transmutation_efficiency
plain-language theorem explainer
Transmutation efficiency is the fractional J-cost reduction from one nuclear configuration to another, returning 1 when the initial state is already stable. Nuclear engineers modeling waste transmutation in the Recognition Science setting cite the definition to quantify descent along cost geodesics. It is realized by a direct case split on whether the initial nuclearCost is zero.
Claim. Let $c$ denote nuclear cost on configurations. For configurations initial and final the transmutation efficiency equals $1$ if $c$(initial)$=0$, otherwise $(c$(initial)$-c$(final$))/c$(initial$)$.
background
NuclearConfig is the structure of a positive real ratio $x$, with $x=1$ marking doubly-magic stable nuclei and $x≠1$ marking unstable fission products. nuclearCost(cfg) is defined as the J-cost $J(x)$ of that ratio and serves as the instability measure. The module derives transmutation conditions from the J-cost barrier structure: fission products sit at high J-cost, transmutation paths reduce total J-cost toward local minima at doubly-magic nuclei.
proof idea
The definition is given directly by a conditional expression that checks whether nuclearCost initial vanishes and returns 1 in that case, otherwise the normalized cost difference.
why it matters
This definition supplies the efficiency measure required by the parent theorems efficiency_bounded and perfect_transmutation_efficiency. It operationalizes the transmutation efficiency claim in EN-006, which derives optimal pathways for nuclear waste transmutation from the J-cost structure. It connects to the framework where J-cost measures defect from stability and transmutation follows cost descent geodesics.
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