magnetismTypesCert
This definition constructs a certificate asserting that exactly five magnetic orderings exist under the configDim = 5 constraint in Recognition Science. Materials researchers modeling diamagnetism through ferrimagnetism would reference it to confirm the completeness of the canonical set. The construction is a direct one-line assignment of the decidable cardinality result to the structure field.
claimThe certificate $C$ asserts that the finite set of magnetic orderings has cardinality exactly five, obtained by direct assignment of the decidable count to the structure field.
background
The module treats magnetism types as determined by configuration dimension, fixing five canonical orderings for D = 5: diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism. The structure MagnetismTypesCert encodes the single assertion that the finite type of these orderings has cardinality five. This rests on the upstream theorem that computes the cardinality by decision procedure, confirming the count without additional hypotheses.
proof idea
The definition is a one-line wrapper that directly supplies the result of the cardinality theorem to the five_types field of the certificate structure.
why it matters in Recognition Science
This definition supplies the concrete certificate required for the materials depth in Recognition Science, closing the enumeration of magnetic orderings at configDim = 5. It aligns with the framework's use of configuration dimension to classify physical behaviors, here fixing the number of magnetism types at five. No downstream uses are recorded, indicating it serves as a terminal fact for this module.
scope and limits
- Does not list the individual magnetism types explicitly.
- Does not derive physical properties or interactions from the types.
- Does not connect to other framework constants such as phi or J-cost.
- Does not address higher-dimensional configurations beyond D=5.
formal statement (Lean)
29def magnetismTypesCert : MagnetismTypesCert where
30 five_types := magnetismType_count
proof body
Definition body.
31
32end IndisputableMonolith.Materials.MagnetismTypesFromConfigDim