physics: imp nodes get the MIDPOINT depth anchor between premises and conclusion

Owner ruling (2026-09-30, live-testing loop — supersedes 02a58db's
exemption): implication nodes ARE depth-anchored after all. Their anchor
is the average of the HIGHEST premise row and the conclusion's row —
depth(imp) = (max(premise depths) + depth(conclusion)) / 2 — so the
junction always sits strictly above every premise and strictly below
the conclusion (a conclusion is >= highest premise + 1 in the logical
graph). Uniform across modes: a half-row in vertical, a ring midway in
radial (owner confirmed both).

Implementation:
- layout.ts: new ImpLink type; SimOptions/incrementalLayout gain
  impLinks (the derived chain linkage). The rank map is now computed
  once alongside the orphan mask: proposition ranks via Tarjan over the
  logical edges, then each supplied link adds its midpoint entry. An
  imp node WITH an anchor is structured (leaves the orphan mask —
  gravity projections treat it like any ranked node); WITHOUT supplied
  links, arg_ ids keep the legacy 02a58db exemption (honest fallback
  for callers that predate the field). The depth force reuses the
  precomputed map — one pass, shared.
- deriveView (core/graph.ts) emits impLinks (one per multi-premise
  live chain — single-premise chains mint no imp node); GraphSnapshot
  carries them; graph-view maps them into CanvasData; settleGraphLayout
  and replay-layout forward them (replay activates a junction's link
  exactly when its chain is delivered).

Tests (+3, 1 rewritten): the 02a58db exemption pin became the MIDPOINT
pin (premises row 0, conclusion row -500, junction pinned to -250);
mixed-depth pin (premises at 0 and 1, conclusion 2, junction at the 1.5
half-row — highest premise, not average-of-premises); legacy fallback
pin (no impLinks = never depth-anchored); deriveView impLinks emission
pin (multi-premise only). The horizontal-pole and ORPHAN RULE pins from
5554c3a survive unchanged — proposition orphans are untouched.

components/graph-canvas.ts

@@ -127,6 +127,9 @@ export interface CanvasData {
 	 *  drawn edges (legacy). Optional so non-graph callers of the
 	 *  renderer stay simple. */
 	logicalEdges?: CanvasEdge[];
+	/** The imp chain linkage — the depth pass anchors each junction at
+	 *  the premises/conclusion midpoint (owner, 2026-09-30). */
+	impLinks?: ReadonlyArray<{ id: string; premises: ReadonlyArray<string>; conclusion: string }>;
 	clusters: CanvasCluster[];
 	colors: CanvasColors;
 	/** Body font family (labels must match the app typography). */
@@ -1310,6 +1313,7 @@ export class GraphCanvasRenderer {
 		const t = this.physicsTuning;
 		this.sim = createGraphSimulation(data.nodes, data.edges, {
 			logicalEdges: data.logicalEdges,
+			impLinks: data.impLinks,
 			gravity: { x: this.simCenter.x, y: this.simCenter.y, strength: t.gravity },
 			alphaDecay: LIVE_ALPHA_DECAY,
 			velocityDecay: t.velocityDecay,

components/graph-view.tsx

@@ -1383,6 +1383,7 @@ export function GraphView() {
 			})),
 			edges: snapshot.edges.map((e) => ({ from: e.from, to: e.to })),
 			logicalEdges: snapshot.logicalEdges.map((e) => ({ from: e.from, to: e.to })),
+			impLinks: snapshot.impLinks,
 			clusters: snapshot.clusters.map((c) => ({ id: c.id, label: c.label, members: c.members })),
 			colors: {
 				node: tokenHex(NODE_COLOR_TOKEN),

scripts/replay-layout.ts

@@ -33,6 +33,7 @@ function main() {
 	const view = deriveView(graph);
 	const edges = view.edges;
 	const logicalEdges = view.logicalEdges;
+	const impLinks = view.impLinks;
 	const viewNodeById = new Map(view.nodes.map((n) => [n.id, n]));
 	const chains = graph.chains;
 	// An implication node is delivered the moment its chain is complete
@@ -112,6 +113,9 @@ function main() {
 							...(depthMode === "radial" ? { baseRadius: 220 } : {}),
 						},
 						logicalEdges: activeLogical,
+						// A junction's anchor lights up exactly when the
+						// chain is delivered (its members all arrived).
+						impLinks: impLinks.filter((l) => delivered.has(l.id)),
 					}),
 		});
 		for (const [id, prev] of before) {

