module module high

`IndisputableMonolith.Foundation.ObserverForcing`

The ObserverForcing module defines recognition events as states with positive cost under recognition and introduces related notions including persistence, coherent recognition, and cooper pairing. Researchers constructing the foundational layer of Recognition Science cite these objects when building the T0-T8 forcing chain. The module is definitional, establishing basic cost properties and uniqueness lemmas without complex derivations.

claimA recognition event is a state $x$ such that $\mathrm{cost}(x) > 0$. Persistent states satisfy $\mathrm{IsPersistent}(x)$ and cooper pairs yield zero cost under the recognition cost function.

background

The module imports IndisputableMonolith.Cost, which supplies the non-negative recognition cost function. It defines RecognitionEvent as a positive state under recognition, together with CoherentRecognition, IsPersistent, identity_persistent, and cooper_pair_cost_zero. The local theoretical setting is the foundation layer of Recognition Science, where recognition events form the basic units from which the Recognition Composition Law and the phi-ladder are derived.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the core definitions for recognition events that underpin observer forcing and feed into the unified forcing chain (T5 J-uniqueness through T8 D=3). It provides the objects referenced when constructing constants in RS-native units and the mass formula on the phi-ladder.

scope and limits

Does not prove any results involving the J function or Recognition Composition Law.
Does not address spatial dimensions, the eight-tick octave, or the alpha band.
Does not contain hypothesis interfaces or scaffolding stubs.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Cost module_import

declarations in this module (20)

structure RecognitionEvent L44
def cost L51
theorem cost_nonneg L54
def identity L58
theorem identity_cost L63
structure CoherentRecognition L74
def IsPersistent L90
theorem identity_persistent L93
theorem persistent_state_unique L97
theorem persistent_event_state_eq_identity L105
theorem cooper_pair_cost_zero L117
theorem cooper_pairing_yields_persistent L124
structure Observer L141
theorem reference_zero_cost L148
theorem reference_unit_state L153
theorem has_distinguishable_events L158
theorem nontrivial_recognition_forces_observer L175
theorem cooper_paired_reference_yields_observer L194
theorem observer_forcing_certificate L227
def observer_forcing_status L251