test(stammbaum): every unit centre sits within its child-units span (#724)

Fixture-wide loop over the canonical forest and a synthetic tree: each unit's
run centre is within [min, max] of its child-unit centres — the ancestor
centring invariant, asserted on real data.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/src/lib/person/genealogy/layout/buildLayout.test.ts

@@ -1,5 +1,6 @@
 import { describe, it, expect } from 'vitest';
 import { buildLayout, NODE_W, NODE_H, COL_GAP, ROW_GAP } from './buildLayout';
+import { buildFamilyForest, type Unit } from './familyForest';
 import canonicalFixture from '../__fixtures__/stammbaum.json';
 import type { components } from '$lib/generated/api';
 
@@ -461,3 +462,43 @@ describe('buildLayout — named-bug guard: deep bloodline (#724)', () => {
 		expect(centerX(layout, d)).toBe(mid);
 	});
 });
+
+// Centre-x of a unit's run, derived from its primary's left edge + run width.
+function unitCenter(layout: ReturnType<typeof buildLayout>, u: Unit): number {
+	const left = layout.positions.get(u.id)!.x;
+	const width = u.members.length * NODE_W + (u.members.length - 1) * COL_GAP;
+	return left + width / 2;
+}
+
+describe('buildLayout — ancestor centring invariant (#724)', () => {
+	const fixtureNodes = canonicalFixture.nodes as unknown as PersonNodeDTO[];
+	const fixtureEdges = canonicalFixture.edges as unknown as RelationshipDTO[];
+
+	it('every unit centre sits within its child units span (canonical + synthetic)', () => {
+		const cases: [string, PersonNodeDTO[], RelationshipDTO[]][] = [
+			['canonical', fixtureNodes, fixtureEdges],
+			[
+				'synthetic',
+				[node('R', 'R', 0), node('c1', 'c1', 1), node('c2', 'c2', 1), node('c3', 'c3', 1)],
+				[parentEdge('R', 'c1'), parentEdge('R', 'c2'), parentEdge('R', 'c3')]
+			]
+		];
+
+		for (const [label, nodes, edges] of cases) {
+			const layout = buildLayout(nodes, edges);
+			const forest = buildFamilyForest(nodes, edges);
+			const walk = (u: Unit) => {
+				if (u.children.length > 0) {
+					const childCenters = u.children.map((c) => unitCenter(layout, c));
+					const lo = Math.min(...childCenters);
+					const hi = Math.max(...childCenters);
+					const c = unitCenter(layout, u);
+					expect(c, `${label}: unit ${u.id} centred in child span`).toBeGreaterThanOrEqual(lo);
+					expect(c, `${label}: unit ${u.id} centred in child span`).toBeLessThanOrEqual(hi);
+				}
+				u.children.forEach(walk);
+			};
+			forest.roots.forEach(walk);
+		}
+	});
+});