src/core/contracts/graph.ts

@@ -319,6 +319,11 @@ export interface GraphSnapshot {
 	 *  depth pass consumes these — inference depth is a property of
 	 *  propositions, never of the geometry point (owner, 2026-09-30). */
 	logicalEdges: GraphEdge[];
+	/** DERIVED imp linkage (one per MULTI-premise live chain): the depth
+	 *  pass anchors each junction at the average of the highest premise
+	 *  row and the conclusion's row (owner, 2026-09-30) — strictly
+	 *  above the premises, strictly below the conclusion. */
+	impLinks: Array<{ id: string; premises: string[]; conclusion: string }>;
 	/** The STORED reasoning chains (merged by (premises, conclusion) at
 	 *  read): the chain table's and the practice pipeline's input — they
 	 * read the truth, never the derived fan-out. */

src/core/graph.ts

@@ -316,7 +316,12 @@ export function getGraph(graphStore: Pick<GraphStore, "readNodes" | "readChains"
  *  regular citizens (half link distance — layout.ts). Dangling chains
  *  (a member node missing) drop here — the deletion cascades should
  *  prevent them; this is the honest belt. */
-export function deriveView(graph: DerivedGraph): { nodes: GraphNode[]; edges: GraphEdge[]; logicalEdges: GraphEdge[] } {
+export function deriveView(graph: DerivedGraph): {
+	nodes: GraphNode[];
+	edges: GraphEdge[];
+	logicalEdges: GraphEdge[];
+	impLinks: Array<{ id: string; premises: string[]; conclusion: string }>;
+} {
 	const names: Record<string, { name: string }> = {};
 	for (const node of graph.nodes) names[node.id] = { name: node.name };
 	const live = new Set(graph.nodes.map((node) => node.id));
@@ -326,6 +331,7 @@ export function deriveView(graph: DerivedGraph): { nodes: GraphNode[]; edges: Gr
 	// direct premise→conclusion arrows over PROPOSITION ids only —
 	// what inference semantics (the depth pass) consumes. The drawn edges
 	// are the canvas image; these are the meaning.
+	const impLinks: Array<{ id: string; premises: string[]; conclusion: string }> = [];
 	const logicalEdges: GraphEdge[] = [];
 	const logicalSeen = new Set<string>();
 	const emitLogical = (from: string, to: string): void => {
@@ -351,10 +357,13 @@ export function deriveView(graph: DerivedGraph): { nodes: GraphNode[]; edges: Gr
 			createdAt: chain.createdAt,
 			provenance: [...chain.provenance],
 		});
+		// The junction's linkage — what the depth pass needs for the
+		// midpoint anchor (owner, 2026-09-30).
+		impLinks.push({ id: chain.id, premises: [...chain.premises], conclusion: chain.conclusion });
 		for (const premise of chain.premises) edges.push({ from: premise, to: chain.id });
 		edges.push({ from: chain.id, to: chain.conclusion });
 	}
-	return { nodes: [...graph.nodes, ...impNodes], edges, logicalEdges };
+	return { nodes: [...graph.nodes, ...impNodes], edges, logicalEdges, impLinks };
 }
 
 // ─── the /api/graph payload ──────────────────────────────────────────────────
@@ -442,6 +451,7 @@ export function graphSnapshot(deps: GraphDeps): GraphSnapshot {
 		propositions: graph.nodes,
 		edges: view.edges,
 		logicalEdges: view.logicalEdges,
+		impLinks: view.impLinks,
 		chains: graph.chains,
 		sessions,
 		fileSources,

src/core/layout-settle.ts

@@ -48,6 +48,7 @@ export function settleGraphLayout(graphStore: {
 	const next = incrementalLayout(view.nodes, view.edges, previous, {
 		clusters: communities,
 		logicalEdges: view.logicalEdges,
+		impLinks: view.impLinks,
 	});
 	graphStore.writePositions(Object.fromEntries(next));
 }

