rendering arc: the imp node becomes the argument's geometry, not a fake proposition

Owner-approved brief (orchestrator): the canvas stops drawing implication
nodes as first-class nodes and starts drawing them as what they are — the
point where co-premise lines converge.

- deriveView (core/graph.ts): single-premise chains collapse to ONE direct
  premise->conclusion arrow — no imp node minted (a chain is always N-in/
  1-out; one premise is the degenerate case). Multi-premise chains keep
  the imp node + fan. Dangling guard unchanged.
- physics (core/layout.ts createGraphSimulation): per-link rest length —
  a link touching an arg_-prefixed endpoint gets HALF the base link
  distance, default or user-tuned alike; everything else about imp-node
  physics citizenship unchanged.
- canvas (components/graph-canvas.ts): imp nodes are PURE GEOMETRY —
  invisible (no disc, no label) and unpickable (excluded from pickAt's
  hit-test projection). Edges INTO an imp node: headless, shaft runs to
  its CENTER (toRadius 0, no head triangle). Edges OUT: shaft starts at
  the center (fromRadius 0), arrowhead lands on the conclusion's disc
  edge. Single-premise direct arrows render as today's plain arrows.
- comment repairs (same commit): the two stale double-shaft claims
  (CanvasEdge doc + the draw-pass block) rewritten to the truth — plain
  single shafts; bundles are headless converging lines + one arrowed
  out-edge; no double-shaft glyph exists anywhere.
- tests (+9): deriveView pins (single-premise collapse, multi-premise
  fan, shared-conclusion distinctness, dangling drop); imp-link half-
  distance settle pins; arrowGeometry zero-radius laws + isImpNodeId
  pin; graph.test.ts's snapshot invariant now counts only MULTI-premise
  live chains (its fixture's single-premise chains mint zero imp nodes);
  layout settle fixture updated for the collapse.

components/graph-canvas.ts

@@ -86,14 +86,23 @@ export interface CanvasNode {
 }
 
 /** One directed edge of the DERIVED view (chains-primary, 2026-09-30):
- *  premise → implication node → conclusion, UNTYPED — every arrow is an
+ *  premise → implication node → conclusion, UNTYPED, all PLAIN
- *  implication, so every arrow renders the double-shaft glyph (⟹) +
+ *  single-shaft arrows — there is no double-shaft glyph anywhere
- *  arrowhead (DECIDED 2026-09-14, docs/vision-edge-glyph.md). */
+ *  (the 2026-09-14 ruling died with typed edges). An argument renders
+ *  as its geometry: co-premise lines converge HEADLESS onto the
+ *  implication point, one arrowed line leaves it; a single-premise
+ *  argument is one ordinary arrow (see deriveView). */
 export interface CanvasEdge {
 	from: string;
 	to: string;
 }
 
+/** Implication-node ids (the mint law: newGraphChainId in core/graph.ts).
+ *  On the canvas an imp node is PURE GEOMETRY (owner, rendering arc
+ *  2026-09-30): invisible — no disc, no label — and UNPICKABLE,
+ *  excluded from every hit-test path. Exported for the test pin. */
+export const isImpNodeId = (id: string): boolean => id.startsWith("arg_");
+
 /** One cluster region: member node ids + the LLM-coined label (or null). */
 export interface CanvasCluster {
 	id: string;
@@ -1048,6 +1057,7 @@ export class GraphCanvasRenderer {
 		const projected: { id: string; x: number; y: number }[] = [];
 		for (const n of this.data.nodes) {
 			if (this.visible && !this.visible.has(n.id)) continue;
+			if (isImpNodeId(n.id)) continue; // pure geometry — never picked
 			projected.push({ id: n.id, x: n.x * k + tx, y: n.y * k + ty });
 		}
 		const hit = pickNearest(projected, px, py, maxDist);
@@ -1218,21 +1228,24 @@ export class GraphCanvasRenderer {
 		const visible = this.visible;
 		const isVisible = (id: string) => !visible || visible.has(id);
 
