IndisputableMonolith.Foundation.CKMHierarchyFromPhiLadder
The module defines the canonical six-quark structure of three generations with two isospin partners each, assigning distinct rungs on the phi-ladder to generate the CKM hierarchy via the mass formula. Physicists deriving fermion spectra in Recognition Science cite these rung assignments to anchor mixing angles in the self-similar fixed point. The module consists of successive definitions for quark count, individual rungs, their ordering, and geometric mass relations.
claimThe module establishes the six-quark structure with three generations and two isospin partners per generation, each assigned a rung on the $phi$-ladder so that masses follow the geometric progression $m = y phi^{r-8+gap(Z)}$ where $y$ is the yardstick and $gap(Z)$ encodes the charge adjustment.
background
Recognition Science places fermion masses on the phi-ladder after the J-uniqueness step and the phi fixed-point construction in the forcing chain. The module imports the base time quantum tau_0 = 1 tick together with cost functions to label the six quarks. It introduces the rung assignments for the up-type and down-type partners across generations and records the strict ordering of those rungs along with the resulting mass-at-rung and geometric-mass relations.
proof idea
This is a definition module, no proofs. It proceeds by successive definitions that fix the total quark count, name the six rung values, state the strict ordering of the rungs, and define the mass functions that convert rung index into physical mass.
why it matters in Recognition Science
The module supplies the rung assignments required to construct the CKM hierarchy directly from the phi-ladder in the Recognition framework. It completes the fermion sector that follows the eight-tick octave and three spatial dimensions of the T7-T8 steps, enabling downstream mass-spectrum and mixing calculations.
scope and limits
- Does not compute numerical CKM matrix elements or mixing angles.
- Does not include leptons or any non-quark fermions.
- Does not incorporate experimental mass values or parameter fitting.
- Does not address renormalization-group flow or higher-order corrections.
depends on (2)
declarations in this module (20)
-
def
quark_count -
theorem
quark_count_eq -
def
up_rung -
def
down_rung -
def
strange_rung -
def
charm_rung -
def
bottom_rung -
def
top_rung -
theorem
quark_rungs_strict_ordering -
def
mass_at_rung -
theorem
mass_at_rung_pos -
theorem
mass_geometric -
theorem
mass_strict_increasing -
def
mass_ratio_top_up -
theorem
mass_ratio_top_up_pos -
theorem
mass_ratio_top_up_above_30000 -
theorem
mass_ratio_top_up_pos_band -
structure
CKMHierarchyFromPhiLadderCert -
def
ckmHierarchyFromPhiLadderCert -
theorem
ckm_hierarchy_one_statement