observer_forcing_certificate

formal source

 224    root: observer-dependence is not a quirk of quantum mechanics but
 225    a logical consequence of any framework that supports coherent
 226    recognition across multiple distinguishable events. -/
 227theorem observer_forcing_certificate :
 228    -- (1) Cost is non-negative
 229    (∀ e : RecognitionEvent, 0 ≤ e.cost) ∧
 230    -- (2) Identity event has zero cost
 231    RecognitionEvent.identity.cost = 0 ∧
 232    -- (3) Identity event is persistent
 233    IsPersistent RecognitionEvent.identity ∧
 234    -- (4) Persistent state is unique (= 1)
 235    (∀ ref : RecognitionEvent, IsPersistent ref → ref.state = 1) ∧
 236    -- (5) Cooper pairing yields persistence for any positive x
 237    (∀ x : ℝ, 0 < x → ∃ e : RecognitionEvent, IsPersistent e) ∧
 238    -- (6) Non-trivial recognition forces an observer
 239    (∀ (events : ℕ → RecognitionEvent),
 240       (∃ n m : ℕ, (events n).state ≠ (events m).state) →
 241       ∃ obs : Observer, obs.recognition.events = events) :=
 242  ⟨RecognitionEvent.cost_nonneg,
 243   RecognitionEvent.identity_cost,
 244   identity_persistent,
 245   persistent_state_unique,
 246   cooper_pairing_yields_persistent,
 247   nontrivial_recognition_forces_observer⟩
 248
 249/-! ## Module Status -/
 250
 251def observer_forcing_status : String :=
 252  "✓ RecognitionEvent (positive state, J-cost interpretation)\n" ++
 253  "✓ Identity event sits at J-cost minimum\n" ++
 254  "✓ CoherentRecognition (multi-event, non-trivial)\n" ++
 255  "✓ IsPersistent reference (Jcost = 0)\n" ++
 256  "✓ Persistent state uniqueness (forces x = 1)\n" ++
 257  "✓ Cooper pairing constructive source\n" ++