Materials Magnetism Types From Config Dim

Magnetism types and configDim

Magnetism in materials appears in five classical orderings: diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism. Diamagnetic materials weakly repel magnetic fields; paramagnetic materials weakly attract them. Ferromagnetic materials, like iron, retain strong magnetization; antiferromagnetic materials have opposing magnetic moments that cancel; ferrimagnetic materials have opposing moments that do not fully cancel, leaving net magnetization.

In the Recognition Science framework, a discrete record of events called a ledger assigns a counting dimension, configDim, to physical orderings. The framework's machine-checked library of formal theorems proves that the number of canonical magnetic orderings equals this dimension, D = 5. The theorem magnetismType_count states that the cardinality of the MagnetismType inductive type is exactly five, verified by computation with no unproved axioms.

This result connects a physical classification to a structural counting principle. The five types are not enumerated ad hoc; they are derived from the configDim value. The library defines a certificate structure, MagnetismTypesCert, that packages the count as a formal guarantee. The definition magnetismTypesCert instantiates this certificate using the theorem, so any consumer of the library can rely on the five-type classification as a proved fact.

The practical consequence is that materials science classifications can be audited against a formal foundation. When a researcher or engineer speaks of the five magnetic orderings, the framework provides a machine-checked certificate that the count is complete relative to its definition. This does not claim that real materials exhaust these types or that the physical distinctions are derived from first principles; it establishes the counting consistency within the framework's formal system.

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

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

def magnetismTypesCert : MagnetismTypesCert where
  five_types := magnetismType_count

What this page does not claim

The framework derives the physical laws of magnetism from configDim alone. Real materials are guaranteed to exhibit exactly one of these five orderings in all conditions. The five types are physically exhaustive beyond the formal definition of MagnetismType.

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)

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