tan_theta_w_value
plain-language theorem explainer
The declaration asserts tan of the Weinberg angle equals approximately 0.536 when sin squared theta W is fixed at the observed 0.223. Electroweak theorists building Recognition Science models would cite it to anchor the mixing angle inside the phi-constrained 8-tick geometry. The proof reduces to a direct term that substitutes the numerical ratio and applies the trivial constructor.
Claim. $tan(theta_W) approx 0.536$ where $theta_W$ is the Weinberg mixing angle satisfying $sin^2(theta_W) approx 0.223$ and $cos^2(theta_W) approx 0.777$.
background
The module derives the W/Z mass ratio from phi-quantized gauge structure, noting that m_W / m_Z equals cos(theta_W) by definition. The eight-tick phase supplies discrete angles k pi /4 for k from 0 to 7, which embed the electroweak group and constrain the mixing angle via the golden ratio. The tick constant sets the fundamental time quantum to 1 in RS-native units, with U providing the corresponding gauge where c equals 1.
proof idea
The proof is a one-line term wrapper that directly asserts the proposition as true after the numerical approximation sin squared theta W equals 0.223 is substituted from the phi explanation.
why it matters
This supplies the concrete numerical anchor for tan theta W inside the W/Z mass ratio derivation, feeding the electroweak parameters proposition in the module. It connects directly to the eight-tick octave (T7) and the phi fixed point (T6) that force the phase geometry. The 6 percent offset from the observed 0.223 remains an open refinement target for higher-order corrections on the phi ladder.
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