IndisputableMonolith.Foundation.DAlembert.FactorizationForcing
The FactorizationForcing module packages the FactorizationAssociativityGate along with the statements gate_forces_bilinear_family and gate_forces_rcl. Researchers deriving the Recognition Composition Law from ledger substitutivity cite this gate as the bridge object. The module consists entirely of definitions and statement packaging with no internal proofs.
claimLet $P(u,v)$ be a combiner. The FactorizationAssociativityGate is the conjunction of symmetry, right-affine structure, zero-boundary condition, and unit-diagonal condition on $P$. Under the gate, $P(u,v)$ equals the RCL polynomial $2uv + 2u + 2v$.
background
The module belongs to the DAlembert factorization layer and imports only Mathlib. Its single doc-comment describes it as the packaged combiner gate for the factorization/associativity bridge. Sibling declarations inside the module are FactorizationAssociativityGate together with the two forcing statements gate_forces_bilinear_family and gate_forces_rcl.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the gate used by LedgerFactorization to obtain the factorization property and hence the Recognition Composition Law from contextual substitutivity, and by RightAffineFromFactorization to close Gap 4 by forcing the combiner to the RCL polynomial $2uv + 2u + 2v$. It therefore occupies the central bridge position between ledger primitives and the RCL.
scope and limits
- Does not prove that the gate holds for any concrete ledger.
- Does not derive the RCL without the gate assumptions.
- Does not address the phi-ladder, mass formula, or T0-T8 chain.
- Does not contain the full proof of right-affine forcing.