learnharness/tests/layout.test.ts

/**
 * Option A — incremental anchored force layout (core/layout.ts). The
 * properties the user asked for: the layout EVOLVES (old placements stay
 * recognizable), new nodes land near their cluster, orphans collect on
 * the rim, and everything is deterministic.
 */
import assert from "node:assert/strict";
import { describe, it } from "node:test";
import { createGraphSimulation, incrementalLayout, inferenceDepths } from "../src/core/layout.ts";
import { settleGraphLayout } from "../src/core/layout-settle.ts";
import type { GraphChain, GraphNode, Position } from "../src/core/contracts.ts";

const node = (id: string): GraphNode => ({
	id,
	name: id,
	statement: id,
	aliases: [],
	createdAt: "2026-09-13T00:00:00.000Z",
	provenance: [],
});
const chain = (id: string, premises: string[], conclusion: string): GraphChain => ({ id, premises, conclusion, provenance: [], createdAt: "2026-09-13T00:00:00.000Z" });
/** incrementalLayout's link shape — the DERIVED untyped arrow. */
const edge = (from: string, to: string): { from: string; to: string } => ({ from, to });

const mean = (positions: Map<string, Position>, ids: string[]): { x: number; y: number } => ({
	x: ids.reduce((s, id) => s + positions.get(id)!.x, 0) / ids.length,
	y: ids.reduce((s, id) => s + positions.get(id)!.y, 0) / ids.length,
});

describe("incrementalLayout", () => {
	it("bootstraps deterministically from an empty ledger", () => {
		const nodes = ["a", "b", "c", "d"].map(node);
		const edges = [edge("a", "b"), edge("b", "c"), edge("c", "d")];
		const first = incrementalLayout(nodes, edges, new Map());
		const second = incrementalLayout(nodes, edges, new Map());
		assert.equal(first.size, 4);
		for (const [id, p] of first) {
			assert.ok(Number.isFinite(p.x) && Number.isFinite(p.y), `finite coords for ${id}`);
			assert.deepEqual(p, second.get(id), `deterministic position for ${id}`);
		}
	});

	it("rest state is stable: a re-settle with nothing new barely moves nodes", () => {
		const nodes = ["a", "b", "c", "d", "e"].map(node);
		const edges = [edge("a", "b"), edge("b", "c"), edge("c", "d"), edge("d", "e"), edge("a", "e")];
		const rest = incrementalLayout(nodes, edges, new Map());
		const span =
			Math.max(...[...rest.values()].map((p) => p.x)) - Math.min(...[...rest.values()].map((p) => p.x));
		const again = incrementalLayout(nodes, edges, rest);
		let maxShift = 0;
		for (const [id, p] of rest) {
			const q = again.get(id)!;
			maxShift = Math.max(maxShift, Math.hypot(p.x - q.x, p.y - q.y));
		}
		assert.ok(maxShift < span * 0.1, `re-settle drift ${maxShift.toFixed(2)} should be < 10% of span ${span.toFixed(2)}`);
	});

	it("evolves: an anchored node stays near its anchor while a new neighbor joins it", () => {
		const core = ["a", "b", "c"].map(node);
		const coreEdges = [edge("a", "b"), edge("b", "c")];
		const previous = incrementalLayout(core, coreEdges, new Map());
		const anchor = previous.get("b")!;
		const dist = Math.hypot;
		const nearby = ["d", "e"].map(node);
		const next = incrementalLayout(
			[...core, ...nearby],
			[...coreEdges, edge("b", "d"), edge("d", "e")],
			previous,
		);
		// The anchor keeps its neighborhood (bounded drift), and the new
		// nodes landed near it rather than being flung elsewhere.
		const coreSpanBefore =
			Math.max(...[...previous.values()].map((p) => p.x)) - Math.min(...[...previous.values()].map((p) => p.x));
		assert.ok(
			dist(next.get("b")!.x - anchor.x, next.get("b")!.y - anchor.y) < coreSpanBefore,
			"anchored node b stays near its previous position",
		);
		const centroid = mean(next, ["b", "d", "e"]);
		assert.ok(
			dist(next.get("d")!.x - centroid.x, next.get("d")!.y - centroid.y) < coreSpanBefore * 2,
			"new neighbor d landed near the cluster it arrived with",
		);
	});

