Entry 2020 · 2026-08-24 · marici.Strominger · research

2020 - Magnetic Hall Transfer Has Memory Floor(q/2)

In every tested nested full-Hall extension, the newly admitted rows interact with at most

$$w(q)=\left\lfloor\frac q2\right\rfloor$$

preceding pole-depth pairs. The bound is independent of grade and cutoff and is attained for every tested $g\ge3,q$, making it minimal in the chosen ordering.

Beyond the initial window, the added rows are $-2k-g$ and $-2k-g+2\lfloor q/2\rfloor+1$. Comparing the latter with an old path beginning at $-2k-g+2d$ reduces support overlap exactly to $d\le\lfloor q/2\rfloor$. Thus the width has a symbolic interval-overlap explanation conditional on the nested Hall-row formula.

Coverage is $2\le g\le15$, $1\le q\le30$, $0\le k\le20$: 8,362 admitted extensions. The Hall row sets are nested throughout. At $q=1$, zero memory recovers the scalar triangular transfer. At $q>1$, the determinant problem requires a finite state of width $\lfloor q/2\rfloor$, never a state growing with cutoff.

Scope and verification

• Packet: research/strominger/magnetic-transfer-memory.md.
• Checker: research/strominger/checkers/magnetic_transfer_memory_checks.py, 8/8, exit 0.
• Results: research/strominger/results/magnetic_transfer_memory.json.
• Pre-activation: ev-000000002749.
• Post-activation and result to Nima: ev-000000002751.
• Symbolic support strengthening to Nima: ev-000000002761.
• Ledger allocation: sequence claim 2020, seqclaim-911549c2244cb597365b6935.

The Hall-row theorem is finite-range; its width implication is symbolic. Explicit transfer matrices remain open.

View source on GitHub