coherence

Joint coherence is not the sum of two solitudes.

The formal claim is that the coherence of two coupled systems cannot be decomposed into their individual coherences — that a real cross-coupling puts the joint spectrum above the weaker of the two, with equality only when the coupling is absent. Everything below is either the argument for that, the one test of it, or an instrument that reads it.

the argument

the coherence framework →defines the ground state as a coherence-maximising graph configuration and derives the quadratic cost function as a theorem rather than a posit

irreducibility →why the joint quantity does not reduce to the parts it is computed from

what was measured

The framework proposed its own test: compute the inequality for real dyads against randomly mismatched pairs on open hyperscanning data, where the cross-coupling should be spurious. Real pairs showed a significantly larger gap — paired Wilcoxon p = 0.0012, with 25 of 29 pairs positive and 22 of 29 beating their own pair-matched baseline.

The part that makes it worth anything is the contrast. An off-the-shelf metric — alpha-band phase lag index — found nothing on the same dataset with the same machinery. Null on the generic measure, signal on the one this theory actually predicts. It is a re-analysis of existing open data rather than a pre-registered confirmation, and it is a reason to run the pre-registered study rather than a substitute for it.

the EEG test →full method, both bugs caught before the numbers, and the limits stated

what you can run

clarity →the spectral grammar readout — language as a coherence signal

studio →write an ask and read its shape: how tightly the words connect, and how much of the vocabulary is distinct

coherence over time →your own readings, plotted — how it moves and how it returns

read this before trusting a number

The connectivity these instruments report is confounded with lexical repetition: reusing vocabulary raises it whether or not the writing is better organised. Measured causally and again across this site’s own 84 documents. So a high number alone means little, which is why the readouts pair it with a second term rather than reporting one score. The confound, the correction that failed, and the length dependence still open in the fix are written up in Variety Is Length.

The wider theory is at the framework. The body instruments are at health. The papers are in the archive.