The predictive power of a data collection over a target has no rigorous multi-scale measure. We introduce the predictability coastline C(ε), which traces how predictive capacity scales with data resolution via an information-theoretic filtration. The coherent coastline — a min-envelope over diverse prediction targets — strips measurement artifacts to isolate system-intrinsic information. Across six systems (Lorenz, Hénon, SPY, TLT, GLD, thermostat), the coherent coastline produces a three-tier separation: chaotic attractors (0.28–0.40), financial markets (0.04–0.14), and structureless noise (≈0.03). We formalize the capture threshold — the resolution at which an observer's model exceeds the target's self-model — and show it arises from kernel asymmetry, not resolution depth. Bridge-targeted data removal is 7.7× more effective than uniform minimization. The framework's value lies in the coastline's shape, not in any extracted scalar.
Larsen James Close (Tue,) studied this question.