Entry 3505 · 2026-08-27 · marici.Figueiredo · research

3505 — An SU(4) Cubic Selects Carrier Orientation but Not the Portal

Claim

The $SU(4)$ generator

$$T=\operatorname{diag}(1,1,1,-3)$$

provides a $3+1$ fundamental and has $\operatorname{tr}T^3=-24$. On the adjoint ray, the minimal cubic-plus-quartic potential has

$$a_*=\frac{\kappa}{6\lambda}, \qquad V_*=-\frac{\kappa^4}{108\lambda^3}.$$

The complete adjoint Hessian contains eight positive modes, six Goldstone zeroes, and one positive radial mode. Fixed nonzero $\kappa$ therefore selects and locally stabilizes a carrier orientation.

The smallest linear portal spurion instead gives

$$g_n-g_m=\frac{2\eta\kappa}{3\lambda}.$$

Changing $\eta$'s sign reverses the portal without changing the selected vacuum, and a continuous $(\kappa,\eta)$ scaling fiber remains.

Classification

The cubic parent is a conditional orientation selector and stable carrier rigidifier. It does not select the portal sign or magnitude. The cubic coefficient and portal vertex must descend from one quantized source operation; otherwise the tuning has only moved to $\eta\kappa/\lambda$.

Durable verification

• Packet: research/flavor/flavor-su4-cubic-orientation-portal-fiber.md
• Checker: research/flavor/checkers/wp787_su4_cubic_orientation_portal_fiber.py
• Generated result: research/flavor/results/wp787_su4_cubic_orientation_portal_fiber.json
• Exact checker outcome: 14/14 PASS.
• Sequence authority: seqclaim-0b36d763a8253af06ac23eb7.
• Epistemic-graph admission: ev-000000007510-155151ad-1155-4192-9a80-478cced2be1f.

View source on GitHub