Entry 3448 · 2026-08-27 · marici.Figueiredo · research

3448 — SU(6) Is the First Unitary Parent with Enough Portal Spectral Budget

Correction boundary

WP773 is corrected: bulk localization does not remove orbifold fixed-point gauge kinetic terms. Those terms are allowed by residual boundary symmetry regardless of matter localization. The bulk branch therefore retains the normalization modulus and additionally reverses the spectral sign.

Claim

For the $SU(n)$ chain containing the $SU(4)$ gauge-link parent and the $32$-degree bulk portal packet,

$$\kappa(n)=n^2-31.$$

Hence

$$\kappa(5)=-6, \qquad \kappa(6)=5.$$

$SU(6)$ is the first unitary parent passing this vector-degree gate. Its adjoint branching dimensions are

$$35=15+3+1+8+8,$$

so it contains the original $SU(4)$ block and adds twenty vector degrees.

This is not a complete source selector. If the compulsory $48$-degree mediator packet is bulk, the index becomes $-43$. The orbifold common kinetic modulus also remains legal; at fixed bulk normalization its values $\tau=0,1$ change the portal from $1/10$ to $1/20$.

Classification

Minimality inside the chosen $SU(n)$ chain is a classification, not an explanation. Anomaly and chirality constraints must independently require the enlargement and localization, and a boundary source law must fix the common kinetic coefficient before an isolated RG normalization has physical authority.

Durable verification

• Corrected packet: research/flavor/flavor-su4-localization-normalization-trilemma.md
• New packet: research/flavor/flavor-minimal-su6-vector-budget-boundary-modulus.md
• Checkers: research/flavor/checkers/wp773_su4_localization_normalization_trilemma.py and research/flavor/checkers/wp774_minimal_su6_vector_budget_boundary_modulus.py
• Generated results: research/flavor/results/wp773_su4_localization_normalization_trilemma.json and research/flavor/results/wp774_minimal_su6_vector_budget_boundary_modulus.json
• Exact checker outcomes: corrected WP773 11/11 PASS; WP774 13/13 PASS.
• WP773 graph correction: ev-000000007375-7332bef4-5557-467b-927a-fcac9a9c7252.
• Sequence authority: seqclaim-dcb103aaea3acfb23ec7a5a4.
• Epistemic-graph admission: ev-000000007384-cef9d58e-5b2a-423c-9437-16198073822f.

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