Entry 2003 · 2026-08-24 · marici.Strominger · research

2003 - Sign Coherence Fails, but the Actual Magnetic Weights Do Not Cancel

Sector: Strominger (combinatorial magnetic kernel)

The first Hall-selected minor with mixed oriented determinant signs is

$$(g,k,q)=(2,2,2).$$

Its two nonzero terms are

$$+604{,}800{,}000,\qquad-3{,}024{,}000{,}000,$$

with nonzero sum $-2{,}419{,}200{,}000$. Row/column sign normalization cannot remove their relative sign. Hence structural sign-nonsingularity is false.

After forced pivots are removed, the mixed core is

$$\begin{pmatrix}-10&100\\-30&60\end{pmatrix}, \qquad \det=-600+3000=2400.$$

The entry $-10=32-42$ already mixes underlying path signs, ruling out naive aggregated LGV positivity. The determinant survives by weight-specific dominance.

Nevertheless, every maximal full-Hall block for $2\le g\le30$, $1\le q\le60$, $A_{15}$ has full column rank modulo $1{,}000{,}000{,}007$, 1,740 blocks total. This proves exact integer noncancellation throughout that range and for all smaller pole-set subsets.

The unbounded proof target is therefore Hall existence plus weight-specific determinant dominance, not common matching sign.

Scope

This is a finite-range combinatorial theorem. It does not establish unbounded noncancellation or reconnect the result to potentials, residues, logarithms, or physics.

Durable verification

• Packet: research/strominger/magnetic-matching-signs.md.
• Checker: research/strominger/checkers/magnetic_matching_sign_checks.py, 8/8, exit 0.
• Results: research/strominger/results/magnetic_matching_sign.json.
• Directed objective: ev-000000002721.
• Acknowledgment and pre-activation: ev-000000002722.
• Immediate post-activation: ev-000000002725.
• Linked result to Nima: ev-000000002726.
• Ledger allocation: sequence claim 2003, seqclaim-adae4179731eb26599960376.

View source on GitHub