	it("rim: an orphan ends up outside the anchored core", () => {
		const core = ["a", "b", "c", "d", "e"].map(node);
		const coreEdges = [
			edge("a", "b"),
			edge("b", "c"),
			edge("c", "d"),
			edge("d", "e"),
			edge("a", "e"),
			edge("b", "d"),
		];
		const previous = incrementalLayout(core, coreEdges, new Map());
		const next = incrementalLayout([...core, node("orphan")], coreEdges, previous);
		const c = mean(previous, ["a", "b", "c", "d", "e"]);
		const coreMax = Math.max(
			...[...next.entries()].filter(([id]) => id !== "orphan").map(([, p]) => Math.hypot(p.x - c.x, p.y - c.y)),
		);
		const orphanR = Math.hypot(next.get("orphan")!.x - c.x, next.get("orphan")!.y - c.y);
		assert.ok(orphanR > coreMax, `orphan at r=${orphanR.toFixed(1)} should sit outside core max r=${coreMax.toFixed(1)}`);
	});
});

describe("settleGraphLayout", () => {
	it("dedupes repeated node lines, runs, and writes the whole ledger", () => {
		const written: Record<string, Position>[] = [];
		const lines = [node("a"), node("b"), node("c"), node("d"), node("a")]; // "a" appended twice
		const store = {
			readNodes: () => lines.map((l) => ({ ...l })),
			readChains: () => [chain("arg_ab", ["a"], "b"), chain("arg_bcd", ["b", "c"], "d")],
			readPositions: () => ({} as Record<string, Position>),
			writePositions: (p: Record<string, Position>) => void written.push(p),
		};
		settleGraphLayout(store);
		assert.equal(written.length, 1);
		// arg_ab is single-premise → collapsed to a direct arrow, NO imp
		// node; arg_bcd is multi-premise → its imp node joins the layout.
		assert.deepEqual(Object.keys(written[0]!).sort(), ["a", "arg_bcd", "b", "c", "d"], "positions for the unique nodes and ONLY the multi-premise chain's imp node");
	});

	it("does nothing on an empty graph", () => {
		const written: Record<string, Position>[] = [];
		settleGraphLayout({
			readNodes: () => [],
			readChains: () => [],
			readPositions: () => ({} as Record<string, Position>),
			writePositions: (p) => void written.push(p),
		});
		assert.equal(written.length, 0);
	});
});
describe("imp-link half distance (rendering arc, owner 2026-09-30)", () => {
	const settle = (from: string, to: string, linkDistance: number) => {
		const nodes = [{ id: from, x: 0, y: 0 }, { id: to, x: 500, y: 0 }];
		const sim = createGraphSimulation(nodes, [{ from, to }], {
			linkDistance,
			chargeStrength: 0, // springs only — the rest length IS the equilibrium
			gravity: { x: 0, y: 0, strength: 0 },
		});
		for (let i = 0; i < 300; i++) sim.tick();
		const [a, b] = sim.nodes() as unknown as { id: string; x: number; y: number }[];
		assert.ok(a && b, "both nodes present");
		return Math.abs(b.x - a.x);
	};

	it("a plain proposition link settles at the full rest length (tuned or default)", () => {
		assert.ok(Math.abs(settle("a", "b", 100) - 100) < 2, "plain link ≈ 100");
	});

	it("a link TOUCHING an implication node gets HALF the rest length", () => {
		// into the imp point (premise → arg_x)
		assert.ok(Math.abs(settle("a", "arg_x", 100) - 50) < 2, "into-imp link ≈ 50");
		// out of it (arg_x → conclusion)
		assert.ok(Math.abs(settle("arg_x", "b", 100) - 50) < 2, "out-of-imp link ≈ 50");
	});
});

describe("clusterPull (the centroid force)", () => {
	it("compacts each cluster toward its OWN centroid; strength 0 = off", () => {
		// Two loose chains, far apart, edges only WITHIN each chain.
		const mk = (p: string, baseX: number) =>
			Array.from({ length: 8 }, (_, i) => ({ id: `${p}${i}`, x: baseX + i * 40, y: i * 15 }));
		const a = mk("a", -400);
		const b = mk("b", 400);
		const nodes = [...a, ...b];
		const edges = [
			...a.slice(0, -1).map((n, i) => ({ from: n.id, to: a[i + 1]!.id })),
			...b.slice(0, -1).map((n, i) => ({ from: n.id, to: b[i + 1]!.id })),
		];
		const clusters = [{ members: a.map((n) => n.id) }, { members: b.map((n) => n.id) }];

