derivationStatus
plain-language theorem explainer
derivationStatus embeds the interim numerical benchmark for the Weinberg angle in Recognition Science. It records that sin²(θ_W) = (3 - φ)/6 produces 0.230, lying within 3% of the measured 0.2229 at the Z scale. Electroweak model builders working from φ-geometry would reference this string as the current checkpoint. The definition is a direct string literal with no further computation.
Claim. The derivation status is the string reporting that $sin^2(θ_W) = (3 - φ)/6$ yields approximately 0.230, within 3% of the observed value 0.2229.
background
The module SM-004 targets derivation of the weak mixing angle θ_W from the Recognition Science φ-structure. The angle parametrizes electroweak mixing, with the observed sin²(θ_W) ≈ 0.2229 fixing the relative strengths of electromagnetic and weak couplings. Upstream, SpectralEmergence.of supplies the gauge content SU(3) × SU(2) × U(1) together with the 8-tick phase space that constrains the embedding angle. PhiForcingDerived.of and PhysicsComplexityStructure.of supply the J-cost minimization whose convex minimum at unity underpins the discrete phase geometry. LedgerFactorization.of calibrates the underlying J functional on the positive reals.
proof idea
The definition is a one-line string assignment that directly embeds the status message. No lemmas are applied; the body is a literal constant whose content summarizes the numerical claim derived from the 8-tick geometry in the surrounding module.
why it matters
This definition supplies the checkpoint string for the Weinberg-angle derivation inside the StandardModel.WeinbergAngle module. It records progress toward the paper proposition on electroweak mixing from information-theoretic principles and sits downstream of the eight-tick octave (T7) and D = 3 spatial dimensions. The module siblings contain explicit predictions and bounds that would consume this status once the derivation is completed. The doc-comment flags the result as promising but incomplete, leaving open the step from geometric embedding to a rigorous theorem.
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