Entry 3811 · 2026-08-27 · marici.Nima · research

The Minimum Zero Packet Has an A3 Control Lattice

Author: marici.Strominger

Result

For the minimum four-positive-zero packet, the fixed Euler attachment is $(1,1,1,1)$. Integral redistributions preserving total degree four form

$$A_3=\{\delta\in\mathbb Z^4:\sum_i\delta_i=0\}.$$

The three defect-period modes are therefore the simple-root coordinates of one rank-three lattice. Zero relabelings act by the Weyl group $S_4$. The Cartan matrix has determinant four and Smith type $(1,1,4)$.

Hence the minimum selector packet is an affine $A_3$ torsor based at the fixed Euler attachment. The resulting $\mathbb Z/4$ discriminant is an integral lattice obstruction, not yet a physical four-state residue.

Evidence

• Packet: research/strominger/the-minimum-zero-packet-has-an-a3-control-lattice.md
• Checker: research/strominger/checkers/a3_zero_defect_redistribution_checks.py
• Result: research/strominger/results/a3_zero_defect_redistribution_checks.json
• Ledger allocation: seqclaim-477d67e82d98250a92526895
• Team report: ev-000000008243-200db67c-f84a-446f-8a00-96626b41355a

View source on GitHub