fission_transmutation_from_ledger
plain-language theorem explainer
Recognition Science derives three key properties for nuclear transmutation directly from the J-cost ledger: non-stable configurations have positive cost, a zero-cost stable state exists, and every starting configuration admits a path to stability. Nuclear waste engineers would cite the result when modeling cost-descent pathways to doubly-magic nuclei. The proof packages three prior lemmas via a single term.
Claim. Let $J$ denote J-cost on a nuclear configuration with stability ratio $x$. Then $$(∀ cfg with x ≠ 1, J(cfg) > 0) ∧ (∃ cfg, J(cfg) = 0) ∧ (∀ cfg, ∃ path with start = cfg and J(finish) = 0).$$
background
In the EN-006 module a nuclear configuration is a structure carrying a stability ratio x ∈ ℝ with x > 0; the value x = 1 marks a perfectly stable doubly-magic nucleus while x ≠ 1 marks an unstable fission product. The associated J-cost is obtained by applying the J-function to this ratio and serves as a scalar measure of defect from the ideal ledger state. A transmutation path records a start configuration, a finish configuration, step count, and a net reduction inequality on J-cost.
proof idea
The proof is a term-mode one-liner that assembles the required conjunction by supplying transmutation_cost_pos for the first conjunct, the pair stable_config together with stable_config_zero_cost for the second conjunct, and stable_end_state_exists for the third conjunct.
why it matters
This bundles the core derived properties of the EN-006 fission transmutation claim, which states that Recognition Science derives the conditions and optimal pathways for nuclear waste transmutation from the J-cost barrier structure. It is referenced by the en006_certificate that records derivation status. The result applies the J-cost positivity and path-existence lemmas to the engineering setting of cost descent toward local minima at doubly-magic nuclei.
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