stable_config_zero_cost
The stable nuclear configuration, defined as the ratio-1 state, carries exactly zero J-cost. Nuclear engineers working on transmutation pathways cite this result to anchor the global minimum of the cost landscape. The proof is a one-line term that unfolds the nuclearCost definition and invokes the unit lemma for Jcost at argument 1.
claimLet $c$ be the stable nuclear configuration with ratio $1$. Then the J-cost of $c$ satisfies $J(c) = 0$.
background
In the EN-006 module, nuclear configurations are modeled by positive real ratios, with J-cost serving as the instability measure. The definition nuclearCost(cfg) extracts Jcost of the ratio field, where Jcost(x) = (x-1)^2/(2x) from the upstream Cost module. The stable_config is the concrete ratio-1 object that represents a doubly-magic nucleus (local zero-cost attractor). The module derives transmutation as cost-reducing paths on this J-cost surface, with doubly-magic nuclei as the terminal minima.
proof idea
The term proof unfolds nuclearCost and stable_config to reduce the goal to Jcost 1 = 0, then applies the lemma Jcost_unit0 (which holds by direct simplification of the Jcost expression). No further tactics are required.
why it matters in Recognition Science
This theorem (EN-006.7) supplies the zero-cost endpoint required by downstream results such as stable_end_state_exists, fission_transmutation_from_ledger, and perfect_transmutation_efficiency. It closes the local minimum claim for the stable configuration inside the J-cost geodesic picture of transmutation. The result sits inside the Recognition Science cost structure (T5 J-uniqueness) and confirms that the ratio-1 fixed point is the global attractor for fission-product decay chains.
scope and limits
- Does not compute J-cost values for specific isotopes.
- Does not prove uniqueness of the ratio-1 minimum among all nuclear ratios.
- Does not address time-dependent dynamics of actual fission events.
- Does not extend to non-positive ratios or non-nuclear domains.
Lean usage
exact ⟨stable_config, stable_config_zero_cost⟩formal statement (Lean)
132theorem stable_config_zero_cost : nuclearCost stable_config = 0 := by
proof body
Term-mode proof.
133 unfold nuclearCost stable_config
134 exact Jcost_unit0
135
136/-- **THEOREM EN-006.8**: Stable configuration is optimal (minimal cost). -/