Reading the result map: where the hub signal is real, and where it is not

The result map is the most important — and most misread — part of this work. Here is how to read it honestly: what the hub signal does, what it does not, and why the effect sizes are small on purpose.

Magnitude is lawful, and graded by market depth

The hub R — the order parameter’s amplitude — carries a small, positive, robust signal about forward realized volatility, after a horizon-matched trailing-volatility control and a spline nonlinearity control. The partial correlation is strongest in the deepest, most continuous markets and decays as microstructure gets noisier:

• Equities / bonds / commodity ETFs: r = +0.062 (13 units, 100% positive, 92% chronological sign-agreement).
• G10 FX: r = +0.054 (5 pairs, 100% positive, 100% chronological).
• Crypto (27-coin panel): r = +0.049 (96% positive, but 48% chronological — pooled-robust, time-unstable; active research frontier).
• Prediction-market belief series: r = +0.022 (spline-control p = 0.15 — lawful-but-faint; active research frontier).

Pooled block-permutation inference puts this below p = 0.003. These are partial correlations after controls, so they are modest by construction. That is the point: a small effect that survives the gauntlet is worth more than a large raw number that dissolves under scrutiny.

Direction is null everywhere — on purpose

The aim ψ — the order parameter’s phase — does not predict the sign of the next move. We pre-registered this as Phase Sovereignty and confirmed it against a powered momentum control on the identical series:

• R→direction: equities −0.010, crypto +0.005, belief −0.028 — indistinguishable from zero.
• The momentum control recovers direction on the same data (e.g. Bitcoin: R→direction = −0.0009 versus momentum −0.247).

So the test is powered to find direction if it were there — and it is not. A coherence reading tells you the system is tightening (volatility), not which way it will break (direction).

Why we lead with the null

Science first, alpha second. Reporting the direction null with equal weight to the magnitude finding is what makes the magnitude finding believable. A method that only ever reports its wins is not a method; it is marketing. The honesty is the moat.

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All figures cited here trace to the locked working paper (Table 1 magnitudes, Table 2 direction nulls). No number is added or changed in web adaptation without re-verification.