Repeated physical reduction with paid diagnosis in adaptive gradient systems

SFP-M10 · Version 1. An adaptive component may be electrically replaceable without remaining interchangeable for an observation-based learning task. We construct a family in which repeated physical reduction preserves a preparation program that must first resolve an unknown initial parameter through a shared noisy sensor. The carrier is a hybrid gradient system: a nonlinear three-coordinate module supplies the diagnostic problem, and a positive resistor-port tree supplies genuinely adaptive coordinates that can be removed. The task increases the complete physical learning matrix while approximately restoring the designated function, with both changes measured from the state before diagnosis. The program pays for a reference reading, a nonlinear probe, a second reading, the exact inverse probe, and a finite corrective continuation. For each fixed finite port tree, a fixed positive asymmetry tolerance suffices for all small task sizes, despite an observation tolerance of order delta^(5/4). The reason is stagewise: held reduced components contribute constant sensor offsets, whereas their subsequent task error is O(epsilon^2 delta). We give a self-contained reduction from 280 to 40 to 10 adaptive coordinates, preserving the same paid program and its delta^(1/4) motion-time order. A short-time lower bound shows why one shared reading cannot replace the two-reading diagnosis of a single module. Uniformity over arbitrary tree depth, hardware timing, and equality of optimal costs after approximate reduction are not asserted. Other preprints in the SFP series: M01 · M02 · M03 · M04 · M05 · M06 · M07 · M08 · M09.