IndisputableMonolith.RecogSpec.Universe
The RecogSpec.Universe module establishes the carrier types that underpin the recognition universe in Recognition Science. It introduces the base carrier type, its wrapper, and the equivalence relating them to support later constructions such as the J-function and phi-ladder. The module contains only definitions and imports Mathlib for type-theoretic primitives. Researchers building the forcing chain or recognition composition law cite these objects as the starting point for the specification layer.
claimThe module specifies the universe via carrier type $C : Type$, wrapper $W : C → Type$, and equivalence relation $∼$ on carriers.
background
The module sits in the RecogSpec domain of Recognition Science, the layer that specifies the universe before the forcing chain derives physical constants from the single functional equation. It introduces the carrier type as the underlying object for all recognition structures and the wrapper as the packaging that allows composition. The module imports only Mathlib and declares no hypotheses, theorems, or numerical constants.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the carrier definitions that feed the T0–T8 forcing chain, J-uniqueness, and the self-similar fixed point phi. It therefore supports the recognition composition law, the eight-tick octave, D = 3, and the native-unit constants c = 1, ħ = phi^{-5}, G = phi^5 / π. As the root of the RecogSpec domain it closes the base scaffolding for the mass formula on the phi-ladder and the Berry creation threshold.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not reference the J-cost function or defect distance.
- Does not specify numerical values for constants such as alpha inverse.
- Does not implement the recognition composition law.