Materials Magnetism Types From Config Dim Magnetism Types Cert

Five canonical orderings

Magnetism in materials is classically organized into five canonical orderings: diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism. Diamagnetism is the weak repulsion any material shows in a magnetic field; paramagnetism is the weak attraction of materials with unpaired electrons; ferromagnetism is the strong alignment of moments that makes iron stick to a fridge; antiferromagnetism is the ordered alternation of opposite moments that cancels out; ferrimagnetism is the ordered arrangement of unequal opposite moments that leaves a net pull. These five are the standard taxonomy taught in solid-state physics, and they cover the everyday magnetic behavior of ordinary matter.

In the Recognition Science framework, a small machine-checked library of formal theorems records this classification as a certificate. The certificate is a structure named MagnetismTypesCert, and it contains exactly one fact: that the number of these five types is five. The library proves this by direct computation, with no axioms and no unfinished proofs. The point of the certificate is not to discover the five types; physicists have known them for over a century. The point is to make the count a formal, checkable object inside the framework's own mathematics, so that later framework results can rely on it without re-deriving it by hand.

The certificate does not claim that these are the only possible magnetic orderings, nor that the framework explains why magnetism exists. It does not assign any magnetic moment, energy scale, or critical temperature to any of the five types. It does not say which materials realize which ordering. It only records the cardinality: five types, no more, no less, as a theorem in the framework's library.

structure MagnetismTypesCert where
  five_types : Fintype.card MagnetismType = 5

theorem magnetismType_count : Fintype.card MagnetismType = 5 := by decide

What this page does not claim

The certificate does not claim these are the only possible magnetic orderings. It does not assign any magnetic moment, energy scale, or critical temperature to any type. It does not say which materials realize which ordering.

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/Materials/MagnetismTypesFromConfigDim.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.

Derived articles

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