src/core/layout.ts

@@ -182,6 +182,14 @@ export interface SimOptions {
 	 *  rank pass (owner, 2026-09-30). Absent = `edges` (legacy
 	 *  behavior). Springs ALWAYS run over `edges` — the drawn arrows. */
 	logicalEdges?: ReadonlyArray<LayoutEdge>;
+	/** The derived imp nodes' chain linkage (id + members), straight
+	 *  from deriveView. Drives the IMP MIDPOINT ANCHOR (owner,
+	 *  2026-09-30): an implication node's depth is the average of the
+	 *  HIGHEST premise row and the conclusion's row — strictly above
+	 *  every premise, strictly below the conclusion, uniform in vertical
+	 *  (a row) and radial (a ring) modes. Absent = imp nodes keep the
+	 *  legacy orphan exemption (never depth-anchored). */
+	impLinks?: ReadonlyArray<ImpLink>;
 	/** Cluster centroid pull (the "virtual node" without the node):
 	 *  members of each cluster accelerate toward their own cluster's
 	 *  centroid. Two O(n) passes per tick — cheaper than a real virtual
@@ -200,6 +208,15 @@ export interface LayoutEdge {
 	to: string;
 }
 
+/** A derived implication node's chain linkage — what the depth pass needs
+ *  to anchor the junction between its premises and their conclusion. */
+export interface ImpLink {
+	/** The imp node's id (arg_-prefixed — the stored chain's id). */
+	id: string;
+	premises: ReadonlyArray<string>;
+	conclusion: string;
+}
+
 export const LINK_DISTANCE = 40;
 /** Implication-node id prefix (the mint law lives in core/graph.ts's
  *  newGraphChainId). Layout-side: links TOUCHING an imp node get HALF
@@ -301,6 +318,7 @@ export function createGraphSimulation(
 	// structure is inference over propositions, not the drawn geometry.
 	const depthEdges = options.logicalEdges ?? edges;
 	let orphan: Uint8Array | null = null;
+	let depthsComputed: Map<string, number> | null = null;
 	if (mode !== "off") {
 		const connected = new Set<string>();
 		const valid = new Set(nodes.map((n) => n.id));
@@ -311,15 +329,42 @@ export function createGraphSimulation(
 			connected.add(e.from);
 			connected.add(e.to);
 		}
+		// Proposition ranks first; then the IMP MIDPOINT ANCHOR (owner,
+		// 2026-09-30): an implication node's depth = (highest premise row
+		// + conclusion row) / 2 — the junction sits strictly above every
+		// premise and strictly below the conclusion (a conclusion is
+		// always ≥ highest premise + 1), uniform in both modes: a row in
+		// vertical, a ring in radial. Imp ids WITHOUT a supplied link
+		// keep the legacy exemption.
+		depthsComputed = inferenceDepths(
+			nodes.filter((n) => !n.id.startsWith(IMP_ID_PREFIX)),
+			depthEdges,
+		);
+		const anchored = new Set<string>();
+		if (options.impLinks) {
+			for (const link of options.impLinks) {
+				const conclusionDepth = depthsComputed.get(link.conclusion);
+				if (conclusionDepth === undefined || link.premises.length === 0) continue;
+				let highest = -Infinity;
+				let complete = true;
+				for (const premise of link.premises) {
+					const d = depthsComputed.get(premise);
+					if (d === undefined) {
+						complete = false;
+						break;
+					}
+					if (d > highest) highest = d;
+				}
+				if (!complete) continue;
+				depthsComputed.set(link.id, (highest + conclusionDepth) / 2);
+				anchored.add(link.id);
+			}
+		}
 		orphan = new Uint8Array(nodes.length);
 		nodes.forEach((n, i) => {
-			// IMP EXEMPTION joins the mask (owner, 2026-09-30): depth is a
+			// IMP nodes with a midpoint anchor are STRUCTURED (they sit on
-			// property of inference over PROPOSITIONS; an implication node
+			// their half-row); unlinked arg_ ids keep the orphan exemption.
-			// is pure geometry — never pinned to a level, keeps the
+			if (!connected.has(n.id) && !(n.id.startsWith(IMP_ID_PREFIX) && anchored.has(n.id))) orphan![i] = 1;
-			// regular forces (cluster pull, springs, and gravity —
-			// horizontal-only in vertical mode, like everyone), and
-			// settles naturally between premise and conclusion levels.
-			if (!connected.has(n.id) || n.id.startsWith(IMP_ID_PREFIX)) orphan![i] = 1;
 		});
 	}
 	const g = options.gravity;
@@ -422,12 +467,9 @@ export function createGraphSimulation(
 	// organic sag.
 	const da = options.depthAnchor;
 	if (da && da.mode !== "off" && da.strength > 0) {
-		// Propositions only: imp ids are absent from the rank map by
+		// The rank map (propositions + imp midpoint anchors) was computed
-		// construction (belt under the orphan-mask exemption).
+		// with the orphan mask above — one pass, shared.
-		const depths = inferenceDepths(
+		const depths = depthsComputed!;
-			nodes.filter((n) => !n.id.startsWith(IMP_ID_PREFIX)),
-			depthEdges,
-		);
 		const strength = da.strength;
 		const spacing = da.spacing;
 		const c = da.center ?? { x: 0, y: 0 };
@@ -487,6 +529,8 @@ export interface IncrementalLayoutOptions {
 	depthAnchor?: DepthAnchor;
 	/** The LOGICAL edge list for the depth pass (see SimOptions). */
 	logicalEdges?: ReadonlyArray<LayoutEdge>;
+	/** The imp chain linkage for the midpoint anchor (see SimOptions). */
+	impLinks?: ReadonlyArray<ImpLink>;
 }
 
