Adaptive Gating Is Just Counting: Scalar-Mediated Energy-Identity Collapse in Federated Continual Learning under Concept Drift

When adaptive inference systems (early exits, token pruning, gated adaptation) report energy savings, what should the savings be attributed to: the adaptive policy, or merely the operating point it induces? Under event-driven binary observation with a constant per-event cost (INA219 stage constants on Raspberry Pi 3B), we show that a controller's policy enters the energy identity only through a single scalar, the trigger count. By a Le Cam two-point argument the policy is unidentifiable from this channel, and gated adaptation stays within 2c_ad of the best count-matched open-loop schedule—on hardware (-0.27 J, Wilcoxon p = 7.1e-4; paired, n = 20). The collapse carries falsifiable content: across all 680 arrival orderings the feasible grid (V in 4, 8, 16, Theta = V.c_ad^harness >= 1, c_ad^harness = 0.2896 J) returns N_fire = floor[A/Theta] exactly; at V = 2 (Theta = 0.5792 < 1) 134/680 (19.7%) deviate at (A,T) = (3,17), diluting to 1.67% at the hardware window (A,T) = (5,300). The policy can matter; it cannot bypass one scalar. The claim is falsified precisely where Theta < 1. Given the event stream, the ledger is auditable without knowing the policy (against under-reporting and replay), and it locates where adaptation can still pay: state-dependent costs (Theorem 2(iii)).