module module moderate

`IndisputableMonolith.Physics.MassHierarchy`

Collects charged-lepton and light-quark masses in GeV, the RS phi-cascade mass map, and the Koide parameter. Phenomenologists matching the phi-ladder formula to PDG data cite the observed tables and cascade lemmas. Mostly definitions plus short algebraic identities; Koide equals 2/3 exactly on the cascade values.

claimDefines observed charged-lepton masses $m_e,m_\mu,m_\tau$ (GeV), up- and down-quark mass triples, the cascade mass step along the $\varphi$-ladder, and the Koide parameter $Q=(m_e+m_\mu+m_\tau)/(\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_\tau})^2$, with the identity $Q=2/3$ for cascade masses.

background

Recognition Science places rest masses on a geometric ladder whose common ratio is the golden number $\varphi$ fixed by T6. The native mass formula is yardstick times $\varphi$ raised to (rung $-8+$ gap$(Z)$). This module sits in the Physics domain and imports only the RS constants (including the tick $\tau_0$).

It records PDG-style GeV values for the three charged leptons and the light up- and down-type quarks, together with a cascade construction that steps masses down from a Higgs-scale seed by successive factors of $\varphi$. The Koide combination of the three charged-lepton masses is the classical empirical ratio that sits near $2/3$; here it is evaluated on the cascade triple.

proof idea

Definition-heavy module, not a single theorem. Observed mass tables are literal numeric definitions. The cascade map and its decrease lemma are direct comparisons of successive $\varphi$-powers. The Koide claim is a short algebraic verification that the three cascade masses satisfy $Q=2/3$ exactly. The Higgs-seed cascade is a parameter pack plus the resulting tower.

why it matters in Recognition Science

Supplies the concrete mass hierarchy data and the exact Koide identity that any later RS spectrum or rung-assignment theorem must match. Anchors the primer mass formula (yardstick $\cdot\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$) against charged-lepton and light-quark numbers. The identity $Q=2/3$ is a sharp, falsifiable signature of pure $\varphi$-cascade kinematics. No downstream edges are recorded yet; the module is a leaf pack for hierarchy and flavor claims still to be wired.

scope and limits

Does not derive the absolute yardstick or Higgs seed from the forcing chain.
Does not treat neutrino masses or seesaw scales.
Does not prove CKM/PMNS mixing or charge assignments.
Does not claim PDG equals RS beyond the tabulated comparison points.
Does not address running couplings or threshold corrections.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (21)

structure ChargedLeptonMasses L52
def observedLeptons L58
structure UpQuarkMasses L65
def observedUpQuarks L71
structure DownQuarkMasses L78
def observedDownQuarks L84
def cascadeMass L94
theorem cascade_decreases L98
def koideParameter L121
theorem koide_is_two_thirds L126
theorem phi_cascade_from_higgs L140
structure CascadeParameters L147
def leptonParams L156
theorem three_generations_from_8_tick L168
theorem no_fourth_generation L174
theorem georgi_jarlskog L185
theorem up_quark_hierarchy L192
def predictions L203
theorem fermion_mass_prediction L212
structure MassHierarchyFalsifier L224
def experimentalStatus L231