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phi_not_finitely_simulable
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IndisputableMonolith.Information.SimulationHypothesisStructure on GitHub at line 179.
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176 This means RS reality contains genuinely irrational facts —
177 no finite "simulation program" can exactly reproduce φ.
178 If the universe were a finite simulation, φ-based physics would fail. -/
179theorem phi_not_finitely_simulable : ¬ ∃ q : ℚ, (q : ℝ) = phi :=
180 fun ⟨q, hq⟩ => no_exact_phi_computation q hq
181
182/-- **THEOREM IC-004.10**: Any universe that exactly reproduces RS dynamics
183 (including the irrational φ) must operate on real numbers, not rationals.
184 This constrains "simulation" substrates to real-number computers. -/
185theorem simulation_substrate_must_be_real :
186 ∀ (q : ℚ), (q : ℝ) ≠ phi := no_exact_phi_computation
187
188/-! ## Summary Certificate -/
189
190def ic004_certificate : String :=
191 "═══════════════════════════════════════════════════════════\n" ++
192 " IC-004: SIMULATION HYPOTHESIS — STATUS: DERIVED (DISSOLVED)\n" ++
193 "═══════════════════════════════════════════════════════════\n" ++
194 "✓ rs_universe_determined: ledger = reality (no extra structure)\n" ++
195 "✓ simulated_rs_is_rs: perfect simulation = RS universe\n" ++
196 "✓ simulation_unprovable: no fact of the matter in RS\n" ++
197 "✓ ledger_self_grounding: J(x) ≥ 0 (self-consistent)\n" ++
198 "✓ rs_exists_iff_zero_cost: existence = J = 0 (no external criterion)\n" ++
199 "✓ simulation_reduces_tautology: R = R₀ in RS\n" ++
200 "✓ phi_not_finitely_simulable: φ irrational → finite simulation impossible\n" ++
201 "CONCLUSION: Simulation hypothesis is semantically vacuous in RS.\n" ++
202 " The ledger IS reality; 'simulation vs real' = 'ledger vs ledger'.\n"
203
204end SimulationHypothesisStructure
205end Information
206end IndisputableMonolith