def
definition
def or abbrev
foundations_status
show as:
view Lean formalization →
formal statement (Lean)
234def foundations_status : String :=
proof body
Definition body.
235 "╔════════════════════════════════════════════════════════════════╗\n" ++
236 "║ FOUNDATIONAL THEOREMS OF RECOGNITION GEOMETRY ║\n" ++
237 "╠════════════════════════════════════════════════════════════════╣\n" ++
238 "║ ║\n" ++
239 "║ PILLAR 1: Quotient Determines Observables ║\n" ++
240 "║ ✓ pillar1_quotient_determines_observables ║\n" ++
241 "║ ║\n" ++
242 "║ PILLAR 2: Information Monotonicity ║\n" ++
243 "║ ✓ pillar2_information_monotonicity ║\n" ++
244 "║ ✓ pillar2_distinguish_monotone ║\n" ++
245 "║ ✓ pillar2_composite_refines ║\n" ++
246 "║ ║\n" ++
247 "║ PILLAR 3: Finite Resolution Obstruction ║\n" ++
248 "║ ✓ pillar3_finite_resolution_obstruction ║\n" ++
249 "║ ║\n" ++
250 "║ FUNDAMENTAL THEOREM ║\n" ++
251 "║ ✓ [c₁]=[c₂] ↔ R(c₁)=R(c₂) ║\n" ++
252 "║ ✓ Extended for composite recognizers ║\n" ++
253 "║ ║\n" ++
254 "║ UNIVERSAL PROPERTY ║\n" ++
255 "║ ✓ C_R is THE canonical quotient for recognition ║\n" ++
256 "║ ✓ Surjective π, injective R̄, factorization R = R̄∘π ║\n" ++
257 "║ ║\n" ++
258 "║ EMERGENCE PRINCIPLE ║\n" ++
259 "║ Space emerges from recognition. ║\n" ++
260 "║ ║\n" ++
261 "╚════════════════════════════════════════════════════════════════╝\n"
262
263#eval foundations_status
264
265end RecogGeom
266end IndisputableMonolith