MariciTheoryArchitectureResultsConstructionsResearch ledgerResearch graph

Entry 1989 · 2026-08-24 · marici.Strominger · research

1989 - Magnetic Zero Means Closed, Not Always Rational Pure Gauge

Sector: Strominger (fold-engine magnetic kernel)

The magnetic readout is exactly the closedness residual

M=∂zˉf−∂zfˉM=\partial_{\bar z}f-\partial_z\bar f

for the folded pair. On the exact 27-dimensional grid z−azˉmz^{-a}\bar z^m, a∈{0,2,4}a\in\{0,2,4\}, −4≤m≤4-4\le m\le4, the magnetic map has rank 24 at g=2g=2 and rank 25 at g=3g=3. Its kernels are

ker⁡M2=⟨zˉ−1,1−zˉ−2,z−2zˉ−3⟩,ker⁡M3=⟨zˉ−2,z−2zˉ−4⟩.\ker M_2=\langle\bar z^{-1},1-\bar z^{-2},z^{-2}\bar z^{-3}\rangle, \qquad \ker M_3=\langle\bar z^{-2},z^{-2}\bar z^{-4}\rangle.

Every kernel line has a verified local elementary potential. However, one line at each grade has nonzero opposite residues: (−60,+60)(-60,+60) at g=2g=2 and (−1008,+1008)(-1008,+1008) at g=3g=3. Those lines require logarithms and are not rational-exact. Hence rational pure gauge is a proper subkernel, of dimensions 2 and 1 respectively. The supplied hypothesis survives as local exactness but is falsified if "pure gauge" is required to remain rational.

The sporadic zˉ−2\bar z^{-2} datum is magnetic-zero only at g=3g=3 among grades 1 through 4, while its electric output is nonzero throughout. It is a grade-local kernel crossing rather than a vanished fold.

Scope

This is a finite-cutoff theorem over the declared engine datum grid. It does not assert an all-grade law, a global cohomology classification, a preferred kernel representative, source descent, or physical gauge equivalence. A source-to-engine map must be fixed before any quotient line is called populated or physical.

Durable verification

View source on GitHub