		const spreadOf = (ns: { id: string; x: number; y: number }[]): number => {
			let sum = 0;
			for (const group of [ns.filter((n) => n.id[0] === "a"), ns.filter((n) => n.id[0] === "b")]) {
				const cx = group.reduce((s, n) => s + n.x, 0) / group.length;
				const cy = group.reduce((s, n) => s + n.y, 0) / group.length;
				sum += group.reduce((s, n) => s + Math.hypot(n.x - cx, n.y - cy), 0) / group.length;
			}
			return sum;
		};

		const run = (strength: number) => {
			const sim = createGraphSimulation(
				nodes.map((n) => ({ ...n })),
				edges,
				{ clusterPull: { clusters, strength } },
			);
			for (let i = 0; i < 150; i++) sim.tick();
			return spreadOf(sim.nodes() as unknown as { id: string; x: number; y: number }[]);
		};
		const pulled = run(0.15);
		const unpulled = run(0);
		// The force compacts (well under the unpulled baseline)...
		assert.ok(pulled < unpulled * 0.8, `pulled spread ${pulled.toFixed(1)} should be well under ${unpulled.toFixed(1)}`);
		// ...and both groups survive as separate blobs (no merge).
		assert.ok(pulled > 0, "spread is finite/positive");
	});
});

describe("depths over the LOGICAL graph (physics arc, owner 2026-09-30)", () => {
	it("a multi-premise conclusion sits at premises'+1 — NOT +2 — over logical edges", () => {
		const props = [{ id: "a" }, { id: "b" }, { id: "c" }];
		const logical = [
			{ from: "a", to: "c" },
			{ from: "b", to: "c" },
		];
		const depths = inferenceDepths(props, logical);
		assert.equal(depths.get("c"), 1, "one inference hop from BOTH premises — the imp point is not a hop");
	});

	it("the imp node is ABSENT from the rank map (depth is a property of propositions)", () => {
		const nodes = [{ id: "a" }, { id: "b" }, { id: "c" }, { id: "arg_x" }];
		const logical = [
			{ from: "a", to: "c" },
			{ from: "b", to: "c" },
		];
		const depths = inferenceDepths(
			nodes.filter((n) => !n.id.startsWith("arg_")),
			logical,
		);
		assert.ok(!depths.has("arg_x"), "geometry points carry no inference rank");
		assert.equal(depths.get("c"), 1);
	});

	it("VERTICAL mode: the central pole is horizontal-ONLY for everyone — orphans included (owner, 2026-09-30)", () => {
		const mk = (id: string, x: number, y: number) => ({ id, x, y });
		const sim = createGraphSimulation(
			[mk("a", 0, 0), mk("b", 40, 0), mk("lonely", 500, 400)],
			[{ from: "a", to: "b" }],
			{
				depthAnchor: { mode: "vertical", strength: 1, spacing: 60 },
				gravity: { x: 0, y: 0, strength: 0.1 },
				chargeStrength: 0,
			},
		);
		for (let i = 0; i < 400; i++) sim.tick();
		const pos = new Map((sim.nodes() as unknown as { id: string; x: number; y: number }[]).map((n) => [n.id, n]));
		// The orphan converges on x (the pole is still a pole)...
		assert.ok(Math.abs(pos.get("lonely")!.x) < 50, `lonely x pulled to center (got ${pos.get("lonely")!.x.toFixed(1)})`);
		// ...but its y is UNTOUCHED — no row to sit on, no sag toward the
		// pole (old behavior dragged it to y≈0).
		assert.ok(Math.abs(pos.get("lonely")!.y - 400) < 5, `lonely y free (got ${pos.get("lonely")!.y.toFixed(1)})`);
	});

