stable_is_attractor
plain-language theorem explainer
The stable nuclear configuration qualifies as a doubly-magic attractor under the J-cost metric of Recognition Science. Nuclear engineers modeling transmutation pathways for fission products would cite this result to anchor cost-descent arguments at the global minimum. The proof is a direct term construction that pairs the stable configuration with its zero-cost property to satisfy the local-minimum bound and uses reflexivity for the configuration match.
Claim. There exists a doubly-magic attractor structure $a$ such that the configuration component of $a$ equals the stable nuclear configuration $s$, where $s$ is the unit configuration with J-cost exactly zero and $a$ satisfies nuclearCost$(a) ≤ 1$.
background
In the EN-006 module on fission product transmutation, Recognition Science treats each nuclear configuration as carrying a J-cost that quantifies its defect from the stability valley near $x ≈ 1$ on the phi-ladder. The stable configuration is the zero-cost point defined as the unit element, corresponding to a doubly-magic nucleus. A DoublyMagicAttractor is a structure pairing a nuclear configuration with the predicate that its nuclear cost is at most 1, placing it within one coherence energy of stability. The upstream theorem stable_config_zero_cost states that the stable configuration has nuclear cost zero, following directly from the Jcost_unit0 property.
proof idea
The term proof constructs the existential witness explicitly. It forms the pair consisting of the stable configuration together with a subterm that rewrites via the zero-cost theorem and normalizes the resulting inequality 0 ≤ 1, then applies reflexivity to establish equality of the configuration fields.
why it matters
This theorem EN-006.9 closes the basic attractor property in the fission transmutation chain, supporting the module claim that every transmutation pathway has a stable endpoint at a doubly-magic nucleus. It instantiates the Recognition Science principle that zero J-cost points act as attractors, consistent with the phi-ladder mass formula and the Recognition Composition Law. The result leaves open the explicit construction of cost-reducing sequences for concrete isotopes such as Cs-137.
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