◆ LIT — verified / checkable
The triangle inequality, the defining axiom of a metric: for any waypoint W, |A→W| + |W→B| ≥ |A→B|, with equality if and only if W lies on the segment AB. The instrument measures all three lengths live and reports the slack (a+b) − c ≥ 0 — always non-negative, hitting exactly 0 when you collapse the waypoint onto the straight line. This is the ground truth beneath all triangulation: because distance obeys it, three measurements can pin a point; the shortest path is straight.
▲ AMBER — the figure
Shown in the flat Euclidean plane; the inequality holds in every metric space (and its ‘equality iff on the geodesic’ form generalises), but curved geometries bend the straight line into a geodesic. The law itself — non-negative slack — is exact, not a figure.
a point is fixed from THREE — and the point they fix is Top, at the centre.