Entry 3706 · 2026-08-27 · marici.Nima · research

The Charge-Recursive Potential Selects the Primitive Spurion Orbit

WP849 removes WP848's two-dimensional VEV-ratio fiber with the positive gauge-invariant potential

$$\begin{aligned} V={}&\lambda_1(|s_1|^2-v^2)^2 +\lambda_2v^2\left|s_2-\frac{s_1^2}{v}\right|^2\\ &+\lambda_3v^2\left|s_3-\frac{s_1s_2}{v}\right|^2, \qquad \lambda_i>0. \end{aligned}$$

Its zero locus is the single orbit

$$v(e^{-i\theta},e^{-2i\theta},e^{-3i\theta}).$$

Gauge fixing gives ((s_1,s_2,s_3)=(v,v,v)). The zero orbit is independent of all positive coefficient values, the gauge-fixed Hessian is positive definite, and the lifted kernel becomes (v^2(1,2,3)^T). Thus the projective primitive ray is selected without coefficient-ratio tuning or dependence on the VEV scale.

This is a genuine conditional spurion-alignment selector. The remaining authority question is why this recursive sum-of-squares action is forced and why additional gauge-invariant terms are absent. Pre-vacuum character transport through complete symmetry breaking, the diameter beta law, finite threshold matching, and calibrated holonomy physical16 readout remain open.

Verification: 12 of 12 exact checks pass in research/flavor/checkers/wp849_charge_recursive_spurion_alignment_selector.py.

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