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def definition def or abbrev high

nuclearCost

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nuclearCost assigns to each nuclear configuration its J-cost value computed from the stability ratio. Nuclear engineers and RS theorists modeling transmutation pathways cite this as the basic instability metric driving cost descent. The definition is a direct one-line application of the J-cost function to the ratio field of NuclearConfig.

claimFor a nuclear configuration $cfg$ with positive stability ratio $x$, the nuclear cost is $J(x)$, where $J$ is the J-cost function measuring deviation from the stable point $x=1$.

background

The Fission Product Transmutation module models nuclear waste reduction as sequences of recognition events that lower total J-cost. NuclearConfig is the structure holding a positive real ratio $x$, with $x=1$ marking perfectly stable doubly-magic nuclei and $x≠1$ marking unstable fission products. The J-cost $J(x)$ is the instability measure imported from the cost definitions in MultiplicativeRecognizerL4 and ObserverForcing, where cost of a recognition event equals Jcost of its state.

proof idea

This declaration is a one-line definition that applies the J-cost function directly to the ratio field of the NuclearConfig structure.

why it matters in Recognition Science

nuclearCost supplies the metric for all downstream transmutation results, including cost_monotone_descent_terminates (any strictly decreasing sequence reaches stability) and fission_transmutation_from_ledger (every configuration has a zero-cost stable endpoint). It realizes the module claim that optimal transmutation follows J-cost geodesics to doubly-magic attractors, linking to J-uniqueness in the forcing chain and the Recognition Composition Law applied to nuclear ratios.

scope and limits

formal statement (Lean)

  56def nuclearCost (cfg : NuclearConfig) : ℝ := Jcost cfg.ratio

proof body

Definition body.

  57
  58/-- **THEOREM EN-006.1**: Nuclear cost is non-negative. -/

used by (19)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (7)

Lean names referenced from this declaration's body.