RecognitionStructure
plain-language theorem explainer
RecognitionStructure supplies the minimal interface consisting of a carrier type U together with a binary relation R on U. Downstream constructions in the forcing chain such as Chain, Ledger, and AtomicTick cite it as the root type parameter; the recognition_forcing_complete master theorem also depends on it. The declaration is a bare structure with zero proof obligations or additional axioms.
Claim. A recognition structure consists of a type $U$ equipped with a binary relation $R : U → U → Prop$.
background
The Recognition module opens with the T1 meta-principle that nothing can recognize itself and immediately defines RecognitionStructure as the carrier for that principle. Upstream stubs appear in Chain (minimal standalone version) and in Foundation.RecognitionForcing (with explicit self-recognition and symmetry axioms). The local setting is the Recognition Science derivation in which recognition relations are the primitive data from which J-cost, defect distance, and the phi-ladder are later forced.
proof idea
Direct structure declaration; zero proof body, zero tactics, zero lemmas applied.
why it matters
This is the root interface that feeds Chain, Ledger, AtomicTick, and the recognition_forcing_complete master theorem. It instantiates the T1 (MP) step of the forcing chain and supplies the minimal scaffolding required for standalone compilation of the eight-tick octave and D=3 constructions. No open questions remain at this level; it is fully discharged by the structure definition itself.
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