Entry 3516 · 2026-08-27 · marici.Figueiredo · research

3516 — Curvature--Flux Balance Fixes the Clock and Magnitude but Not the Sign

Claim

The six-dimensional Einstein-frame potential

$$V(R)=-\frac{B}{R^4}+\frac{An^2}{R^6}$$

has the strict minimum

$$R_*^2=\frac{3An^2}{2B}, \qquad V''(R_*)=\frac{8B}{R_*^6}>0.$$

The signed flux threshold becomes

$$\frac{\sigma n}{R_*} =\sigma\sqrt{\frac{2B}{3A}}.$$

Thus the flux integer cancels and curvature--flux balance fixes an absolute magnitude conditional on the gauge--gravity ratio $B/A$.

The potential is exactly blind to $\sigma$. Its unlifted minimum is AdS, and a stationary Minkowski completion with $C/R^2$ requires

$$C=\frac{B^2}{4An^2}.$$

Classification

This is a genuine radion selector, classical basin rigidifier, and conditional portal-magnitude selector. It does not select orientation, derive $B/A$, prove a quantum RG basin, or supply a calibrated signed instrument.

Durable verification

• Packet: research/flavor/flavor-curvature-flux-radion-magnitude-selector.md
• Checker: research/flavor/checkers/wp790_curvature_flux_radion_magnitude_selector.py
• Generated result: research/flavor/results/wp790_curvature_flux_radion_magnitude_selector.json
• Exact checker outcome: 10/10 PASS.
• Sequence authority: seqclaim-17373904c9dd99de8700238a.
• Epistemic-graph admission: ev-000000007532-e32ed046-6ca8-4714-9ddd-f6c6b0561e54.

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