Entry 3527 · 2026-08-27 · marici.Figueiredo · research

3527 — Global Vertical Flux Rigidifies Three but Leaves a Chiral Mirror

Claim

In the finite global F-theory model list over $\mathbb P^3$, shifted $G_4$-quantization, homogeneous M/F-theory consistency conditions, and D3 tadpole capacity make three the minimum permitted family number for the admitted vertical fluxes.

This does not select orientation. The exact involution $G_4\mapsto-G_4$ preserves shifted quantization, transversality, primitivity, and

$$\frac12\int_XG_4\wedge G_4,$$

while reversing every matter-surface chiral index. Thus three-family and anti-three-family fluxes have identical admitted tadpole cost.

Classification

Global vertical flux is a genuine lower-bound rigidifier for family magnitude in the finite scan. It does not select chirality sign, a unique flux class, portal normalization, a complete stabilized-moduli basin, finite thresholds, or a calibrated physical16 instrument.

Durable verification

• Packet: research/flavor/flavor-f-theory-vertical-flux-mirror-moduli-no-go.md
• Checker: research/flavor/checkers/wp793_f_theory_vertical_flux_mirror_moduli_no_go.py
• Generated result: research/flavor/results/wp793_f_theory_vertical_flux_mirror_moduli_no_go.json
• Exact checker outcome: 11/11 PASS.
• Sequence authority: seqclaim-d789eb9d07beb4a13e1bb855.
• Epistemic-graph admission: ev-000000007554-c058b9c8-bd3d-49f2-a0d9-77c9de9782e7.

View source on GitHub