IndisputableMonolith.Physics.GrandUnificationFromRS
Module linking SU(5) grand unification to Recognition Science by equating generator counts: SU(5) has 24 generators and the RS half-order object B_{3/2} has order 24. Particle theorists citing an RS origin for GUT gauge structure would reference the match lemmas and the GUT certificate. Argument is definitional counts plus direct numerical equalities.
claimThe module introduces a GUT model type, the SU(5) generator count, and the RS half-order $B_{3/2}$, then records $|\mathfrak{su}(5)|=24$, $|B_{3/2}|=24$, and the match $|\mathfrak{su}(5)|=|B_{3/2}|$, packaged as a GUT certificate.
background
Grand unification posits a simple gauge group containing the Standard Model; the minimal choice is SU(5), whose Lie algebra has dimension 24. Recognition Science supplies discrete counting objects forced by the eight-tick and dimensional chain; one of them is written here as the half-order $B_{3/2}$.
This module sits in the Physics layer of the monolith. It only imports Mathlib and defines local counts: a GUT model tag, su5GeneratorCount, b3HalfOrder, and a certificate bundle. No continuum field theory or coupling running is developed; the sole bridge is the integer identity 24 = 24.
proof idea
Definition module with thin equality lemmas. Generator and order counts are closed terms evaluating to 24; the match lemma is transitivity (or rfl after normalization) of those two equalities. The certificate is a structure packing the match. No analytic or representation-theoretic argument beyond the dimension count.
why it matters in Recognition Science
Gives the RS side a named landing spot for the classic SU(5) generator count, so later Physics results can cite a single certificate rather than raw numerals. Downstream work that needs "GUT from RS" as a hypothesis can take GUTCert / gutCert as the interface. Ties the discrete RS counting story (octave, D=3 forcing) to the oldest GUT group without claiming beta-function or proton-decay predictions.
scope and limits
- Does not derive the SU(5) Lagrangian or Yukawa sector from RS.
- Does not address coupling unification or the desert scale.
- Does not treat SO(10), E6, or flipped SU(5).
- Does not prove uniqueness of SU(5) among simple groups inside RS.
- Does not compute proton lifetime or magnetic monopole density.