Concept

Equilibrium — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
-0.500-0.25000.2500.50011.251.501.752nodes the stem spends per rung, log₁₀transition late by, in rungsone rung late8 rates · rise 0.4 → 0.0012worst mean lag 0.087 rungs

The lag that is not there

A pattern built out of its own history should hold its old parastichy pair past the point where a fresh lattice would have changed, and the gap should grow as the shoot is hurried. Over a fifteenfold range of rate it does not — every transition lands within a tenth of a rung of where the static ladder puts it.

emergence · tracking
-0.25000.2500.500123456lag, in nodescorrelation between a divergence and the one that many nodes latersampling band4 runs each · 243 divergences per runmatched at 0.75° of scatter

The sequence has a memory

Every measurement this collection has made of a stem's divergence angles throws the order away. A spread is invariant to shuffling. Put the angles back in order and there is a large correlation between one and the next — 0.54 with no noise at all — which is the rule correcting itself, and which nothing had looked at.

cylinder · sequence
field 0.0052.10.70° of scatterfield 0.00750.01.00° of scatterfield 0.010.01.12° of scatterjostle 0.22.10.89° of scatterjostle 0.41.10.87° of scatterjostle 0.81.11.12° of scatterplacement 0.20.00.78° of scatterplacement 0.40.00.94° of scatterplacement 0.80.01.42° of scatter3 runs each · a basin change is half a local spacingplacement noise: zero by construction

Which minimum was chosen

The rule takes an argmin, so there are two completely different things noise can do to it: move the answer, or move the question. One of them can change what is chosen and the other cannot, ever — and the difference is exactly zero against one or two placements in a thousand, at amplitudes where every other measurement says the two are identical.

emergence · noise entry
field1.64°intact to 0.015, broken by 0.02jostle1.72°intact to 1, broken by 1.4placement1.42°intact to 0.8, broken by 13 runs per amplitudescatters 19% apart

The boundary belongs to the pattern

Three kinds of noise, in three incommensurable units, destroy a lattice at the same place — about a degree and a half of divergence scatter. The previous phase measured that of two kinds and called it a scale rather than a constant. With a third it looks less like a coincidence and more like a property of what a lattice is.

emergence · scatter tolerance

Named alongside it

The objects these essays reach for when they reach for this one.

Divergence angleEnsembleMeasurementNoiseThe placement ruleBasinIdentifiabilityLattice offsetRiseSummary statisticToleranceTracking

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