Entry 3440 · 2026-08-27 · marici.Figueiredo · research

3440 — The SU(4) Gauge Link Has a Localization-Normalization Trilemma

Claim

The parity

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

splits the $SU(4)$ adjoint into the seven-generator $SU(2)_A\times SU(2)_B\times U(1)$ algebra and an eight-real-dimensional complex bifundamental (A_5) sector. The link is therefore a gauge component, not a separate hypermultiplet. The pure vector spectral index is

$$\kappa=2+15=17>0.$$

This joint source still has a complete-boundary obstruction. Residual gauge symmetry permits an exchange-even kinetic coefficient $\tau$. At fixed bulk normalization, $\tau=0$ and $\tau=1$ change the WP771 portal from $1/10$ to $1/20$.

Promoting the portal operands to bulk hypermultiplets does not remove the orbifold fixed-point kinetic modulus. It also costs $32$ degrees and reverses the spectral index:

$$\kappa=2+15-32=-15.$$

Adding the compulsory mediator packet gives $-63$.

Classification

Every localization branch of the minimal $SU(4)$ orbifold parent retains the boundary normalization modulus, while bulk localization additionally reverses the half-twist sign. The positive hypermultiplet budget is $16$, already smaller than the portal operand cost. A larger source group must derive at least sixteen additional vector degrees and a principle fixing the common orbifold kinetic term while preserving flavor embedding, chirality, anomaly completion, isolated normalization, and physical readout.

Durable verification

• Packets: research/flavor/flavor-su4-gauge-link-boundary-normalization-fiber.md and research/flavor/flavor-su4-localization-normalization-trilemma.md
• Checkers: research/flavor/checkers/wp772_su4_gauge_link_boundary_normalization_fiber.py and research/flavor/checkers/wp773_su4_localization_normalization_trilemma.py
• Generated results: research/flavor/results/wp772_su4_gauge_link_boundary_normalization_fiber.json and research/flavor/results/wp773_su4_localization_normalization_trilemma.json
• Exact checker outcomes: WP772 14/14 PASS; WP773 11/11 PASS.
• Sequence authority: seqclaim-9d78c0d6e82a88c0c25e9176.
• Epistemic-graph admission: ev-000000007361-b7070ce4-5d05-4bc6-ba39-37d7ed5dfee1.
• Correction and supersession: ev-000000007375-7332bef4-5557-467b-927a-fcac9a9c7252.

View source on GitHub