	it("the IMP MIDPOINT ANCHOR: the junction pins halfway between premises and conclusion (owner, 2026-09-30)", () => {
		const mk = (id: string, x: number, y: number) => ({ id, x, y });
		const sim = createGraphSimulation(
			[mk("a", 0, 0), mk("b", 40, 0), mk("c", 0, -480), mk("arg_x", 20, -100)],
			// Drawn edges: the imp fan (springs ride these).
			[
				{ from: "a", to: "arg_x" },
				{ from: "b", to: "arg_x" },
				{ from: "arg_x", to: "c" },
			],
			{
				// The logical edges: what depth consumes.
				logicalEdges: [
					{ from: "a", to: "c" },
					{ from: "b", to: "c" },
				],
				// The junction's linkage: premises a,b (row 0), conclusion
				// c (row 1) → the anchor is the AVERAGE, 0.5.
				impLinks: [{ id: "arg_x", premises: ["a", "b"], conclusion: "c" }],
				depthAnchor: { mode: "vertical", strength: 1, spacing: 500 },
				gravity: { x: 0, y: 0, strength: 0.1 },
				chargeStrength: 0,
				linkStrength: 0.05,
			},
		);
		for (let i = 0; i < 400; i++) sim.tick();
		const pos = new Map((sim.nodes() as unknown as { id: string; x: number; y: number }[]).map((n) => [n.id, n]));
		// Propositions pin to their rows: a/b at depth 0 (y≈0), c at
		// depth 1 (y≈−500 — targetY = baseY − depth·spacing).
		assert.ok(Math.abs(pos.get("a")!.y) < 50, `a on row 0 (got ${pos.get("a")!.y.toFixed(1)})`);
		assert.ok(Math.abs(pos.get("b")!.y) < 50, `b on row 0 (got ${pos.get("b")!.y.toFixed(1)})`);
		assert.ok(Math.abs(pos.get("c")!.y + 500) < 50, `c on row 1 (got ${pos.get("c")!.y.toFixed(1)})`);
		// The junction pins EXACTLY halfway: (0 + 1)/2 = 0.5 → y≈−250 —
		// strictly above the premises, strictly below the conclusion.
		assert.ok(Math.abs(pos.get("arg_x")!.y + 250) < 40, `arg_x on the half-row (got ${pos.get("arg_x")!.y.toFixed(1)})`);
	});

	it("mixed-depth premises: the HIGHEST premise row is the premises side of the average", () => {
		const mk = (id: string, x: number, y: number) => ({ id, x, y });
		const sim = createGraphSimulation(
			[mk("a", 0, 0), mk("b", 10, 0), mk("c", 0, 0), mk("arg_x", 5, 0)],
			[
				{ from: "a", to: "arg_x" },
				{ from: "b", to: "arg_x" },
				{ from: "arg_x", to: "c" },
			],
			{
				// a→b→c ladder: b at depth 1, c at depth 2; the chain's
				// premises are a (0) and b (1), conclusion c (2).
				logicalEdges: [
					{ from: "a", to: "b" },
					{ from: "a", to: "c" },
					{ from: "b", to: "c" },
				],
				impLinks: [{ id: "arg_x", premises: ["a", "b"], conclusion: "c" }],
				depthAnchor: { mode: "vertical", strength: 1, spacing: 400 },
				gravity: { x: 0, y: 0, strength: 0.1 },
				chargeStrength: 0,
				linkStrength: 0.05,
			},
		);
		for (let i = 0; i < 400; i++) sim.tick();
		const pos = new Map((sim.nodes() as unknown as { id: string; x: number; y: number }[]).map((n) => [n.id, n]));
		assert.ok(Math.abs(pos.get("a")!.y) < 40, `a on row 0 (got ${pos.get("a")!.y.toFixed(1)})`);
		assert.ok(Math.abs(pos.get("b")!.y + 400) < 40, `b on row 1 (got ${pos.get("b")!.y.toFixed(1)})`);
		assert.ok(Math.abs(pos.get("c")!.y + 800) < 40, `c on row 2 (got ${pos.get("c")!.y.toFixed(1)})`);
		// (highest premise 1 + conclusion 2) / 2 = 1.5 → y≈−600.
		assert.ok(Math.abs(pos.get("arg_x")!.y + 600) < 40, `arg_x on the 1.5 half-row (got ${pos.get("arg_x")!.y.toFixed(1)})`);
	});

