From Edges to Curves: Calibration of Autonomous Coupling Characterization in Live Systems

Autonomous agents tending a shared substrate—physical, computational, or mathematical—affect each other through coupling channels invisible to each agent individually. A companion paper (DOI 10.5281/zenodo.21962956) established that agents can discover this coupling by guardrail-bounded probing. The present work asks the next question: how accurately can the coupling be measured? We present the characterization walk: the sending agent probes its parameter at self-chosen levels while the others hold fixed as sensors; each level yields a median reading carrying an error bar computed from the local noise; the next level is always placed where an unsampled gap could hide the most response; and the walk stops when what remains unknown is priced below the trials it would cost to remove. The procedure is calibrated against closed-form planted truth that the walking agents never see, across a 32-cell grid: coupling strength 0.0–0.9, Gaussian noise to σ = 0.10, four response shapes, six wiring topologies, and two regimes of non-stationarity. Every certified point falls within its own reported uncertainty (worst 1.76σ). Curves are certified at coupling 0.1 and at noise σ = 0.10 —including the exact condition at which the block-step detector of the companion paper no longer detects. No planted sentinel—dead parameter, reverse direction, empty channel, zero coupling—produces structure. Under noise that grows through a run, the error bars fatten in real time and the truth stays inside them; under fast drift the walk refuses to converge rather than return a fabricated average. The contribution is a measured certificate—working range, error, allocation, and refusal conditions—for autonomous characterization of hidden coupling. The accompanying archive contains the full evidence bundle: 32 per-cell curve exports with per-point error bars, the master results table, run identifiers for every measurement, and the script that regenerates every table and figure in the paper from the data.