Methodology

What is measured

li Jade treats a relationship as association(X, Y, geography, season, lag, time). Four questions stay visible: relationship strength, relationship stability, pattern persistence, and forecast skill. The Li Index names their joint remainder. It does not replace them.

Li Index (Λ) — provisional

The Li Index is a measure of coherence — remaining usable order in a relationship. That is operational negentropy: not a thermodynamic quantity, and not a moral score. A high Λ means the association still has a shape you can spend on a decision. A low Λ means it has decohered toward noise.

Λ = (S · P · K · E)^1/4

Geometric mean: one weak term pulls Λ down. Coherence is conjunctive. Bands: Decohered (<0.25), Partial (0.25–0.45), Coherent (0.45–0.65), Strongly coherent (≥0.65). Version 0.2-provisional. If K is missing it is labelled, and a three-term mean is used. Λ never authorises a regime-shift claim. Forecast S and K use a stated ceiling (MAE 2.5 °C or Brier 0.25).

What would falsify the index: the band flips under the published baselines (full record, to-1999, last 20, last 30) without that flip being shown; out-of-sample skill disappears while Λ stays “strongly coherent”; an independent nearby station disagrees on S; a null association (|r| ≈ 0) is labelled strongly coherent.

The name follows Grier’s Negawatt Philosophy: conservation as coherence and lawful design; life as negentropic; Confucian Lǐ as principled pattern. A Negawatt is conserved energy. A Li Index is conserved relationship — the structure you were relying on, still there or not.

Strength labels — provisional

Strength always names its metric, geography, season, lag, sample period and uncertainty. Spearman is reported alongside Pearson. The simpler method is preferred when it answers the question.

Drift versus break versus regime shift

• Drift — a change in recent versus historical r whose bootstrap 95% interval excludes zero.
• Structural break — a Pettitt change-point on the underlying series (for example wet-season totals), reported as a candidate when p < 0.05. Pettitt is not applied to overlapping rolling-correlation windows.
• Regime shift — a transition between persistent multi-variable configurations. Not labelled from a score.

Confidence

High / Medium / Low / Insufficient evidence. Factors: sample size, agreement of Pearson and Spearman, out-of-sample skill versus climatology, and whether the conclusion is stable across historical, recent, 20-year and 30-year baselines. Confidence is shown separately from strength. There is no 0–100 score in v0.1.

We never claim

We never label a relationship as being in regime shift merely because a score crossed a threshold.

• We never present demonstration values as factual results.
• We never treat a historical relationship as still valid merely because it once was.
• We never infer forecast degradation from isolated misses.
• We never treat a periodogram peak as a cycle.
• We never collapse synoptic pathway with moisture source.