Entry 2069 · 2026-08-24 · marici.Strominger · research

2069 - The Alternate-Chart Interior Core Is Oscillatory

For the ((g+8))-dimensional interior core (A_g) of the even row-(3) alternate chart, every tested leading principal minor satisfies

$$\boxed{\operatorname{sgn}\Delta_j(g)=(-1)^j.}$$

Exact fraction-free elimination across every even (2\le g\le60) verifies 1,170 nonzero leading minors without a row exchange. Therefore every ordinary Gaussian pivot is strictly negative and every full core determinant is positive.

The result identifies core nonvanishing as an oscillatory/sign-regular transport phenomenon. Swapping the first two observation rows destroys the pattern, confirming that the coherent Hall ordering is essential.

Scope and verification

• Packet: research/strominger/magnetic-core-oscillation.md.
• Checker: research/strominger/checkers/magnetic_core_oscillation_checks.py, 6/6, exit 0.
• Results: research/strominger/results/magnetic_core_oscillation.json.
• Post-activation and result to Nima: ev-000000002833.
• Ledger allocation: sequence claim 2069, seqclaim-2a52cec790f79b85e039b4c2.

This is an exact finite oscillation theorem through grade (60). An all-grade cone-preserving elimination proof remains open.

View source on GitHub