DoublyMagicNuclide
plain-language theorem explainer
The inductive type enumerates the five doubly magic nuclides He-4, O-16, Ca-40, Ca-48, and Ni-56. Nuclear structure researchers cite this enumeration to verify the count of configurations where proton and neutron numbers match magic values. The definition uses explicit constructors and derives finite type and equality structures automatically.
Claim. $D = {He-4 (Z=2,N=2), O-16 (8,8), Ca-40 (20,20), Ca-48 (20,28), Ni-56 (28,28)}$, the finite set of doubly-magic nuclides with equal proton and neutron magic numbers drawn from {2, 8, 20, 28, 50, 82, 126}.
background
Recognition Science identifies doubly-magic nuclides as those with proton number Z and neutron number N both equal to a magic number. The module lists five canonical examples that achieve configuration dimension D = 5. These are He-4, O-16, Ca-40, Ca-48, and Ni-56. The inductive definition supplies a concrete finite enumeration for use in counting and certification theorems.
proof idea
This is a direct inductive definition with five explicit constructors. The deriving clause automatically installs instances for DecidableEq, Repr, BEq, and Fintype.
why it matters
The definition populates the set counted by the theorem doublyMagic_count and certified by the structure NuclearMagicCert. It encodes the five canonical doubly-magic nuclides asserted in the module documentation. This supplies the concrete list needed to connect RS-derived constants to observed nuclear shell closures.
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