 /**
@@ -626,6 +670,7 @@ export function incrementalLayout(
 				? { ...options.depthAnchor, center: options.depthAnchor.center ?? { x: cx, y: cy } }
 				: options.depthAnchor,
 		logicalEdges: options.logicalEdges,
+		impLinks: options.impLinks,
 	});
 	const dMode = options.depthAnchor?.mode ?? "off";
 	const dCenter = options.depthAnchor?.center ?? { x: cx, y: cy };

tests/graph.test.ts

@@ -1079,4 +1079,12 @@ describe("deriveView (the argument's geometry)", () => {
 		// Proposition ids only — no arg_ endpoint ever rides the logical set.
 		assert.ok(view.logicalEdges.every((e) => !e.from.startsWith("arg_") && !e.to.startsWith("arg_")));
 	});
+
+	it("impLinks: one linkage per MULTI-premise chain — the depth pass's midpoint input", () => {
+		const view = deriveView({
+			nodes: [prop("a"), prop("b"), prop("c")],
+			chains: [chain("arg_ab", ["a", "b"], "c"), chain("arg_ac", ["a"], "c")],
+		});
+		assert.deepEqual(view.impLinks, [{ id: "arg_ab", premises: ["a", "b"], conclusion: "c" }]);
+	});
 });

tests/layout.test.ts

@@ -244,7 +244,7 @@ describe("depths over the LOGICAL graph (physics arc, owner 2026-09-30)", () =>
 		assert.ok(Math.abs(pos.get("lonely")!.y - 400) < 5, `lonely y free (got ${pos.get("lonely")!.y.toFixed(1)})`);
 	});
 
-	it("the depth force EXEMPTS the imp node like an orphan (never pinned to a row)", () => {
+	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)],
@@ -260,26 +260,86 @@ describe("depths over the LOGICAL graph (physics arc, owner 2026-09-30)", () =>
 					{ 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,
-				// Weak springs: the rows pin crisply while the exempt imp
-				// node still floats (its signal is WHERE it isn't — on
-				// no row).
 				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).
+		// 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 imp node is exempt: NOT stamped onto c's row (old behavior
+		// The junction pins EXACTLY halfway: (0 + 1)/2 = 0.5 → y≈−250 —
-		// pinned it to −500 as a depth-1 "node"); springs alone place
+		// strictly above the premises, strictly below the conclusion.
-		// it between the levels.
+		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)})`);
-		assert.ok(Math.abs(pos.get("arg_x")!.y) < 250, `arg_x unpinned, floats between levels (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)})`);
 	});
 });