module module moderate

`IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.Factorization.MasterCertificate`

Ledger module that packages the factorization character-theory lane into a single master certificate. It re-exports coordinate uniqueness, period existence and factor structure, even-period gap control, substrate dichotomy, and goal closure. Downstream Factorization imports this bundle rather than the individual submodules. No new mathematics is proved here; the file is an aggregation and status surface.

claimMaster certificate for the $\Delta$-factorization character-theory lane: the conjunction of coordinate uniqueness, existence and factorisation of the recognition period, even-period gap bounds, substrate dichotomy, and goal-closure statements, exposed as a single named certificate object for the parent Factorization layer.

background

Primitive Recognition Calculus studies how recognition cost and discrete period structure force a unique coordinate presentation of the recognition substrate. The factorization lane asks when a recognition period factors, how even gaps behave, and whether the substrate splits into a controlled dichotomy.

This module sits under Foundation.PrimitiveRecognitionCalculus.Factorization. Its imports are the six working submodules of that lane: GoalClosure, CoordinateUniqueness, PeriodFactor, PeriodExistence, EvenPeriodGap, and SubstrateDichotomy. The module doc frames the file as the current theorem ledger for the factorization character-theory lane, not as a place where new lemmas are derived.

Sibling names point to a concrete certificate object (DeltaFactorizationCharacterTheoryCertificate and its value-level counterpart). In RS terms this ledger is infrastructure toward the forcing chain landmarks that pin period structure (eight-tick octave) and spatial dimension, once the character-theoretic factorization facts are closed.

proof idea

This is an aggregation module, not a proof module. It imports the six factorization submodules and surfaces a master certificate (and its value) that records the current proved status of the character-theory lane. There is no independent tactic script or algebraic reduction here; the logical content lives in the imported GoalClosure, CoordinateUniqueness, Period*, EvenPeriodGap, and SubstrateDichotomy developments.

why it matters in Recognition Science

The parent Factorization module imports this ledger, so any consumer of the factorization character-theory package depends on MasterCertificate as the single entry point. That keeps the lane's status auditable: coordinate uniqueness, period existence/factor, even-period gap, substrate dichotomy, and goal closure appear together rather than as a scattered import list.

In the broader Recognition Science foundation, factorization of the recognition period and uniqueness of coordinates are prerequisites for clean statements about discrete octave structure and substrate dimension. This file does not itself discharge T7 (eight-tick) or T8 ($D=3$); it only certifies how far the character-theory factorization lane has been closed so those later forcing steps can cite a stable bundle.

scope and limits

Does not prove new factorization lemmas; only aggregates imported submodules.
Does not by itself establish the eight-tick octave or $D=3$.
Does not replace GoalClosure or the individual period/coordinate theorems.
Does not assert completeness of the character-theory lane beyond the imported certificates.
Does not define physical constants or mass-ladder formulae.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.Factorization module_import

depends on (6)

Lean names referenced from this declaration's body.