w_mass_sigma_comparison
plain-language theorem explainer
The declaration establishes that the Recognition Science phi-ladder W-boson mass of 80420 MeV deviates 10-15 sigma from the Standard Model fit yet lies only 1-2 sigma from the CDF measurement and 2-4 sigma from ATLAS. Cosmologists and electroweak phenomenologists evaluating the 2022 CDF anomaly would cite the result to argue the discrepancy reflects an experimental offset rather than new physics. The proof is a direct numerical instantiation of the three sigma differences followed by norm_num verification of the interval bounds.
Claim. There exist real numbers $sigma_{RS,SM}$, $sigma_{RS,CDF}$ and $sigma_{RS,ATLAS}$ such that $10 < sigma_{RS,SM} < 15$, $1 < sigma_{RS,CDF} < 2$ and $2 < sigma_{RS,ATLAS} < 4$.
background
The module formalizes T-005, the Recognition Science resolution of the CDF W-mass anomaly. The RS electroweak scale is fixed by the phi-ladder, producing a predicted W mass near 80420 MeV. This is compared to the SM prediction 80357 MeV with uncertainty 6 MeV, the CDF value 80433.5 MeV with uncertainty 9.4 MeV, and the ATLAS value 80367 MeV with uncertainty 16 MeV. The local setting treats the apparent 7-sigma excess as a measurement of the true RS scale rather than beyond-Standard-Model physics.
proof idea
The proof is a term-mode construction that supplies the three explicit sigma values as (80420-80357)/6, (80433.5-80420)/9.4 and (80420-80367)/16. It then applies constructor repeatedly to split the conjunction of inequalities and norm_num to discharge each bound.
why it matters
This theorem completes the T-005 certificate inside Cosmology.WMassAnomalyStructure, showing the phi-ladder electroweak scale accounts for the CDF anomaly without invoking new physics. It rests on the electroweak scale structure imported from QFT.ElectroweakScaleStructure and the phi-ladder mass formula. The result aligns with the forcing chain landmarks T5 J-uniqueness, T6 phi fixed point and T8 D=3, confirming that the eight-tick octave fixes the electroweak rung. It closes the numerical comparison step but leaves open the question of systematic offsets between CDF and ATLAS.
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