Chemistry Nuclear Magic Isotopes From Rs Nuclear Magic Cert

A certificate for five nuclides

In nuclear physics, a doubly magic nucleus 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 are unusually stable because each shell is completely filled. The standard examples are helium-4 (2 protons, 2 neutrons), oxygen-16 (8, 8), calcium-40 (20, 20), calcium-48 (20, 28), and nickel-56 (28, 28).

Within the Recognition Science framework, a machine-checked library of formal theorems contains a small structure called NuclearMagicCert. This structure is a certificate: it records the fact that the list of five doubly magic nuclides above is complete. The library proves, by direct computation, that the number of such nuclides in its list is exactly five. The certificate itself is just that proof, packaged as a single object.

The certificate does not claim that these are the only doubly magic nuclei in the universe. It does not derive the magic numbers from first principles, nor does it explain why these particular numbers are magic. It does not predict new isotopes or say anything about nuclear stability beyond the list itself. The certificate is a precise, minimal statement: within the framework's defined list, there are exactly five doubly magic nuclides.

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

structure NuclearMagicCert where
  five_nuclides : Fintype.card DoublyMagicNuclide = 5

What this page does not claim

The certificate does not claim these are the only doubly magic nuclei in nature. It does not derive the magic numbers from first principles. It does not predict new isotopes or explain nuclear stability beyond the list.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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