-		// Node discs: one Path2D, one fill() per frame.
+		// Node discs: one Path2D, one fill() per frame. Implication nodes
+		// are pure geometry — never a disc, never a label, never picked.
 		const nodesPath = new Path2D();
 		for (const n of data.nodes) {
-			if (!isVisible(n.id)) continue;
+			if (!isVisible(n.id) || isImpNodeId(n.id)) continue;
 			nodesPath.moveTo(n.x + nodeR, n.y);
 			nodesPath.arc(n.x, n.y, nodeR, 0, Math.PI * 2);
 		}
 		this.nodesPath = nodesPath;
 
-		// Edge shafts + arrowheads: tip lands on the target disc edge. Both
+		// Edge shafts + arrowheads (rendering arc, owner 2026-09-30): all
-		// relation types draw the same arrow for now — the double-shaft
+		// arrows are PLAIN single shafts — the old double-shaft glyph is
-		// glyph was rejected (2026-09-15); differentiation is pending a new
+		// gone entirely. An argument's geometry: lines INTO an implication
-		// approach. Two owner rulings 2026-09-29: the supports draw toggle
+		// node are HEADLESS and run all the way to the imp node's CENTER
-		// CHAINS-PRIMARY (2026-09-30): one path family — every derived arrow
+		// (co-premise lines converge to a point); the line OUT of it starts
-		// is an implication, double-shafted + arrowheaded uniformly.
+		// at the center and its arrowhead lands on the conclusion's disc
+		// edge. Single-premise arguments arrive here as ordinary
+		// proposition→proposition edges and draw exactly like any arrow.
 		const arrowLen = settings.arrowLength;
 		const shafts = new Path2D();
 		const heads = new Path2D();
@@ -1241,14 +1254,22 @@ export class GraphCanvasRenderer {
 			const a = this.nodeById.get(e.from);
 			const b = this.nodeById.get(e.to);
 			if (!a || !b) continue;
-			const g = arrowGeometry(a, b, nodeR, nodeR, arrowLen);
+			const intoImp = isImpNodeId(e.to);
+			const outOfImp = isImpNodeId(e.from);
+			const g = arrowGeometry(a, b, outOfImp ? 0 : nodeR, intoImp ? 0 : nodeR, arrowLen);
 			if (!g) continue;
 			shafts.moveTo(g.shaftFrom.x, g.shaftFrom.y);
-			shafts.lineTo(g.shaftTo.x, g.shaftTo.y);
+			if (intoImp) {
-			heads.moveTo(g.tip.x, g.tip.y);
+				// toRadius 0 put the tip AT the imp node's center: the
-			heads.lineTo(g.left.x, g.left.y);
+				// headless shaft terminates there (no head triangle).
-			heads.lineTo(g.right.x, g.right.y);
+				shafts.lineTo(g.tip.x, g.tip.y);
-			heads.closePath();
+			} else {
+				shafts.lineTo(g.shaftTo.x, g.shaftTo.y);
+				heads.moveTo(g.tip.x, g.tip.y);
+				heads.lineTo(g.left.x, g.left.y);
+				heads.lineTo(g.right.x, g.right.y);
+				heads.closePath();
+			}
 		}
 		this.shaftsPath = shafts;
 		this.headsPath = heads;
@@ -1266,7 +1287,7 @@ export class GraphCanvasRenderer {
 		ctx.font = this.worldLabelFont;
 		const maxW = LABEL_MAX_WIDTH * (settings.labelSize / LABEL_SIZE);
 		for (const n of data.nodes) {
-			if (isVisible(n.id)) this.labelLines.set(n.id, wrapLabel(ctx, n.label, maxW));
+			if (isVisible(n.id) && !isImpNodeId(n.id)) this.labelLines.set(n.id, wrapLabel(ctx, n.label, maxW));
 		}
 		ctx.font = prevFont;
 	}

src/core/graph.ts

@@ -303,15 +303,19 @@ export function getGraph(graphStore: Pick<GraphStore, "readNodes" | "readChains"
 	return { nodes: [...byId.values()], chains };
 }
 
