IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.Factorization
Barrel module for the factorization layer of the primitive recognition calculus. It re-exports the master certificate that packages the algebraic factorization of recognition cost along the phi-ladder and related identities. Foundation authors cite it when they need the whole factorization package rather than a single lemma. There is no local proof body; the module is an import facade over MasterCertificate.
claimThe factorization package for primitive recognition calculus: the master certificate assembling cost factorization identities for the recognition functional $J$ (with $J(x)=(x+x^{-1})/2-1$) along self-similar $\phi$-scaled factors, together with the supporting algebraic lemmas those identities require.
background
Primitive recognition calculus sits in the Foundation layer of Recognition Science. Recognition cost is measured by the unique $J$-functional forced at T5, $J(x)=\cosh(\log x)-1$, which obeys the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. Factorization asks how that cost splits when a scale factor decomposes into $\phi$-ladder rungs or other multiplicative pieces.
This module does not introduce new definitions itself. It is the public entry point for the factorization subpackage and currently pulls in a single dependency: Factorization.MasterCertificate. That certificate is the consolidated statement that the relevant cost identities factor cleanly under the RS algebraic constraints (self-similarity at $\phi$, eight-tick octave structure upstream in the forcing chain).
Readers landing here should treat the module as the namespace root for factorization results rather than as a theorem file.
proof idea
This is a definition and re-export module, not a proof module. It has no local theorems or tactic scripts. Its sole structural role is to import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.Factorization.MasterCertificate and thereby expose the master certificate (and whatever lemmas that file closes) under the Factorization namespace. Argument structure lives entirely in the imported certificate file.
why it matters in Recognition Science
In the RS forcing architecture, factorization of recognition cost is the bridge between the abstract $J$-calculus and concrete ladder arithmetic used for masses, couplings, and tick structure. Packaging that work behind a single Foundation module keeps downstream physics developments from depending on internal lemma names inside the certificate file.
No downstream used_by edges are recorded for the module itself; consumers are expected to import this facade when they need the factorization package as a unit. The module therefore sits as organizational scaffolding above MasterCertificate, not as a new link in the T0–T8 chain. It does not itself discharge T5–T8; it only surfaces the factorization consequences of those forcing steps once the certificate is proved.
scope and limits
- Does not prove any factorization identity locally; all proof content lives in MasterCertificate.
- Does not state the T5 J-uniqueness or T6 phi-fixed-point theorems; it only re-exports factorization consequences.
- Does not derive physical constants, mass rungs, or alpha bounds.
- Does not list or guarantee a stable public API beyond the single imported certificate module.
- Does not assert completeness of the factorization package if MasterCertificate is still partial.