Lemma 4: Isotropic Leakage

Claim: the dynamic coupling does not remain perfectly within the channels. It leaks isotropically into the 3D substrate, reducing the effective dynamic term by a factor of 1/(84π).

The 21-channel dynamic coupling radiates into three-dimensional space (AP10: three spatial dimensions). In 3D, a source radiating isotropically distributes energy across a solid angle of 4π steradians.

The dynamic coupling has 84 dimensional expressions (21 channels × 4 dimensions, from Layer 1). Each dimensional expression leaks into the full solid angle.

The leakage per dimensional expression per solid angle is 1/(84π). The total leakage fraction of the dynamic coupling is:

Leakage fraction = 1/(84π) = 0.00379

The effective dynamic term is:

α_em × 21 × (1 − 1/(84π)) = 0.15266

The 84 that appears in the leakage denominator is the same 84 from the static count (Layer 1: 21 channels × 4 dimensions).

The manifold’s dimensional structure both generates the static resistance and normalises the leakage. This is not a coincidence. The dimensional expressions are the channels through which the leakage occurs.

The leakage is normalised by the very structure it leaks through.

KS-30.2: The assumption of perfectly isotropic leakage gives 1/(84π) exactly. Anisotropic leakage (preferential radiation along specific channels or faces) would modify the correction.

The 5 ppb residual is consistent with a small anisotropic contribution at O(α²_em). See §8.