transmutation_efficiency
plain-language theorem explainer
Transmutation efficiency computes the fractional reduction in J-cost when moving a nuclear configuration from initial to final state. Nuclear engineers evaluating fission product pathways would cite the quantity when measuring descent toward stable nuclei. The definition implements a direct piecewise ratio on the nuclearCost function with a unit value at zero initial cost.
Claim. $e(i,f) := 1$ if $J(i)=0$, else $(J(i)-J(f))/J(i)$, where $J$ denotes nuclear cost on configurations parameterized by stability ratio $x$ ($x=1$ for stable nuclei).
background
NuclearConfig is a structure holding a positive real stability ratio $x$, with $x=1$ marking doubly-magic stable nuclei and $x≠1$ marking unstable species. nuclearCost maps each configuration to its J-cost via Jcost of the ratio, serving as the instability measure in the ledger framework.
proof idea
The definition is a direct piecewise expression on nuclearCost: it returns 1 when the initial cost vanishes, otherwise the normalized difference of the two costs.
why it matters
This definition supplies the efficiency metric consumed by efficiency_bounded (proving the interval [0,1]) and perfect_transmutation_efficiency (showing unit efficiency to stable_config). It occupies the EN-006.13 position in the fission transmutation chain, linking J-cost descent to quantitative performance inside the Recognition Science derivation of transmutation pathways.
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