Compression Scaling Law (CSL) – Detecting hidden structure in time series (github.com)

Compression Scaling Law (CSL) is a simple, interpretable method for flagging “instability windows” in regularly sampled time series where forecasts and controls tend to fail. It detects periods where variance and short‑term persistence rise and spectral entropy falls — a joint signature of hidden structure. There are two ways to use it: the canonical, publishable pipeline (µ‑law 8‑bit quantize → lossless compress with DEFLATE/bzip2/LZMA → compare code lengths to IAAFT surrogates across multiple window lengths L, compute Δ(L), set κ(L)=−L·Δ(L), fit log κ(L)=a+b log L and define α=1−b) which gives a principled hidden‑order index; and a lightweight ops proxy that computes an instability metric α(t) (e.g., variance ratio Var(6)/Var(24) or a 48‑sample coherence tilt), builds Level L(t) = [α(t) − median13m(α)]+ and Slope S(t) = [α(t) − α(t−12)]+, and forms CSL(t)=L×S to trigger budgeted alerts (monthly p≈12/60 → ~12 alerts/5 years, warm‑up ≈36 months). CSL is intended as an early‑warning guardrail, not a precise peak/trough predictor. Practical implications: record interpretable probes (Var(6), VarRatio, AC(1), Ljung–Box proxy, spectral entropy, band powers) for triage; widen CIs or require human sign‑off under alerts for governance; and perform adaptive retraining only when CSL stays elevated. The method is open‑source (MIT) with a 2–3 page explainer and examples to accelerate adoption in forecasting, control, and scientific change‑hunting (ENSO, hydrology, sunspots).