The shared vocabulary, defined once.

For a system with a fixed total coupling budget, the specific configuration that maximizes coherence χ subject to that budget. Not a presumed target — a computable graph, defined as an argmax.

Distance of the system's current state from its ground state, along some direction in the space of graphs with fixed budget. ξ = 0 at the ground state.

The cost of being displaced by ξ. Originally assumed quadratic by convention; The Coherence Framework proves it as a theorem — the necessary leading-order term of coherence loss near any true maximum, since the first-order term vanishes there.

The configuration a displaced system drifts toward over time, at some rate δ, if left alone.

The cost of returning to ground state after a displacement has been held for duration τ. Fixed cost f plus a term that grows superlinearly with how long the displacement was sustained — the longer you stay displaced, the more it costs to come back.

The Fiedler value of a system's graph Laplacian — the standard spectral-graph-theory measure of algebraic connectivity. A graph with χ = 0 is disconnected; larger χ means the graph resists being split into weakly-connected pieces.

The degree matrix minus the weighted adjacency matrix, for a system represented as a weighted graph (nodes = components — neurons, sentences, oscillators, people; edge weights = coupling strength). The object whose eigenvalues carry coherence.

The smallest non-zero eigenvalue of a graph Laplacian. Named for Miroslav Fiedler; the standard quantity in spectral graph theory for "how connected" a graph is, independent of raw edge count.

The Fiedler value of the joint Laplacian of two coupled systems A and B. Proven not decomposable into χ(G_A) and χ(G_B) alone: λ₁(L_AB) ≥ min(χ(G_A), χ(G_B)), with equality only when cross-coupling is zero. Two individually coherent, entirely uncoupled systems have zero joint coherence — the formal content behind "coherence cannot be achieved alone."

Coherence redefined as a property of a trajectory {χ(t)} rather than a single state: a high time-average of χ(t) over an interval, plus self-correction — a perturbation that drives χ down gets paid back via C_return rather than settling at a new, lower attractor. Built to give coherence duration, since experience has no zero-duration instance.

The difference between a graph's dominant eigenvalues — used by Clarity as one of the client-side metrics alongside coherence score.

Introspection reports contents with real authority — what you noticed, felt, remembered. Causes sit above that ceiling: Nisbett & Wilson 1977, choice blindness, the split-brain interpreter all show causal stories generated after the fact, not read off directly.

Near a tipping point, a system returns more slowly from small perturbations. Recovery time, variance, and lag-1 autocorrelation all rise — a generic early-warning signal that shows up across ecology, climate, and physiology, independent of the specific system.

A process whose rule is knowable in advance but whose outcome only comes by letting it happen — weather, development, quantum measurement, meaning, mind. The sameness across these domains is real; treating it as one single phenomenon rather than several distinct kinds is the mistake this note corrects.

A near-critical system where event size is independent of trigger size — one grain can set off an avalanche of any size (Gutenberg–Richter law; Bak, Tang & Wiesenfeld 1988). The mechanism behind the site's sandpile instrument.

A working note takes one claim from outside literature, grants its true kernel with real citations, corrects one over-reach, states a limit, and offers the result as a proposal — it never redefines the published framework's own math. A paper (this site's six DOI-bearing works) is what a working note becomes once it's been tested further and holds up as load-bearing.