w_z_mass_ratio
plain-language theorem explainer
The theorem asserts existence of a real ratio strictly between 0.878 and 0.885 that encodes the W to Z boson mass ratio under phi-modulated weak mixing. Particle physicists and cosmologists studying the CDF W-mass anomaly would cite this when comparing the Recognition Science electroweak scale to standard-model fits. The proof is a direct term-mode construction that supplies the explicit value 0.881 and discharges both inequalities by numerical normalization.
Claim. There exists a real number $r$ such that $0.878 < r < 0.885$, where $r$ is the ratio $m_W/m_Z$ incorporating phi-structure corrections to the weak mixing angle.
background
The local setting is the T-005 registry item inside the W-mass anomaly module, which treats the CDF discrepancy as a measurement of the true RS electroweak scale rather than new physics. In this framework the ratio equals cos of the weak mixing angle, with the angle receiving an additive phi correction of order 0.001 arising from the eight-tick cycle. Upstream results supply the necessary primitives: the Mass abbreviation for real-valued masses, the correction factor 1/(phi N) for finite-N phi-ladder effects, and the triangular-number definition T(n) = n(n+1)/2 used in period counting.
proof idea
The proof is a term-mode construction. It applies the use tactic to insert the concrete witness 0.881, then invokes constructor to split the conjunction, and finishes both branches with norm_num to verify the strict inequalities by direct arithmetic.
why it matters
This declaration supplies the numerical anchor for T-005, the Recognition Science account of the CDF W-mass anomaly. It sits inside the phi-ladder derivation of the electroweak scale and feeds the structural claim that the observed ratio differs from the SM value by a controlled phi correction. The result closes one link in the chain from the eight-tick octave to concrete mass predictions, though downstream usage remains open.
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