IndisputableMonolith.Physics.Hierarchy
The Physics.Hierarchy module proves Generation Torsion Universality: the three fermion generations are separated by topological gaps fixed by cubic voxel geometry with E_p = 11 and F = 6, yielding rung separations Δ₁ = 11 and Δ₂ = 6 (scaled for quarks). Mass hierarchy modelers in Recognition Science cite it to close the lepton-quark gap structure. The module assembles this by importing and composing necessity results from lepton, quark, and mixing modules without new axioms.
claimThe generation gaps satisfy $\Delta_1 = 11$ rungs and $\Delta_2 = 6$ rungs (or scaled for quarks), derived from cubic voxel topology with $E_p = 11$, $F = 6$.
background
Recognition Science derives physics from one functional equation through the T0-T8 forcing chain, with T8 fixing D = 3 spatial dimensions that induce the cubic voxel. This module operates in the Physics domain and imports the RS time quantum $\tau_0 = 1$ tick from Constants.
LeptonGenerations.Necessity proves the muon and tau masses forced from the electron mass plus geometric constants. MixingGeometry encodes the cubic voxel topology constraints on mixing matrices. QuarkMasses derives masses via the Quarter-Ladder Hypothesis, though it relies on PDG targets outside the parameter-free core.
The module doc-comment states the Generation Torsion Universality theorem with the explicit rung gaps.
proof idea
The module assembles its argument by importing the lepton necessity proofs, the cubic voxel constraints from MixingGeometry, and the quarter-ladder derivations from QuarkMasses, then combining them to establish the universal torsion gaps. No standalone proofs appear; it functions as a composition layer referencing the imported results.
why it matters in Recognition Science
This module establishes the Generation Torsion Universality theorem that underpins the mass hierarchy on the phi-ladder. It feeds the GenerationStructure and hierarchy_coherence siblings by supplying the fixed rung separations. The E_p = 11 and F = 6 parameters connect directly to the D = 3 dimensions forced at T8 and the geometric foundation in MixingGeometry.
scope and limits
- Does not compute explicit fermion mass values.
- Does not derive mixing angles or phases.
- Does not prove exactly three generations exist.
- Does not address neutrino mass generation.