IndisputableMonolith.Foundation.ObserverForcing
ObserverForcing defines recognition events as positive states under recognition and equips them with cost, coherence, and persistence properties. It extends the Cost module with sibling definitions for identity, persistent states, and cooper pairs. Researchers formalizing observer models in Recognition Science reference these when constructing forcing structures.
claimA recognition event $e$ is a positive state under recognition with associated cost function satisfying $c(e) > 0$. Persistent states are unique and cooper pairing yields zero-cost persistent states.
background
The module belongs to the Foundation domain and imports Mathlib together with IndisputableMonolith.Cost. Its single doc comment states that a recognition event is a positive state under recognition. Sibling definitions introduce cost, identity, CoherentRecognition, IsPersistent, identity_persistent, persistent_state_unique, cooper_pair_cost_zero, and cooper_pairing_yields_persistent, all resting on the imported cost structures.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the basic objects for recognition events that support higher-level development in the Recognition Science framework, including the forcing chain steps. No direct used_by entries appear in the supplied head.
scope and limits
- Does not derive J-uniqueness or the phi fixed point.
- Does not establish the eight-tick octave or D=3.
- Does not compute RS-native constants or mass formulas.
- Does not address Berry creation thresholds or alpha bounds.
depends on (1)
declarations in this module (20)
-
structure
RecognitionEvent -
def
cost -
theorem
cost_nonneg -
def
identity -
theorem
identity_cost -
structure
CoherentRecognition -
def
IsPersistent -
theorem
identity_persistent -
theorem
persistent_state_unique -
theorem
persistent_event_state_eq_identity -
theorem
cooper_pair_cost_zero -
theorem
cooper_pairing_yields_persistent -
structure
Observer -
theorem
reference_zero_cost -
theorem
reference_unit_state -
theorem
has_distinguishable_events -
theorem
nontrivial_recognition_forces_observer -
theorem
cooper_paired_reference_yields_observer -
theorem
observer_forcing_certificate -
def
observer_forcing_status