Entry 3472 · 2026-08-27 · marici.Figueiredo · research

3472 — The Bounded Matter Completion Allows Family Flux but Destroys the Spectral Basin

Claim

Give the complete $SU(6)$ family $15+2\overline6$ common $U(1)_F$ charge $+1$. Its mixed anomaly coefficient is $3$. The smallest nontrivial vectorlike representation pair $6+\overline6$, with charges $(-3,-3)$, cancels that coefficient.

The residual linear and cubic anomaly equations require singlet charges with

$$\sum_i s_i=9, \qquad \sum_i s_i^3=297.$$

Within the declared box $|s_i|\le12$, there is no solution with fewer than four singlets; the first solution is

$$(-7,4,4,8).$$

At flux three, the full matter tower has weighted degree

$$81+108+69=258,$$

and the inherited equal-weight diagnostic is

$$\kappa=2+36-258=-220.$$

All anomalies remain canceled under global charge reversal, and the net linear charge is zero.

Classification

Ordinary added matter accommodates common-sign family flux but does not select its orientation or the required tadpole, and it destroys the favorable spectral basin. The remaining qualitatively different branch is a geometrically quantized Green--Schwarz constructor.

Durable verification

• Packet: research/flavor/flavor-added-matter-u1-completion-spectral-no-go.md
• Checker: research/flavor/checkers/wp780_added_matter_u1_completion_spectral_no_go.py
• Generated result: research/flavor/results/wp780_added_matter_u1_completion_spectral_no_go.json
• Exact checker outcome: 10/10 PASS.
• Sequence authority: seqclaim-c98c69ce2b30efd3991d5f2f.
• Epistemic-graph admission: ev-000000007447-37da48da-781d-49f9-bd81-8fca7c9372df.

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