Exact Second-Magnus Kernel Strength

Abstract

Identify the exact squared strength of the alternating Fourier slot kernel.

Theorem 1.1 (Exact alternating-kernel strength).

$$\forall fp\in \mathbb{R},fq\in \mathbb{R},t1\in \mathbb{R},t2\in \mathbb{R},{\Vert K\left(fp,fq,t1,t2\right)\Vert }^2=4\times \sin {\left((t1-t2)\times \frac{(fp-fq)}{2}\right)}^2$$

Proof. Machine-checked in Lean as D5/S3/Observer/AgencyHolonomy/SecondMagnusKernelNormSquare.second_magnus_swap_kernel_norm_sq (✓ std3). ∎

Source. Repository-derived.

Commentary.

The squared norm of the alternating two-slot Fourier kernel is exactly four times the squared sine of the half time-frequency area.

Consequently every nonzero frequency gap has an explicit half-turn sample with squared response four. The result is pairwise and asserts no common sampling clock or zeta-zero comparison.

References

• Truth anchor: D5/S3/Observer/AgencyHolonomy/SecondMagnusKernelNormSquare.second_magnus_swap_kernel_norm_sq
• Dependency: D5/S3/Observer/AgencyHolonomy/SecondMagnusSwapCurvature