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def definition def or abbrev

foundations_status

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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

depends on (20)

Lean names referenced from this declaration's body.