en006_certificate
plain-language theorem explainer
EN-006 certificate defines a formatted string that reports the derived status of fission product transmutation theorems under the J-cost function. Nuclear engineers and waste-reduction researchers would cite it as a compact summary of cost-descent properties to stable nuclei. The definition assembles the string by direct concatenation of fixed header and theorem-reference lines.
Claim. The EN-006 certificate is the string enumerating: nuclear cost non-negativity $J(cfg) ≥ 0$, zero cost exactly for doubly-magic nuclei, positive cost for fission products, and monotonic cost reduction along any valid transmutation path to a stable endpoint.
background
Recognition Science models nuclear configurations by a J-cost function that quantifies deviation from ideal stability, with fission products located far from the stability valley at $x ≈ 1$. Doubly-magic nuclei (Z,N = 2,8,20,28,50,82,126) act as local minima where J-cost reaches zero. The module derives transmutation as a sequence of recognition events that descend this cost landscape, with efficiency bounded in [0,1] by the sibling theorem efficiency_bounded.
proof idea
The definition is a direct string literal formed by concatenating a fixed header block with eleven bullet lines that name the sibling theorems (nuclear_cost_nonneg, transmutation_reduces_cost, efficiency_bounded, fission_transmutation_from_ledger) and a closing RS insight sentence. No tactics or lemmas are applied beyond string assembly.
why it matters
The certificate supplies the human-readable closure for the EN-006 module, confirming that transmutation equals J-cost descent to doubly-magic attractors. It directly supports the module claim that optimal pathways exist via cost-monotone descent and aligns with the Recognition Science forcing chain where J-uniqueness and the phi-ladder govern stability. No downstream uses are recorded.
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