hypothesis6
plain-language theorem explainer
Hypothesis 6 defines the real number (φ³ − 1)/(φ³ + 1) as a candidate expression for cos θ_W. Researchers testing φ-constrained electroweak mixing would cite it when comparing golden-ratio predictions against the observed W/Z mass ratio of 0.881. The declaration is a direct one-line assignment with no lemmas or reductions.
Claim. The hypothesis posits that the Weinberg angle satisfies $cos θ_W = (φ³ − 1)/(φ³ + 1)$.
background
Recognition Science obtains φ as the self-similar fixed point (T6) of the forcing chain and uses it to quantize gauge parameters. The module SM-003 examines whether the W/Z mass ratio, equal to cos θ_W by definition, emerges from φ-constrained SU(2) × U(1) mixing. Upstream results supply collision-free ledger structures and algebraic tautologies that keep all such expressions inside the eight-tick neutrality framework.
proof idea
The declaration is a direct definition that assigns the closed-form expression (phi^3 - 1) / (phi^3 + 1) to hypothesis6. No lemmas are invoked and no tactics are executed.
why it matters
The definition supplies one candidate φ-expression for cos θ_W that is referenced by bestCabibboFit and the sibling hypothesis6 inside CKMMatrix. It fills the paper proposition on electroweak parameters from RS, yet yields 0.618 against the observed 0.881 and therefore highlights the open task of locating the correct φ-formula inside the eight-tick octave.
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