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IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.Factorization.GoalClosure

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Module that freezes the residual vocabulary and readout commitments allowed when the prime-coordinate factorization path reaches the D4 finish line. It packages named residuals, transform provenance, and a GoalClosureCertificate so MasterCertificate can treat the factorization goal as closed. The content is mostly inductive names, exactness lemmas, and a single certificate constructor rather than a deep analytic argument.

claimAt the D4 finish line of the prime-coordinate factorization path, only a fixed finite set of residual names is admitted. A readout commitment records that the current residual is one of those names, that the prime-coordinate transform provenance is the declared one, and that the commitment recovers the prime divisor exactly. A goal-closure certificate asserts that this commitment is exact and closed.

background

In the Primitive Recognition Calculus factorization stack, integers (or rung data) are rewritten in a prime-coordinate chart so that divisor structure becomes a residual readout rather than an open search. The upstream module PrimeCoordinateTransform supplies the change of coordinates and the residual that remains after the transform.

This module sits at the D4 finish line: the stage where that residual must be named from a closed list and tied to a provenance record. Sibling definitions introduce the residual name type, the current residual, the readout commitment (exactness and closedness), transform provenance, and the recovery statement that the commitment still yields the prime divisor.

The local theoretical setting is bookkeeping for a forcing-style factorization goal: once the residual is one of the allowed D4 names and the commitment lemmas hold, downstream certificates may treat the goal as discharged without reopening the coordinate transform.

proof idea

Definition-and-certificate module, not a long analytic development. It fixes the residual name enum and the current residual pointer, defines the readout commitment and provenance records, then proves thin lemmas: the residual is the named one, the commitment is exact, the commitment is closed, provenance matches the current transform, and the commitment recovers the prime divisor. GoalClosureCertificate and goal_closure_certificate bundle those facts into a single exportable witness for importers.

why it matters in Recognition Science

MasterCertificate imports this module to obtain a finished D4 factorization witness rather than an open residual. Without a closed residual vocabulary and an exact readout commitment, the prime-coordinate path could not be sealed inside the broader Primitive Recognition Calculus certificate chain.

In Recognition Science terms this is infrastructure under the foundation factorization layer: it does not itself force phi, the eight-tick octave, or D = 3, but it makes the prime-coordinate divisor readout a checkable closed object so higher certificates can cite a single goal-closure fact. The parent surface is MasterCertificate; the paper-facing role is the D4 finish-line residual lock.

scope and limits

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