TransmutationStep
TransmutationStep encodes a nuclear configuration change from initial to final ratio such that J-cost does not increase. Nuclear engineers modeling waste reduction in Recognition Science would cite it to formalize each descent step toward stability. The definition is introduced as a record whose sole constraint is the inequality nuclearCost final ≤ nuclearCost initial.
claimA transmutation step consists of nuclear configurations $C_i$ and $C_f$ (each with positive stability ratio) satisfying $J(C_f) ≤ J(C_i)$, where $J$ is the J-cost measuring deviation from the stable point at ratio 1.
background
NuclearConfig is the structure holding a positive real ratio x, with x = 1 denoting a stable doubly-magic nucleus and x ≠ 1 an unstable fission product. The function nuclearCost extracts the J-cost of this ratio, serving as the instability measure in the EN-006 module on fission-product transmutation. The module derives transmutation pathways as sequences of recognition events that descend this cost toward local minima at shell closures.
proof idea
The structure is defined directly by its three fields: initial configuration, final configuration, and the field reduces_cost carrying the inequality nuclearCost final ≤ nuclearCost initial. No tactics or lemmas are applied; the declaration is a pure record type.
why it matters in Recognition Science
TransmutationStep supplies the inductive step for the EN-006 theorems on cost descent. It is invoked by transmutation_reduces_cost to project the inequality, by cost_reduction_bounded to bound the reduction by the initial cost, and by strict_transmutation_progress to witness strict progress from any unstable ratio. In the framework it realizes the cost-monotone descent required by J-uniqueness and the recognition composition law, directing pathways to zero-cost attractors.
scope and limits
- Does not assert existence of a transmutation step for a given initial configuration.
- Does not encode the physical reaction mechanism or energy barrier.
- Does not guarantee that iterated steps terminate at a stable nucleus.
- Does not constrain the path taken between initial and final ratios.
formal statement (Lean)
94structure TransmutationStep where
95 initial : NuclearConfig
96 final : NuclearConfig
97 /-- Each step reduces J-cost. -/
98 reduces_cost : nuclearCost final ≤ nuclearCost initial
99
100/-- **THEOREM EN-006.4**: Transmutation reduces or maintains cost. -/