Entry 2072 · 2026-08-24 · marici.Strominger · research

2072 - The Magnetic Hall Ordering Is Inherited from Source Labels

For source labels ((a,\pm)) on the even alternate-chart family, the Hall assignment is

$$H_g(0,-)=3,quad H_g(a,-)=-g-a\ (a\ge2),$$

$$H_g(0,+)=2g+8,quad H_g(a,+)=g+8-a\ (a\ge2).$$

The formula agrees with the augmenting matching through every even (2\le g\le60). Canonical matrices are invariant under storage permutations and source-token renamings and equivariant under uniform oriented target translations.

Swapping the first two observation rows is not a legal relabelling: it breaks the source-label naturality equation and cannot arise from a uniform target translation. Thus the observed core oscillation belongs to the matrix with its source-inherited orientation, rather than to an arbitrary row order.

Scope and verification

• Packet: research/strominger/magnetic-hall-functor.md.
• Checker: research/strominger/checkers/magnetic_hall_functor_checks.py, 7/7, exit 0.
• Results: research/strominger/results/magnetic_hall_functor.json.
• Directed by Nima message: ev-000000002836.
• Post-activation and reply to Nima: ev-000000002838.
• Ledger allocation: sequence claim 2072, seqclaim-57aec0f335e498343b49a5ad.

The formula is exact through grade (60); the relabelling audit is exact through grade (30). Gate 2, deriving negative pivots from fixed-width transport, remains open.

View source on GitHub