IndisputableMonolith.Physics.WBosonAbsoluteScoreCard
Scorecard packaging the absolute W-boson mass prediction from RS electroweak inputs. It records cos²θ_W = (3+φ)/6, interval bounds on the Weinberg factors, the tree-level identity m_W/m_Z = cos θ_W, and a zero-free-parameter certificate over three RS-derived inputs. Electroweak mass auditors cite it when checking the W ladder against the Z rung and VEV relation. Content is closed-form algebra plus interval arithmetic on φ and α⁻¹.
claimModule-level scorecard for the absolute $W$ mass: $\cos^2\theta_W=(3+\varphi)/6$ from the RS Weinberg angle; strict bounds on $\cos^2\theta_W$ and $\sin^2\theta_W$; positivity of $\cos^2\theta_W$; tree-level $m_W/m_Z=\cos\theta_W$; and a certificate that the prediction uses three RS inputs with zero free parameters.
background
Recognition Science fixes the Weinberg angle by a golden-ratio closed form rather than a fit. Here $\varphi=(1+\sqrt{5})/2$ is the self-similar fixed point of the forcing chain, and the module takes
$$\cos^2\theta_W=(3+\varphi)/6$$
as the RS native value (with $\sin^2\theta_W=1-\cos^2\theta_W$).
Upstream, ElectroweakMasses places the $Z$ at rung 1 of the electroweak sector: $m_Z=2\varphi^{51}/10^6$ MeV. VEVConsistency then removes the Higgs VEV as an independent knob via the tree-level relation $v^2=m_Z^2\sin^2\theta_W\cos^2\theta_W,\alpha^{-1}/\pi$. PhiBounds and AlphaBounds supply rigorous interval enclosures on $\varphi$ and $\alpha^{-1}$ so the scorecard inequalities are machine-checkable, not floating-point claims.
Sibling objects name the closed form, four-sided bounds on $\cos^2$ and $\sin^2$, positivity, the $W/Z$ ratio identity, the three-input packing, and the final absolute-score certificate.
proof idea
Definition-and-bounds module, not a single deep theorem. The closed form $\cos^2\theta_W=(3+\varphi)/6$ is recorded as a named constant; positivity and the four inequalities $\cos^2$/$\sin^2$ above and below explicit rationals are discharged by algebraic rearrangement plus the imported $\varphi$ interval bounds. The ratio lemma is the standard tree-level identity $m_W=m_Z\cos\theta_W$. Free-parameter bookkeeping packages the three RS inputs (Z mass ladder, Weinberg closed form, $\alpha^{-1}$ band) and asserts the free-parameter count is zero. The top certificate aggregates those facts into one audit object.
why it matters in Recognition Science
Gives a single audit surface for the absolute $W$ mass in the RS electroweak sector: closed-form Weinberg angle, bounded trig factors, $W/Z$ ratio, and a zero-free-parameter claim. It sits downstream of ElectroweakMasses (Z rung), VEVConsistency (VEV fixed by $m_Z$, $\theta_W$, $\alpha$), and the $\varphi$/$\alpha^{-1}$ interval modules. No further modules currently import it (leaf scorecard), so its role is certification rather than further derivation. Landmark ties: $\varphi$ from T6, the $\alpha^{-1}$ band in $(137.030,137.039)$, and the mass-ladder yardstick used for gauge bosons. A referee reading only this page can see whether the $W$ prediction is parameter-free once the Z rung and Weinberg form are granted.
scope and limits
- Does not derive the Weinberg closed form from the forcing chain; it records and bounds it.
- Does not prove loop-level or radiative corrections to m_W/m_Z = cos θ_W.
- Does not re-derive m_Z; it imports the electroweak rung assignment.
- Does not claim experimental agreement beyond the certified symbolic inputs.
- Does not fix the Higgs VEV here; that lives in VEVConsistency.
depends on (5)
declarations in this module (13)
-
theorem
cos2_theta_W_closed_form -
theorem
cos2_gt -
theorem
cos2_lt -
theorem
sin2_gt -
theorem
sin2_lt -
theorem
cos2_pos -
theorem
wz_ratio_is_cos_theta -
def
free_params_w_mass -
theorem
zero_free_params -
inductive
WMassInput -
theorem
three_inputs -
structure
WBosonAbsoluteScoreCardCert -
theorem
wBosonAbsoluteScoreCardCert_holds