Drift and its z-score: separating a real structural move from noise.

The drift set

Four comparisons, each a different time horizon's argument.

Table 4 computes four deltas, and each carries its own meaning. 4−6 is the fast lens against the medium: the earliest directional shift the pipeline can see, and correspondingly the noisiest. 4−12 measures fast against the structural rolling lens — a wider gap, slower to fire, more meaningful when it does. 6−12 asks whether a medium-term shift is persisting against structure. And 12−Cum is the deepest question: has the structural rolling condition itself moved away from the lifetime anchor? Read as a set, they describe the shape of a change — a move visible in 4−6 only is a candidate; one visible across all four is a system genuinely relocating.

Why normalize

The same drift is a shrug in one metric and an alarm in another.

Raw drift can't be compared — across metrics, across branches, or even across periods within one branch. A metric whose weekly readings swing wildly produces large drifts constantly and means nothing by them; a metric that normally sits still produces a small drift that's genuinely extraordinary. Dividing drift by σ12 — the structural volatility anchor — converts the number into units of that metric's own normal variation, which makes it comparable everywhere. This is the first point in the entire pipeline where signal strength becomes comparable across the whole system: Normal at z +1.8 and Trend No-Partial at z −1.2 is a statement about structural divergence that no raw reading could support.

The denominator discipline

σ12, never σ6 — and the reason is architectural.

One of the sharpest corrections in the SDE's build history concerned exactly which sigma normalizes the drift, and the verdict was unambiguous: σ12 is the denominator. The separation is deliberate — σ6 already has a job in Table 3, where the σ6/σ12 ratio is the instability-expansion signal, and reusing it as the normalization anchor collapses two distinct diagnostic layers into one. The practical consequence is severe: normalizing against a fast-moving sigma means the denominator itself lurches around, so the z-score jumps for reasons that have nothing to do with the drift it's supposed to be measuring, and the entire interpretation layer becomes unstable. σ6 diagnoses stability; σ12 anchors normalization. Keeping them apart is what makes the z-score trustworthy.

• σ12 as denominator = a stable ruler. σ6 as denominator = a ruler that stretches while you measure.
• The z-score is a supporting diagnostic, not a standalone decision engine — the guide says so explicitly.
• A high z-score whose Table 6 interpretation agrees is high-priority review material; a high z-score alone is a question.

Reading the bands

Magnitude is confidence; sign is direction; context decides both.

The bands convert |z| into decision language: below 0.5 is noise — drift exists but is weak relative to structural volatility; 0.5 to 1.0 is moderate and early, worth watching but not decisive alone; 1.0 to 1.5 is meaningful, active enough to matter; above 1.5 is strong deviation, the metric moving materially away from its structural norm. Sign carries direction, with the metric-specific inversion for drawdown that Table 6 must respect. And context governs both: a strong z-score in a metric whose σ6/σ12 ratio shows expanding instability deserves less confidence than the same number in a settled series — which is exactly why the stability table sits upstream of the z-score rather than beside it.

The key idea

Normalization is what makes structural comparison possible at all.

Without the z-layer, the SDE would produce five metrics' worth of drift numbers that couldn't be ranked, compared, or triaged — every reading would require its own intuition about what counts as large. The z-score collapses all of that into one scale where 1.5 means the same thing everywhere: this metric has moved materially away from its own normal. That's what lets an operator scan seven entities across five metrics and know instantly where to look first.