stable_config
The stable configuration is the nuclear state whose ledger ratio equals 1, marking the zero point of J-cost for doubly-magic nuclei. Modelers of transmutation sequences cite this object as the terminal attractor under cost descent. The definition packages the real number 1 with its positivity proof inside the NuclearConfig structure.
claimThe stable configuration is the element $N$ of the structure NuclearConfig whose stability ratio equals 1.
background
NuclearConfig structures a nuclear state by its positive real ledger ratio x, where the value x = 1 identifies doubly-magic nuclei at local J-cost minima. The module EN-006 derives transmutation pathways as sequences that reduce total J-cost toward this minimum, with the cost function imported from the multiplicative recognizer and observer forcing layers. Upstream results establish that cost is non-negative, with equality to zero only at the stable ratio.
proof idea
The definition is a direct structure constructor that packages the real number 1 together with the proof that it is positive. No lemmas are applied.
why it matters in Recognition Science
This definition supplies the zero-cost attractor required by the fission transmutation theorems, including fission_transmutation_from_ledger and stable_end_state_exists. It realizes the local minimum at doubly-magic nuclei predicted by the J-cost barrier structure. The construction closes the existence part of the optimal transmutation path to stability.
scope and limits
- Does not identify specific isotopes or their measured binding energies.
- Does not prove uniqueness of the zero-cost state beyond the ratio model.
- Does not extend to continuous transmutation dynamics or time evolution.
Lean usage
theorem example_use : ∃ cfg : NuclearConfig, nuclearCost cfg = 0 := ⟨stable_config, stable_config_zero_cost⟩formal statement (Lean)
129def stable_config : NuclearConfig := ⟨1, one_pos⟩
proof body
Definition body.
130
131/-- **THEOREM EN-006.7**: The stable configuration has zero cost. -/