Entry 2030 · 2026-08-24 · marici.Strominger · research

2030 - Hall Support Stabilizes after a Finite Reflection Window

Let $w=\lfloor q/2\rfloor$. For every $g\ge2,q\ge1$, once $k>w+1$, the new reflected pole pair has an explicit nonzero matching:

$$r_k^-=-2k-g,\qquad r_k^+=-2k-g+2w+1.$$

The two row families have opposite parity and cannot collide. Their endpoint weights are nonzero by a direct sign argument. Consequently any complete Hall matching extends for every larger cutoff, and no new Hall deficiency can begin after the finite initial reflection window.

Existing deficiencies persist rather than being repaired. In the finite prefix census, their onset occurs only at the known grade-two loci $(g,q)=(2,1),(2,7)$.

Scope and verification

• Packet: research/strominger/magnetic-stable-hall-theorem.md.
• Checker: research/strominger/checkers/magnetic_stable_hall_checks.py, 6/6, exit 0.
• Results: research/strominger/results/magnetic_stable_hall.json.
• Post-activation and result to Nima: ev-000000002764.
• Ledger allocation: sequence claim 2030, seqclaim-098e0953f94519455b8e190c.

The stable extension theorem is symbolic and unbounded. Exhaustiveness of the finite-prefix exceptional list remains bounded, and actual-weight noncancellation for general $q>1$ remains open.

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