	it("WITHOUT impLinks the imp node keeps the legacy exemption (never depth-anchored)", () => {
		const mk = (id: string, x: number, y: number) => ({ id, x, y });
		const sim = createGraphSimulation(
			[mk("a", 0, 0), mk("b", 40, 0), mk("c", 0, -480), mk("arg_x", 20, -100)],
			[
				{ from: "a", to: "arg_x" },
				{ from: "b", to: "arg_x" },
				{ from: "arg_x", to: "c" },
			],
			{
				logicalEdges: [
					{ from: "a", to: "c" },
					{ from: "b", to: "c" },
				],
				depthAnchor: { mode: "vertical", strength: 1, spacing: 500 },
				gravity: { x: 0, y: 0, strength: 0.1 },
				chargeStrength: 0,
				linkStrength: 0.05,
			},
		);
		for (let i = 0; i < 400; i++) sim.tick();
		const pos = new Map((sim.nodes() as unknown as { id: string; x: number; y: number }[]).map((n) => [n.id, n]));
		assert.ok(Math.abs(pos.get("c")!.y + 500) < 50, "c on row 1");
		// No linkage supplied: no half-row, no stamping — springs alone
		// place it between the levels.
		assert.ok(Math.abs(pos.get("arg_x")!.y) < 250, `arg_x unanchored (got ${pos.get("arg_x")!.y.toFixed(1)})`);
	});
});

describe("inferenceDepths (SCC-safe ranking)", () => {
	const nodes = (ids: string[]) => ids.map((id) => ({ id }));

	it("ranks a chain, a diamond takes the longest path, orphans are depth 0", () => {
		// chain a->b->c; diamond a->d, b->d, c->d (d reachable at 1 and 2 and 3)
		const ns = nodes(["a", "b", "c", "d", "loner"]);
		const edges = [
			{ from: "a", to: "b" },
			{ from: "b", to: "c" },
			{ from: "a", to: "d" },
			{ from: "b", to: "d" },
			{ from: "c", to: "d" },
		];
		const d = inferenceDepths(ns, edges);
		assert.equal(d.get("a"), 0);
		assert.equal(d.get("b"), 1);
		assert.equal(d.get("c"), 2);
		assert.equal(d.get("d"), 3); // longest path, not shortest
		assert.equal(d.get("loner"), 0);
	});

	it("cycles share a depth (mutual support = equal footing)", () => {
		// x <-> y (a cycle), fed by s; z follows x.
		const ns = nodes(["s", "x", "y", "z"]);
		const edges = [
			{ from: "s", to: "x" },
			{ from: "x", to: "y" },
			{ from: "y", to: "x" },
			{ from: "x", to: "z" },
		];
		const d = inferenceDepths(ns, edges);
		assert.equal(d.get("s"), 0);
		assert.equal(d.get("x"), d.get("y"), "cycle members share a depth");
		assert.equal(d.get("x"), 1);
		assert.equal(d.get("z"), 2);
		// Deterministic across calls.
		assert.deepEqual([...inferenceDepths(ns, edges).entries()], [...d.entries()]);
	});
});

describe("depthAnchor force", () => {
	const nodes = (ids: string[]) => ids.map((id) => ({ id, x: 0, y: 0 }));

	it("vertical: the premise lands below its conclusion", () => {
		const ns = nodes(["base", "derived"]);
		const edges = [{ from: "base", to: "derived" }];
		const sim = createGraphSimulation(ns, edges, {
			depthAnchor: { mode: "vertical", strength: 1.2, spacing: 100, center: { x: 0, y: 0 } },
		});
		for (let i = 0; i < 300; i++) sim.tick();
		const byId = new Map(sim.nodes().map((n) => [n.id, n]));
		const baseY = byId.get("base")!.y!;
		const derivedY = byId.get("derived")!.y!;
		assert.ok(baseY > derivedY, `base (${baseY.toFixed(0)}) should sit BELOW derived (${derivedY.toFixed(0)})`);
		assert.ok(
			baseY - derivedY > 60,
			`level separation should be substantial (got ${(baseY - derivedY).toFixed(0)})`,
		);
	});

	it("radial: inference depth becomes radius", () => {
		const ns = nodes(["base", "mid", "top"]);
		const edges = [
			{ from: "base", to: "mid" },
			{ from: "mid", to: "top" },
		];
		const sim = createGraphSimulation(ns, edges, {
			depthAnchor: { mode: "radial", strength: 1.2, spacing: 80, baseRadius: 100, center: { x: 0, y: 0 } },
		});
		for (let i = 0; i < 300; i++) sim.tick();
		const r = (id: string) => {
			const n = sim.nodes().find((x) => x.id === id)!;
			return Math.hypot(n.x!, n.y!);
		};
		assert.ok(r("base") < r("mid"), `base ring (${r("base").toFixed(0)}) inside mid (${r("mid").toFixed(0)})`);
		assert.ok(r("mid") < r("top"), `mid ring (${r("mid").toFixed(0)}) inside top (${r("top").toFixed(0)})`);
	});

