ew_cert_exists
The theorem establishes existence of an Electroweak verification certificate by direct construction. Researchers citing Recognition Science mass predictions would reference it to confirm that the Z-boson prediction satisfies the interval (91075.09, 91075.10) MeV, stays within 0.13 percent relative error of experiment, and yields the W/Z ratio equal to the RS cosine of the Weinberg angle. The proof is a one-line term that packages three prior theorems into the EWCert structure.
claimThere exists a certificate $C$ such that the predicted $Z$-boson mass satisfies $91075.09 < z_0 < 91075.10$ (in MeV), the relative error $|z_0 - m_Z^exp|/m_Z^exp < 0.0013$, and the predicted $W/Z$ ratio equals the RS value of $cos θ_W$.
background
The module derives electroweak boson masses from the Recognition Science phi-ladder. The Z boson is placed at rung 1, so its mass is given by $m_Z = 2 φ^{51}/10^6$ MeV. The W mass follows from the gauge relation $m_W = m_Z cos θ_W$ with the RS Weinberg angle satisfying $sin^2 θ_W = (3 - φ)/6$. EWCert is the structure that packages three concrete verification conditions on these predictions: the Z mass lies in a 0.01 MeV window, the relative error to the experimental value is below 0.13 percent, and the W/Z ratio equals the RS cosine. The three upstream theorems supply exactly these three fields.
proof idea
The proof is a one-line term construction. It builds an anonymous instance of EWCert by supplying the three fields directly from the sibling theorems z_mass_bounds, z_relative_error, and wz_ratio_eq_cos. No additional tactics or reductions are required; the term simply records that the three properties hold simultaneously.
why it matters in Recognition Science
This declaration closes the local verification of the electroweak mass predictions inside the Recognition Science framework. It shows that the phi-ladder assignment for the Z boson together with the derived Weinberg angle reproduces experimental values to the stated precision. The result sits downstream of the mass formula and the RCL-derived constants; it supplies the concrete certificate that higher-level consistency checks can invoke. No open scaffolding remains in this module.
scope and limits
- Does not derive the Weinberg angle from the forcing chain.
- Does not extend the certificate to the Higgs mass.
- Does not claim agreement beyond the 0.13 percent relative-error threshold.
- Does not address higher-order radiative corrections.
formal statement (Lean)
137theorem ew_cert_exists : Nonempty EWCert :=
proof body
Term-mode proof.
138 ⟨{ z_in_range := z_mass_bounds
139 z_error := z_relative_error
140 wz_is_cos := wz_ratio_eq_cos }⟩
141
142end
143
144end IndisputableMonolith.Masses.ElectroweakMasses