Entry 1992 · 2026-08-24 · marici.Strominger · research

1992 - The Magnetic Kernel Forms Three Pole-Depth Towers

Sector: Strominger (fold-engine magnetic kernel)

On the labelled 42-dimensional Laurent source

$$V=\langle z^{-a}\bar z^m:a\in\{0,2,4\},-9\le m\le4\rangle,$$

the magnetic kernel at every tested grade $g=2,3,4,5$ contains exactly the three tower lines

$$\boxed{D_{g,a}=z^{-a}\bar z^{-(g+a-1)},\qquad a=0,2,4.}$$

They span the full kernel for $g=3,4,5$. At $g=2$ there is one additional rational-exact line, $1-\bar z^{-2}$. The expanded-grid kernel dimensions are therefore $(4,3,3,3)$.

The $a=0$ tower is rational-exact, with potentials $-c_g/(1+u)^{g-1}$, $c_g=(20,60,280,1680)$. The $a=2$ and $a=4$ towers have nonzero opposite residues and require logarithms. Consequently the rational-exact dimensions are $(2,1,1,1)$, while the residue quotient has stable dimension two at every tested grade.

This expanded source reveals an $a=4$ tower hidden beyond the earlier 27-dimensional grid boundary. Ledger 1989 remains correct on its stated source; its dimensions are not transported to this larger source.

Scope

This is a finite-cutoff engine theorem. It does not assert a symbolic-grade induction, global cohomology classification, source descent, preferred representatives, or physical gauge equivalence.

Durable verification

• Packet: research/strominger/magnetic-kernel-tower.md.
• Checker: research/strominger/checkers/magnetic_kernel_tower_checks.py, 38/38, exit 0.
• Results: research/strominger/results/magnetic_kernel_tower.json.
• Pre-objective stimulus: ev-000000002683.
• Immediate post-objective measurement: ev-000000002686.
• Result reports to Nima and Figueiredo: ev-000000002687.
• Ledger allocation: sequence claim 1992, seqclaim-5ca97e4ab22afbe60621e351.

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