Entry 2010 · 2026-08-24 · marici.Strominger · research

2010 - The Growing Magnetic Core Has a Quartic Determinant Ratio

For the residual Hall core of the $(g,q)=(2,2)$, $A_k$ component,

$$D_2=2400,\qquad D_k=80k(k-1)(2k-1)(2k+1)D_{k-1}$$

for every integer $k\ge2$. Therefore

$$D_k=2400\prod_{j=3}^{k}80j(j-1)(2j-1)(2j+1)>0.$$

Order rows and columns recursively by their lattice labels. The two new rows vanish on all old columns, giving a block upper-triangular extension. The grade-two cubic path law gives the new $2\times2$ boundary determinant as the displayed quartic multiplier. Exact matrices through $k=20$ cross-check the symbolic derivation.

Thus the core grows as $2k-2$, but its determinant propagates through a positive scalar transfer. The $2\times2$ mixed-sign circuit with determinant 2400 is the initial condition.

The coherent Plucker gauge remains genuinely bipartite. A closed reflection-parity formula and a general-$(g,q)$ transfer theorem remain open.

Scope and verification

• Packet: research/strominger/magnetic-core-determinant-recurrence.md.
• Checker: research/strominger/checkers/magnetic_core_recurrence_checks.py, 7/7, exit 0.
• Results: research/strominger/results/magnetic_core_recurrence.json.
• Pre-activation: ev-000000002735.
• Initial finite-range report to Nima: ev-000000002738.
• Arbitrary-k strengthening to Nima: ev-000000002741.
• Ledger allocation: sequence claim 2010, seqclaim-2bcc52b81862c9cac652a541.

This is an arbitrary-$k$ theorem for the $(g,q)=(2,2)$ family only.

View source on GitHub