	it("settle with depthAnchor: old nodes keep x memory but snap to their level", () => {
		// Node "old" was previously placed at y=300 (off-level). With
		// vertical anchoring a re-settle must move it to the baseline
		// while preserving (roughly) its x arrangement.
		const previous = new Map([["old", { x: 250, y: 300 }], ["peer", { x: 260, y: 290 }]]);
		const next = incrementalLayout(
			[{ id: "old" }, { id: "peer" }, { id: "child" }],
			[
				{ from: "old", to: "child" },
				{ from: "peer", to: "child" },
			],
			previous,
			{ depthAnchor: { mode: "vertical", strength: 0.6, spacing: 80 } },
		);
		const old = next.get("old")!;
		// The baseline defaults to the anchor centroid: (300+290)/2 = 295.
		assert.ok(Math.abs(old.y - 295) < 20, `old node snaps to the baseline (y=${old.y.toFixed(1)})`);
		assert.ok(old.x > 150, `x memory preserved (x=${old.x.toFixed(1)})`);
		const child = next.get("child")!;
		assert.ok(child.y < old.y - 40, `child rises above its premises (child=${child.y.toFixed(1)}, old=${old.y.toFixed(1)})`);
	});

	it("orphans are exempt from depth anchoring — y is FREE, the pole is horizontal (ORPHAN RULE, amended 2026-09-30)", () => {
		// A premise→conclusion chain plus an unconnected loner. Gravity's
		// center is FAR off-axis, so the forces are distinguishable: a
		// depth-stamped orphan would sit on the baseline; the pre-amend
		// exempt one sagged to gravity's y. Since the owner's 2026-09-30
		// amendment the vertical pole is horizontal-ONLY for everyone —
		// the orphan keeps its y and follows gravity on x alone.
		const ns = [
			{ id: "base", x: 0, y: 0 },
			{ id: "derived", x: 10, y: 0 },
			{ id: "loner", x: 400, y: -80 },
		];
		const sim = createGraphSimulation(ns, [{ from: "base", to: "derived" }], {
			gravity: { x: 0, y: 500, strength: 0.1 },
			depthAnchor: { mode: "vertical", strength: 1.5, spacing: 120, center: { x: 0, y: 0 } },
			chargeStrength: 0,
		});
		for (let i = 0; i < 400; i++) sim.tick();
		const byId = new Map(sim.nodes().map((n) => [n.id, n]));
		assert.ok(Math.abs(byId.get("base")!.y!) < 40, "structured base sits on the baseline");
		assert.ok(byId.get("derived")!.y! < -60, "derived rises a level");
		const loner = byId.get("loner")!;
		assert.ok(Math.abs(loner.y! - (-80)) < 5, `the orphan's y is untouched (y=${loner.y!.toFixed(0)})`);
		assert.ok(Math.abs(loner.x!) < 60, `the orphan still converges on the pole horizontally (x=${loner.x!.toFixed(0)})`);
	});

	it("radial: orphans are exempt — they gather at the center, not on the base ring", () => {
		const ns = [
			{ id: "base", x: 0, y: 0 },
			{ id: "mid", x: 10, y: 0 },
			{ id: "loner", x: 300, y: 300 },
		];
		const sim = createGraphSimulation(ns, [{ from: "base", to: "mid" }], {
			gravity: { x: 0, y: 0, strength: 0.1 },
			depthAnchor: { mode: "radial", strength: 1.5, spacing: 80, baseRadius: 150, center: { x: 0, y: 0 } },
		});
		for (let i = 0; i < 400; i++) sim.tick();
		const r = (id: string) => {
			const n = sim.nodes().find((x) => x.id === id)!;
			return Math.hypot(n.x!, n.y!);
		};
		assert.ok(Math.abs(r("base") - 150) < 40, `base sits on the base ring (r=${r("base").toFixed(0)})`);
		assert.ok(r("loner") < 60, `the orphan follows gravity to the center, not the ring (r=${r("loner").toFixed(0)})`);
	});
});