Chemistry Nuclear Magic Isotopes From Rs Doubly Magic Nuclide

The five canonical nuclides

In nuclear physics, a doubly magic nuclide has both its proton count and its neutron count equal to one of the magic numbers 2, 8, 20, 28, 50, 82, or 126. These nuclides show unusual stability because both shells are closed. The standard examples are helium-4, oxygen-16, calcium-40, calcium-48, and nickel-56. Each appears in textbooks and in the chart of nuclides.

The Recognition Science framework's machine-checked library of formal theorems records exactly these five as the canonical set. The declaration DoublyMagicNuclide is an inductive type with five constructors, one per nuclide, and a theorem proves that the count is five. The proof is by computation, so the list is exhaustive within the framework's definition. The framework does not derive the magic numbers themselves; it takes the set {2, 8, 20, 28, 50, 82, 126} as a given input from nuclear physics.

What the declaration establishes is a clean, finite enumeration. It gives a name to each of the five nuclides and certifies that there are exactly five in this class. It does not claim that these are the only doubly magic nuclides in nature, nor that the framework predicts their existence. It also does not claim any new physics about nuclear stability. The value is organizational: a formal object that other theorems can refer to without ambiguity.

The practical consequence is that any later proof about doubly magic nuclides can start from a fixed, machine-checked list. A reader who wants to know what the framework says about these nuclei gets a precise answer: five, no more, no less. The physics of why these are magic, and whether other doubly magic nuclei exist, remains outside this declaration.

theorem doublyMagic_count : Fintype.card DoublyMagicNuclide = 5 := by decide

inductive DoublyMagicNuclide where
  | he4
  | o16
  | ca40
  | ca48
  | ni56
  deriving DecidableEq, Repr, BEq, Fintype

What this page does not claim

The declaration does not prove that these are the only doubly magic nuclides that exist in nature. The framework does not derive the magic numbers from first principles. The declaration says nothing about nuclear stability or binding energies.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/NuclearMagicIsotopesFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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