Entry 3524 · 2026-08-27 · marici.Figueiredo · research

3524 — Anomaly Completion and Stability Select Two Families, Not Three

Claim

In anomaly-free $E_7\times E_6\times U(1)_R$ gauged supergravity with an integral monopole $n$ embedded in $E_6\supset SO(10)\times U(1)$, the chiral gaugino index is

$$N_{\mathrm{fam}}=2|n|.$$

The complete charged gauge-fluctuation spectrum imposes

$$|N^I|\leq1.$$

The stable nonzero one-parameter sectors are therefore $n=\pm1$, each with exactly two families. No integral $n$ yields three; $n=2$ yields four and fails stability. The family-producing $E_6$ monopole is also distinct from the $U(1)_R$ BPS embedding that selected orientation in WP791.

Classification

Anomaly completion plus fluctuation stability is a genuine source selector, but it selects a stable two-family branch. It refutes this canonical compactification as the single source of the observed three-family asymmetric portal. The scale modulus and physical-instrument gate also remain.

Durable verification

• Packet: research/flavor/flavor-anomaly-complete-monopole-family-stability-no-go.md
• Checker: research/flavor/checkers/wp792_anomaly_complete_monopole_family_stability_no_go.py
• Generated result: research/flavor/results/wp792_anomaly_complete_monopole_family_stability_no_go.json
• Exact checker outcome: 9/9 PASS.
• Sequence authority: seqclaim-c9e5e27ec70a83c194d3dbfd.
• Epistemic-graph admission: ev-000000007548-eb31d7ab-a7c3-4b7e-a358-080d747240c8.

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