Entry 3509 · 2026-08-27 · marici.Figueiredo · research

3509 — The Supersymmetric Prepotential Orients a Half-Ray, Not a Portal Point

Claim

On the $SU(4)$ Coulomb ray, the five-dimensional cubic prepotential has

$$\mathcal F(a)=6ra^2-4ka^3, \qquad G(a)=\mathcal F''(a)=12r-24ka.$$

At the formal fixed-point face $r=0$, positivity fixes the sign of $a$ relative to the level $k$. Extended gauge structure also fixes the fundamental signed masses to

$$(a,a,a,-3a),$$

removing WP787's independent matter vertex.

However, the prepotential is kinetic geometry rather than the WP787 scalar potential. Unbroken supersymmetry leaves $a$ as a flat Coulomb modulus, and the scalar masses are $(a^2,a^2,a^2,9a^2)$. The points $a=-s$ and $a=-2s$ share the same level, positive cone, and relative threshold ratio three while their scalar contrasts differ by four.

Classification

The supersymmetric prepotential parallelizes topological level, kinetic geometry, and matter charge. It selects a relative orientation half-ray but not a vacuum point, absolute threshold, signed scalar portal, or calibrated readout.

Durable verification

• Packet: research/flavor/flavor-5d-susy-prepotential-coulomb-modulus-no-go.md
• Checker: research/flavor/checkers/wp788_5d_susy_prepotential_coulomb_modulus_no_go.py
• Generated result: research/flavor/results/wp788_5d_susy_prepotential_coulomb_modulus_no_go.json
• Exact checker outcome: 12/12 PASS.
• Sequence authority: seqclaim-ce3b1830d0d40c5cf6e09c61.
• Epistemic-graph admission: ev-000000007516-66361a06-bb14-4e02-bfd5-9407ed4edfa7.

View source on GitHub