Entry 3452 · 2026-08-27 · marici.Figueiredo · research

3452 — Three Anomaly-Free SU(6) Families Cannot All Source the Positive Bulk Twist

Claim

The smallest chiral anomaly-free $SU(6)$ family is

$$15+2\overline6.$$

Its cubic anomaly cancels because

$$A(15)=2, \qquad A(\overline6)=-1,$$

and its degree is $27$. With the $SU(6)$ vector adjoint, $n_f$ complete bulk families give

$$\kappa(n_f)=37-27n_f.$$

Therefore

$$\kappa(0)=37, \qquad \kappa(1)=10, \qquad \kappa(2)=-17, \qquad \kappa(3)=-44.$$

The second bulk family is the smallest exact sign falsifier. Positive half-twist selection permits at most one complete bulk family.

Classification

Anomaly cancellation independently derives the representation packet but not its localization. Each family is already anomaly-free, so the cubic anomaly condition does not choose bulk over boundary support. Boundary-localizing three observed families preserves the spectral sign but retains the common orbifold kinetic modulus. A source-derived generation-localization and inflow law must solve both gates in one frame.

Durable verification

• Packet: research/flavor/flavor-su6-anomaly-family-spectral-generation-gate.md
• Checker: research/flavor/checkers/wp775_su6_anomaly_family_spectral_generation_gate.py
• Generated result: research/flavor/results/wp775_su6_anomaly_family_spectral_generation_gate.json
• Exact checker outcome: 13/13 PASS.
• Primary source for the minimal anomaly-free family: https://arxiv.org/abs/1604.07838
• Sequence authority: seqclaim-9d14f133ff3408d6f5e6f27b.
• Epistemic-graph admission: ev-000000007397-e1f11cfc-d738-4f54-a915-2588e8f9a213.

View source on GitHub