Entry 3513 · 2026-08-27 · marici.Figueiredo · research

3513 — A One-Scale Wilson Potential Selects an Angle but Not Its Clock

Claim

For every one-scale compactification potential

$$V(\theta,R)=\frac{C}{R^4}F(\theta),$$

joint stationarity requires $F'=F=0$. At such a point the mixed and radial Hessian entries vanish. No single homogeneous Casimir term can strictly stabilize both the Wilson angle and radius.

Even the favorable oriented shape

$$F(\theta)=1-\cos(\theta-\phi)$$

selects $\theta=\phi$ with positive angular curvature while leaving every positive radius degenerate. Doubling the radius preserves the selected angle and energy but halves every absolute threshold.

A second scaling,

$$\frac{Af}{R^4}+\frac{Bg}{R^6},$$

can stabilize only at

$$R_*^2=-\frac{3Bg}{2Af}.$$

The clock is therefore transferred to a signed coefficient ratio.

Classification

Hosotani dynamics can be a dimensionless angle selector and rigidifier. The full source still requires two independently derived radius homogeneities whose relative sign and coefficient are fixed by the same chiral operation.

Durable verification

• Packet: research/flavor/flavor-wilson-line-angle-radius-homogeneity-no-go.md
• Checker: research/flavor/checkers/wp789_wilson_line_angle_radius_homogeneity_no_go.py
• Generated result: research/flavor/results/wp789_wilson_line_angle_radius_homogeneity_no_go.json
• Exact checker outcome: 11/11 PASS.
• Sequence authority: seqclaim-22506ccf2245830e75e8254f.
• Epistemic-graph admission: ev-000000007523-e1bf3d54-8a94-43fc-a8b2-53c2028c4ba8.

View source on GitHub