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computation_limits_summary
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IndisputableMonolith.Information.ComputationLimitsStructure on GitHub at line 179.
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176/-! ## Summary: Computation Limits from RS -/
177
178/-- Summary of computation limits derived in RS. -/
179def computation_limits_summary : List String := [
180 "IC-002.1: Fundamental tick τ₀ > 0 (minimum time quantum)",
181 "IC-002.2: Maximum computation rate = 1/τ₀ > 0",
182 "IC-002.4: φ is irrational (exact simulation requires transcendental precision)",
183 "IC-002.7: No rational algorithm exactly computes φ",
184 "IC-002.8: Landauer energy k_B T ln(2) > 0 (cost to erase 1 bit)",
185 "IC-002.9: Landauer bound scales linearly with temperature",
186 "IC-002.11: Bremermann limit = 2/ℏ > 0 (operations/second/joule)",
187 "IC-002.14: φ > 1 (RS hierarchies grow exponentially)"
188]
189
190/-- IC-002 Status Certificate -/
191def ic002_certificate : String :=
192 "═══════════════════════════════════════════════════════\n" ++
193 " IC-002: COMPUTATION LIMITS — STATUS: DERIVED\n" ++
194 "═══════════════════════════════════════════════════════\n" ++
195 "✓ tick_pos: τ₀ > 0\n" ++
196 "✓ max_rate_pos: 1/τ₀ > 0\n" ++
197 "✓ computation_limits: Irrational φ (core constraint)\n" ++
198 "✓ no_exact_phi_computation: ∀ q : ℚ, q ≠ φ\n" ++
199 "✓ landauer_energy_pos: k_B T ln(2) > 0\n" ++
200 "✓ landauer_scales_with_temp: monotone in T\n" ++
201 "✓ bremermann_limit_pos: B = 2/ℏ > 0\n" ++
202 "✓ phi_powers_unbounded: φⁿ → ∞\n"
203
204end ComputationLimitsStructure
205end Information
206end IndisputableMonolith