fission_transmutation_from_ledger

formal source

 224
 225/-- The RS fission transmutation theorem.
 226    Derives key properties of transmutation from J-cost structure. -/
 227theorem fission_transmutation_from_ledger :
 228    (∀ cfg : NuclearConfig, cfg.ratio ≠ 1 → 0 < nuclearCost cfg) ∧
 229    (∃ cfg : NuclearConfig, nuclearCost cfg = 0) ∧
 230    (∀ cfg : NuclearConfig, ∃ path : TransmutationPath,
 231      path.start = cfg ∧ nuclearCost path.finish = 0) := by
 232  exact ⟨transmutation_cost_pos, ⟨stable_config, stable_config_zero_cost⟩,
 233         stable_end_state_exists⟩
 234
 235/-- Alias for registry lookup. -/
 236theorem fission_transmutation_structure :
 237    (∃ cfg : NuclearConfig, nuclearCost cfg = 0) :=
 238  ⟨stable_config, stable_config_zero_cost⟩
 239
 240/-- Certificate: EN-006 Fission Product Transmutation — DERIVED -/
 241def en006_certificate : String :=
 242  "═══════════════════════════════════════════════════════════\n" ++
 243  "  EN-006: FISSION PRODUCT TRANSMUTATION — STATUS: DERIVED\n" ++
 244  "═══════════════════════════════════════════════════════════\n" ++
 245  "✓ nuclear_cost_nonneg:             J(cfg) ≥ 0 for all configs\n" ++
 246  "✓ nuclear_cost_zero_iff_stable:    J(cfg) = 0 ↔ cfg is doubly-magic\n" ++
 247  "✓ transmutation_cost_pos:          J(fission product) > 0\n" ++
 248  "✓ transmutation_reduces_cost:      each step: J(final) ≤ J(initial)\n" ++
 249  "✓ stable_is_optimal:              J(stable) = 0 ≤ J(cfg)\n" ++
 250  "✓ stable_end_state_exists:        ∀ fission product, ∃ path to stability\n" ++
 251  "✓ strict_transmutation_progress:  unstable → always a better config exists\n" ++
 252  "✓ efficiency_bounded:             efficiency ∈ [0, 1]\n" ++
 253  "✓ perfect_transmutation_efficiency: transmute to stable → 100% efficiency\n" ++
 254  "✓ fission_transmutation_from_ledger: complete theorem\n" ++
 255  "Key RS insight: Transmutation = J-cost descent; doubly-magic = attractors\n" ++
 256  "Optimal path: steepest descent in J-cost landscape to stable end\n"
 257