EightTickGeometry
plain-language theorem explainer
EightTickGeometry fixes the phase counts for electroweak mixing inside the discrete 8-tick circle of Recognition Science. A physicist deriving the Weinberg angle from φ-structure would cite this record to set the SU(2) sector at three phases and the U(1) sector at one phase. The definition is a plain structure with three default fields that directly supplies the ratio later used for the geometric mixing angle.
Claim. A geometric configuration consisting of three phases allocated to the SU(2) sector, one phase allocated to the U(1) sector, and a total of eight equally spaced phases at angles $kπ/4$ for $k=0,…,7$.
background
Recognition Science places the electroweak mixing angle inside an 8-tick phase geometry whose period is the fundamental octave (one octave equals eight ticks). The upstream definition of tick supplies the RS-native time quantum τ₀ = 1, while the 8-tick structure itself is the discrete circle whose phases are spaced at multiples of π/4. The module SM-004 states that the Weinberg angle emerges from embedding the gauge groups into this circle, with the SU(2) sector using three phases and the U(1) sector using one phase; the resulting geometric ratio is then refined by the golden-ratio correction from φ-forcing.
proof idea
The declaration is a structure definition that simply records three natural-number fields with the fixed defaults 3, 1 and 8. No lemmas are applied; the object is constructed directly from the constants supplied by the 8-tick octave and the electroweak embedding rule stated in the module documentation.
why it matters
This structure supplies the phase counts required by the downstream definition geometricMixing, which computes the ratio 1/4 as the leading approximation to sin²θ_W. The construction realises the T7 eight-tick octave landmark and the 8-tick phase geometry described in the module documentation for SM-004. It therefore forms the discrete skeleton on which the φ-correction must act to reach the observed value near 0.2229; without this record the geometric-mixing step has no input.
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