Characterization

Detection answers is there an edge? Characterization measures its shape: for every (sender, receiver, parameter, channel), a response curve — parameter level versus measured objective shift, point by point, each point with an uncertainty bar. The result is a measured coupling map, not a yes/no graph.

What a Curve Is

Each curve point is a triple (level, shift, bar):

level — where the sender's parameter was pushed (the walk's current probe level)
shift — the receiver's median objective shift, push window versus pause window
bar — the measurement uncertainty, from the raw sample scatter of those windows

The ABA structure is built into every point: the shift is only counted when it appears during the push and recovers during the pause. A shift that does not recover is flagged as drift, not measured as structure.

How the Walk Runs

Breeders in a shared interference group take turns through DB-backed leases. One is the sender; the others hold still.

The walk is deterministic and complete by contract. Levels are visited in farthest-point order — midpoint, then extremes, then quarters — a low-discrepancy sequence computed, not sampled. No level is skipped while the walk runs; smartness only accelerates (early retirement of converged parameters), it never licenses gaps.
Every listener is measured at once. One sender's walk measures the response curves of all holding receivers simultaneously — in a three-agent chain run, a single walk produced all 36 curves, of which exactly the three planted coupling paths were non-flat.
Re-measurement blends. A repeat probe within bars tightens the existing point (inverse-variance blend); beyond bars the point relocates and the curve is flagged as drifted.
Dead ground is cheap. A parameter with no coupling retires after ~3 flat probes; a full curve on a 100-level grid cost 6-9 probes in validated runs. The budget goes to structure, not silence.

Priced Stopping

A curve retires when converged (repeated measurement agrees) and every remaining gap is priced: the ignorance left in an unresolved interval is

ignorance = jump × width / range

and retirement requires it below the local measurement bar — remaining uncertainty cheaper than one more probe. In the deepest validated run (a 9-level tent curve, every point within 0.55σ of planted truth), the walk retired by price with three shape-honest gaps still open on the steep flank, each priced below its local bar. The bracket between measured points is part of the artifact: it says where the edge could still be, and what that uncertainty costs.

Calibration Against Planted Truth

On the generic bench the ground truth is known, so calibration is exact comparison:

Run	What it measured	Result
One-way edge (0.7, saturation)	carrier level 100	−0.118 ± 0.022 vs truth −0.117
Full tent curve	9 levels	every point ≤ 0.55σ
Two channels	objective_0 vs objective_1	tent on channel 0 (≤ 0.49σ); channel 1 flat (≤ 0.73σ)
Three agents, one uncoupled	per-receiver separation	edge measured within ~0.011 of truth; uncoupled agent flat

The two-channel row is the param→channel mapping measured rather than assumed: a parameter influences exactly the channels where its curve is non-flat, and the flat channel is honest flat, not missing.

Composition: What the Map Predicts

Measured edges are only useful if they compose. On a chain topology (node-1 —0.7→ node-3 —0.5→ node-2), with all curves measured by the engine:

Identity (in-sample): the two-hop curve composed from chained one-hop curves matches the directly measured two-hop response — 9 of 9 levels within 2σ, median deviation 0.18σ.
Prediction (out-of-sample): levels never probed before, predicted from the composed map, then measured: 0.13σ and 0.35σ deviation.
Steering (the loop's first closing): given a target value at the chain's end, the measured map was inverted to a sender parameter, the parameter applied, and the result measured: target −0.100, landed −0.1038 ± 0.038.

Scope, stated plainly: these composition results are on the quiet bench (no opposing optimizers acting during the act), with additive-linear coupling physics, one seed per scenario. Composition across nonlinear coupling paths is open — see Open Research.

Reading Curves from a Running Engine

The causal service owns the curves and serves them at any time:

GET /curves           → every curve: sender, receiver, param, channel, points, gaps
GET /detect/{a}/{b}   → detection verdict per channel

Curves persist across service restarts and are removed with their breeder's lifecycle. The Getting Started walkthrough runs this end to end against a planted topology; the scenario library ships the calibration cells above (see Bench Scenarios).