YMSector
plain-language theorem explainer
YMSector enumerates the five canonical Yang-Mills configurations on the recognition lattice as gluon condensate, plasma, quark-gluon, hadronic, and vacuum. Lattice gauge theorists cite it when certifying the discrete mass gap via J-cost positivity. The declaration is a direct inductive type whose Fintype instance follows from the five constructors.
Claim. An enumeration of five Yang-Mills sectors on the recognition lattice: gluon condensate, plasma, quark-gluon plasma, hadronic phase, and vacuum.
background
The module formulates the Yang-Mills mass gap on the recognition lattice, where any non-vacuum field configuration carries strictly positive J-cost. The vacuum is the configuration in which every gauge bond sits at rung zero. The five sectors listed here realize the configuration-space dimension D = 5 required for the lattice gap statement.
proof idea
Inductive definition with five explicit constructors; the DecidableEq, Repr, BEq, and Fintype instances are obtained by automatic derivation.
why it matters
The enumeration is required by the YMLatticeGapCert structure, which records that J-cost vanishes only at the vacuum and is positive elsewhere, and by the theorem that the cardinality is exactly five. It supplies the discrete-sector foundation for the lattice version of the Yang-Mills mass gap inside the Recognition Science framework; the module notes that the continuum bridge remains an open multi-year program.
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