Visible Non-Overcompensation in BSD Valuation Flows Along Rational Prime Isogenies

We study edge-level variation of the Tate-Shafarevich group order along prime-isogeny edges, as recorded in the Cremona database (where |Sha| values are often BSD-predicted), in a primary sample of 50, 000 Cremona isogeny classes (21, 367 prime-isogeny edges) and an independently drawn, non-overlapping holdout sample of 4, 969 classes (2, 127 edges). For an l-isogeny, define the Tamagawa-torsion visible flow aₚhi and the Sha edge difference Sₚhi. Across all 23, 494 combined edges we observe aₚhi * Sₚhi <= 0 with zero exceptions. We show that this sign-opposition is equivalent, under BSD edge accounting, to the visible non-overcompensation inequality: the period-regulator channel may oppose the Tamagawa-torsion channel but is never observed to overcompensate it. In the primary sample, exact absorption accounts for 98. 7% of opposing cases, partial absorption occurs on only 149 edges, and overcompensation is absent. Shuffle null models give deviations of -33 sigma and -42 sigma. We interpret the result not as a new theorem for Sha, but as a reproducible edge-level organization of classical BSD/isogeny compensation mechanisms. Underlying mechanisms are governed by classical isogeny theory (Cassels' isogeny formula, Dokchitser-Dokchitser local Tamagawa classification, BSD isogeny compatibility). The database |Sha| values are often BSD-predicted, so the full compensation identity is a BSD-consistency audit.