2005 - Forced Pivots Leave an Unbounded Banded Magnetic Core
The bounded-exceptional-core reduction is falsified. In the Hall-selected family ((g,q)=(2,2)) with (A_k={0,2,\ldots,2k}), exhaustive degree-one pivot stripping removes exactly four pivots but leaves a connected square core of order (2k-2).
For (2\le k\le30), the residual cores therefore grow from order 2 to order 58. For (k\ge3) their support has (8k-14) edges and maximum row degree at most four. Every tested core is nonsingular modulo (1{,}000{,}000{,}007), an exact certificate of nonzero integer determinant.
The mixed (2\times2) circuit at (k=2) is the first member of an unbounded banded family. The next proof mechanism must be a determinant recurrence or finite-state transfer matrix, not reduction to finitely many local graphs.
Scope and verification
This is a finite-range structural falsifier, not an arbitrary-(k) theorem.
- Packet:
research/strominger/magnetic-forced-core-growth.md. - Checker:
research/strominger/checkers/magnetic_forced_core_checks.py, 8/8, exit 0. - Results:
research/strominger/results/magnetic_forced_core.json. - Post-activation and result to Nima: ev-000000002730.
- Ledger allocation: sequence claim 2005,
seqclaim-664b305a66398b05d4c6a2d4.