boson_verification_cert_exists
plain-language theorem explainer
The theorem asserts existence of a certificate confirming that electroweak boson parameters satisfy Recognition Science bounds derived from the phi-ladder. Mass-spectrum researchers in unified theories would cite it to close the verification for W, Z, and Higgs rungs. The proof is a direct term-mode construction that assembles the certificate record from four pre-established lemmas supplying the required inequalities and equalities.
Claim. There exists a structure certifying that $0.2302 < sin^2 theta_W < 0.2304$, $0.7696 < cos^2 theta_W < 0.7698$, the squared W/Z mass ratio equals $cos^2 theta_W$, and the electroweak sector satisfies $B_{pow}=1$ with $r_0=55$.
background
The module treats electroweak boson masses on the phi-ladder via the formula $m(EW,r)=2 phi^{50+r}/10^6$ MeV for $B_{pow}=1$ and $r_0=55$. The Weinberg angle enters through $sin^2 theta_W=(3-phi)/6$, which forces the relation $M_Z=M_W/cos theta_W$ and therefore the squared mass ratio equal to $cos^2 theta_W$. BosonVerificationCert packages four independent facts: explicit numerical bounds on $sin^2 theta_W$ and $cos^2 theta_W$, the algebraic identity linking the mass ratio to $cos^2 theta_W$, and the sector parameters $B_{pow}=1$, $r_0=55$.
proof idea
The term proof directly constructs the certificate record. It supplies the field weinberg_angle with the theorem sin2_theta_W_bounds, the field cos2_theta with cos2_theta_W_bounds, the field wz_ratio_from_phi with wz_ratio_eq_cos2, and the field sector_params with electroweak_sector_params. No further tactics are required; the four lemmas already deliver exactly the propositions demanded by the structure.
why it matters
The result supplies the terminal verification step for the electroweak sector inside the phi-ladder mass formula. It confirms that the forced Weinberg angle from phi lies inside the PDG interval and that the W/Z ratio follows from the Recognition Composition Law without additional assumptions. Because the module is quarantined from certified surface derivations, the certificate isolates the consistency check rather than a first-principles mass prediction.
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