recognizer_refinement
plain-language theorem explainer
Composing two recognizers on a shared configuration space yields a finer observable quotient: the composite quotient surjects onto each component quotient. Anyone citing recognition composition or observable refinement at the T0/T4 layer points here. The declaration is a one-line public alias of the RecogGeom refinement theorem.
Claim. For recognizers $R_1$ and $R_2$ on a common configuration carrier, the composite quotient $C_{R_{12}}$ admits surjective maps onto both component quotients $C_{R_1}$ and $C_{R_2}$. Equivalently, adjoining more recognizers strictly refines the observable structure (finer partition of configurations).
background
RecognitionCore is the public aggregator for the recognizer / signature layer of the forcing chain (T0–T4). A recognizer is a map from configurations to an event space; its kernel induces an indistinguishability quotient $C_R$, the observable structure admitted by that recognizer. Gauge is absence of a distinguishing recognition act: states related by the quotient cannot be separated by the admitted family.
Composition of recognizers is the geometric operation that builds a joint observable from two (or more) component recognizers. The upstream Refinement Theorem states the fundamental fact: the composite quotient refines both components. Explicitly, there are surjective maps $\pi_1 : C_{R_{12}} \to C_{R_1}$ and $\pi_2 : C_{R_{12}} \to C_{R_2}$. Finer means every $R_1$-class (resp. $R_2$-class) splits into one or more composite classes; no information is lost, and joint recognition can only distinguish more.
This module packages that theorem as a stable citation name alongside forced-quotient, completeness-via-separation, and lattice-from-kernel results.
proof idea
One-line public alias: the abbrev is definitionally equal to RecogGeom.refinement_theorem. That theorem is itself a pair of surjectivity lemmas for the left and right quotient maps of a composite recognizer, packaged as a conjunction. No extra argument is introduced at this layer.
why it matters
Listed among RecognitionCore's public citation targets: composing recognizers refines the quotient, so more recognizers give a finer observable structure. That is the geometric content behind "a single Boolean observable is atomic, not complete; physical content is carried by the admitted recognizer family." It sits at the T0/T4 recognizer layer that precedes J-uniqueness (T5), $\varphi$ (T6), the eight-tick octave (T7), and $D=3$ (T8).
Downstream use is presently empty in the graph, but the name is the stable entry point for any argument that enlarges a recognizer family and needs the induced quotient to get finer (signature completeness, separating families, lattice refinement). It pairs with the magnitude-of-mismatch / forces infrastructure that underwrites single-valued comparison on carriers, and with the composition package that also treats associativity of recognition composition.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.