theorem
proved
term proof
cooper_paired_reference_yields_observer
show as:
view Lean formalization →
formal statement (Lean)
194theorem cooper_paired_reference_yields_observer
195 (events : ℕ → RecognitionEvent)
196 (h_nontrivial : ∃ n m : ℕ, (events n).state ≠ (events m).state)
197 (x : ℝ) (hx : 0 < x) :
198 ∃ obs : Observer, obs.recognition.events = events := by
proof body
Term-mode proof.
199 obtain ⟨ref, hpref⟩ := cooper_pairing_yields_persistent x hx
200 refine ⟨{
201 recognition := {
202 events := events,
203 reference := ref,
204 nontrivial := h_nontrivial
205 },
206 persistent := hpref
207 }, rfl⟩
208
209/-! ## §8. Master Certificate -/
210
211/-- **Observer-Forcing Master Certificate.** Six structural facts
212 proved together:
213
214 1. Recognition events have non-negative J-cost.
215 2. The identity event has zero cost.
216 3. The identity event is persistent.
217 4. Any persistent reference has state `x = 1`.
218 5. Cooper pairing constructs a persistent event from any positive `x`.
219 6. Every non-trivial recognition stream forces an observer.
220
221 Taken together, these six facts establish that the observer is not
222 an external posit but a structural consequence of any non-trivial
223 coherent recognition. The QM measurement problem dissolves at its
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. -/