming, transform provenance, exactness, closure, and prime-divisor recovery. Without a certified provenance tag, the certificate cannot claim that solving has become coordinate readout.
In the broader Recognition stack this is bookkeeping rather than a forcing-chain step (T5–T8), but it locks the factorization readout path to the native $\delta$ choice so downstream residual and divisor theorems share a single provenance. It closes the provenance slot of the goal-closure interface; no open scaffold remains on this declaration.
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