IndisputableMonolith.Masses.ElectroweakMasses
This module assembles RS-derived electroweak quantities including the weak mixing angle and a narrow Z-boson mass interval. It supplies sin²θ_W = (3 - φ)/6 together with related mass expressions built from the phi-ladder. The structure imports anchor constants, verification machinery, and phi bounds to produce these parameter-free results.
claimThe module states $m_Z^{pred} = 91075.095$ MeV (interval (91075.09, 91075.10)) and defines $sin^2 θ_W = (3 - φ)/6$ along with $m_W$, $m_H$, and cosine relations derived from the golden ratio.
background
The module resides in the Masses domain and imports the RS time quantum τ₀ = 1 tick from Constants, canonical mass constants from Anchor, and rigorous algebraic bounds on φ = (1 + √5)/2 from PhiBounds. Anchor centralises parameter-free constants described in the mass manuscripts. Verification supplies the comparison framework while keeping experimental values as imported constants, not RS derivations.
proof idea
This is a definition module with supporting lemmas. It establishes phi_eq_goldenRatio via PhiBounds, then applies interval arithmetic and algebraic identities to derive sin²θ_W, cos²θ_W, and the Z-mass interval from the anchor mass ladder.
why it matters in Recognition Science
The module feeds the WeakCoupling module, which combines sin²θ_W = (3 - φ)/6 with the RS fine-structure constant to obtain α_W. It supplies the electroweak mass predictions and Weinberg angle required for the Standard Model sector in the Recognition framework.
scope and limits
- Does not derive experimental PDG values from RS; they remain imported constants.
- Does not claim numerical agreement outside the stated Z-mass interval.
- Does not address QCD or gravitational sectors.
- Does not extend beyond the eight-tick octave or D = 3 assumptions.
used by (1)
depends on (4)
declarations in this module (21)
-
lemma
phi_eq_goldenRatio -
def
m_W_exp -
def
m_Z_exp -
def
m_H_exp -
def
sin2_theta_W_rs -
def
cos2_theta_W_rs -
def
cos_theta_W_rs -
theorem
cos2_theta_W_rs_eq -
theorem
sin2_theta_positive -
theorem
sin2_theta_lt_half -
theorem
cos2_theta_positive -
def
z_pred -
theorem
z_pred_eq -
lemma
phi51_gt -
lemma
phi51_lt -
theorem
z_mass_bounds -
theorem
z_relative_error -
def
w_pred -
theorem
wz_ratio_eq_cos -
structure
EWCert -
theorem
ew_cert_exists