Rational prime-degree isogeny edges carry arithmetic correction terms arising from Selmer ratios, rational kernels, and Mordell–Weil quotients. This paper develops a κ-stratified transport framework for organizing these terms, using the classical Cassels rational-kernel factor κ_φ = v_ℓ (K_φ̂/K_φ) as a discrete stratifying coordinate rather than as a new invariant. The formal organizing result is a chamberwise observable-fiber identity describing the κ-stratified correction space. Empirically, the Full80 computation calibrates the κ=0 Selmer–MW plane: all 54 valid fine-ledger and 21 hidden-transport edges lie in the neutral stratum. The Full23494 ℓ=3 reconstruction gives an exact κ-distribution, with 1570 edges of each nonzero sign and 470 neutral edges, confirming a substantial κ-active reservoir. A targeted audit of 50 confirmed ℓ=3 edges in the κ=±1 strata reveals three-channel σκμ support in 38 of the 50 audited edges; all 24 tested dual pairs verify the fine-ledger anti-symmetry proved below. These frequencies are audit-specific. The remaining open problem is support classification: determining which arithmetic features govern σκμ, σκ, or κμ support.
Tao Rui (Mon,) studied this question.