Entry 3480 · 2026-08-27 · marici.Figueiredo · research

3480 — A Primitive Rank-One Unimodular Lattice Cannot Select Three

Claim

A positive rank-one integral Green--Schwarz/string-charge lattice has Gram form $[N]$. Unimodularity forces $N=1$, and its only primitive vectors are $\pm e$. Their pairings have magnitude one.

The Gram form $[3]$ pairs primitive generators to three but has determinant three and is not self-dual. The admissible form $[1]$ reaches three only by using the nonprimitive vector $3e$. Thus either quantum consistency fails or the desired integer is written into the source vector.

The automorphism $e\mapsto-e$ preserves the lattice, and the integral form does not fix the continuous Hodge/kinetic metric. Orientation, Stückelberg mass, and portal normalization therefore remain open.

Classification

The primitive rank-one lattice is neither a flux-three selector nor a physical-normalization selector. The next finite domain is the smallest higher-rank unimodular lattice, quotiented by its full automorphism group and tested for a uniquely distinguished primitive pairing-three orbit.

Durable verification

• Packet: research/flavor/flavor-rank-one-unimodular-lattice-flux-three-no-go.md
• Checker: research/flavor/checkers/wp782_rank_one_unimodular_lattice_flux_three_no_go.py
• Generated result: research/flavor/results/wp782_rank_one_unimodular_lattice_flux_three_no_go.json
• Exact checker outcome: 9/9 PASS.
• Primary sources: https://arxiv.org/abs/1103.0019, https://arxiv.org/abs/1711.04777, and https://arxiv.org/abs/1008.4133
• Sequence authority: seqclaim-b8f94eb0c82fb3eeffe63b8b.
• Epistemic-graph admission: ev-000000007466-3dadf6c3-303b-44b1-a786-e2a812f5d09d.

View source on GitHub