module module high

`IndisputableMonolith.Foundation.ObserverForcing`

ObserverForcing defines recognition events as positive states under recognition and supplies supporting objects such as cost and persistence. It extends the Cost module inside the Foundation domain. Researchers building the base layer of Recognition Science cite these objects when constructing observer forcing. The module consists entirely of definitions and short lemmas.

claimA recognition event is a positive state under recognition. The associated cost function is nonnegative and the identity state is persistent.

background

The module belongs to the Foundation domain and imports only Mathlib together with IndisputableMonolith.Cost. Cost supplies the underlying cost function used to measure recognition. The supplied doc-comment states that a recognition event is a positive state under recognition. Sibling declarations introduce RecognitionEvent, cost_nonneg, identity, IsPersistent, and cooper_pair_cost_zero.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

These definitions supply the observer concept required by later results on coherent recognition and persistent states. They sit early in the forcing development and prepare the ground for theorems that link recognition events to the single functional equation.

scope and limits

Does not contain any theorem proofs.
Does not import modules beyond Mathlib and Cost.
Does not reference the phi ladder or eight-tick octave.
Does not connect to physical constants such as alpha or G.

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