IndisputableMonolith.Physics.Hierarchy
Physics.Hierarchy assembles the generation structure for leptons and quarks under Recognition Science. It establishes universal topological gaps of 11 rungs from first to second generation and 6 rungs from second to third, derived from cubic voxel parameters E_p=11 and F=6. The module integrates upstream results on lepton mass forcing, quark masses via quarter-ladder, and mixing geometry. Researchers deriving standard model hierarchies from the phi-ladder would cite it. The structure is an assembly of imported necessity theorems.
claimThe three generations are separated by topological gaps satisfying $Δ_1=11$ rungs (first to second) and $Δ_2=6$ rungs (second to third), with scaling permitted for quarks, where the gaps originate from the cubic voxel parameters $E_p=11$ and $F=6$.
background
Recognition Science places particle masses on a phi-ladder whose rung separations encode generation structure. The base time quantum is $τ_0=1$ tick. LeptonGenerations.Necessity forces the muon and tau masses from the electron mass using geometric constants derived earlier in the chain. MixingGeometry encodes the cubic voxel topology that constrains CKM and PMNS mixing matrices. QuarkMasses derives quark masses under the quarter-ladder hypothesis, though it incorporates external PDG targets outside the parameter-free core.
proof idea
The module is an assembly of imported results. It pulls the lepton necessity proofs, the geometric mixing foundations, and the quark mass derivations, then defines the generation structure and hierarchy coherence to unify the rung gaps. No new lemmas or tactics are introduced inside the file.
why it matters in Recognition Science
This module fills the Generation Torsion Universality step that links T10 lepton necessity and T12 quark masses. It supplies the topological foundation for the mass hierarchy and mixing parameters from the cubic voxel, consistent with the eight-tick octave and D=3. Downstream spectrum calculations reference the fixed 11 and 6 rung separations as forced by the framework.
scope and limits
- Does not derive the rung gaps from first principles inside this file.
- Does not compute explicit particle mass values.
- Does not extend the model beyond three generations.
- Does not resolve the external PDG inputs used in quark mass derivations.