Entry 3459 · 2026-08-27 · marici.Figueiredo · research

3459 — Flux Three Generates Three Chiral Modes and Triples the Spectral Tower

Claim

For a unit-charged Dirac field on a magnetized two-torus,

$$\operatorname{ind}D=qm.$$

Flux $m=3$ therefore gives a genuine three-dimensional chiral zero-mode space. Unlike WP776's multi-kink peaks, this is real kernel multiplicity. Changing to $m=-3$ reverses chirality.

The same flux controls every Landau-level degeneracy:

$$d_{\mathrm{LL}}=|qm|=3.$$

Thus one $27$-degree $SU(6)$ anomaly-family field contributes weighted tower degree

$$3(27)=81.$$

The equal-weight diagnostic gives

$$2+35-81=-44.$$

This numerical agreement does not authorize transport of the five-dimensional potential: the flux background defines a new six-dimensional spectrum whose full effective potential must be recomputed.

Classification

Magnetic flux is a genuine index-three generation constructor but no spectral economy. Flux quantization also permits every integer and selects neither magnitude three nor its orientation. A complete six-dimensional tadpole and anomaly packet must derive the oriented flux sector and its gauge normalization before the portal can be claimed.

Durable verification

• Packet: research/flavor/flavor-flux-three-index-spectral-degeneracy.md
• Checker: research/flavor/checkers/wp777_flux_three_index_spectral_degeneracy.py
• Generated result: research/flavor/results/wp777_flux_three_index_spectral_degeneracy.json
• Exact checker outcome: 9/9 PASS.
• Primary source for the magnetized-torus index: https://arxiv.org/abs/1709.09784
• Sequence authority: seqclaim-5bdb82a4a56dcaafaf57c6d0.
• Epistemic-graph admission: ev-000000007413-39d20bb7-9324-4b4c-bf68-dacd87480f53.

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