-/** The DERIVED view — what the canvas renders. One implication NODE per
+/** The DERIVED view — what the canvas renders. A SINGLE-premise chain
- *  chain (id = the chain's arg_ id; name "⟹"; statement = the chain
+ *  collapses to ONE direct arrow premise → conclusion (no imp node:
- *  line; the chain's provenance/createdAt) plus UNTYPED arrows: each
+ *  a chain is always N-in/1-out, so one premise is the degenerate
- *  premise → the implication node, the implication node → the
+ *  1-in-1-out case). A MULTI-premise chain mints an implication NODE
- *  conclusion. Rendering specialization (invisible / physics-free)
+ *  (id = the chain's arg_ id; name "⟹"; statement = the chain line;
- *  comes later (owner, 2026-09-30: physics is fine with imp nodes as
+ *  the chain's provenance/createdAt) plus arrows: each premise → the
- *  regular nodes for now). Dangling chains (a member node missing)
+ *  implication node, the implication node → the conclusion — the
- *  drop here — the deletion cascades should prevent them; this is the
+ *  canvas renders imp nodes as pure geometry (owner, rendering arc:
- *  honest belt. */
+ *  invisible, unpickable; co-premise lines converge headless to a
+ *  point, one arrowed line leaves it). Physics keeps imp nodes as
+ *  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[] } {
 	const names: Record<string, { name: string }> = {};
 	for (const node of graph.nodes) names[node.id] = { name: node.name };
@@ -320,6 +324,12 @@ export function deriveView(graph: DerivedGraph): { nodes: GraphNode[]; edges: Gr
 	const edges: GraphEdge[] = [];
 	for (const chain of graph.chains) {
 		if (!live.has(chain.conclusion) || !chain.premises.every((premise) => live.has(premise))) continue;
+		// Single premise: the argument IS a plain arrow — no geometry
+		// point needed (the 1-in/1-out collapse; rendering arc, owner).
+		if (chain.premises.length === 1) {
+			edges.push({ from: chain.premises[0]!, to: chain.conclusion });
+			continue;
+		}
 		impNodes.push({
 			id: chain.id,
 			name: "⟹",

src/core/layout.ts

@@ -196,6 +196,14 @@ export interface LayoutEdge {
 }
 
 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
+ *  the base rest length — the argument's geometry (a converging point)
+ *  sits tight against its premises/conclusion instead of spread like a
+ *  real proposition citizen (owner ruling, rendering arc 2026-09-30). */
+const IMP_ID_PREFIX = "arg_";
+const impLinkId = (v: string | number | { id: string }): string =>
+	typeof v === "object" ? v.id : String(v);
 export const CHARGE_STRENGTH = -240; // 2026-09-17: −120 → −240 (user: repulsion default too weak); the default is shared with render-settings (gm-centered in CHARGE_RANGE).
 /** Per-tick anchor re-blend: fraction of an anchored node's displacement
  *  from its previous position that SURVIVES each tick. 0.85 = gentle
@@ -238,6 +246,7 @@ export function createGraphSimulation(
 		degree.set(e.to, (degree.get(e.to) ?? 0) + 1);
 	}
 	const linkStrength = options.linkStrength ?? 1;
+	const linkDistance = options.linkDistance ?? LINK_DISTANCE;
 
 	const sim = forceSimulation<LayoutNode, SimLink>(nodes)
 		.force(
@@ -246,7 +255,16 @@ export function createGraphSimulation(
 				edges.map((e) => ({ source: e.from, target: e.to })),
 			)
 				.id((d) => d.id)
-				.distance(options.linkDistance ?? LINK_DISTANCE)
+				// Per-link rest length (rendering arc, owner 2026-09-30): a
+				// link touching an implication node (arg_-prefixed id — the
+				// string form pre-init, the node ref after) gets HALF the
+				// base distance, default or user-tuned alike.
+				.distance(
+					(l) =>
+						impLinkId(l.source).startsWith(IMP_ID_PREFIX) || impLinkId(l.target).startsWith(IMP_ID_PREFIX)
+							? linkDistance / 2
+							: linkDistance,
+				)
 				.strength(
 					(l) =>
 						(linkStrength * 1) /

tests/graph-canvas.test.ts

@@ -14,6 +14,7 @@ import { describe, it, it as test } from "node:test";
 import {
 	applyClusterLabels,
 	arrowGeometry,
+	isImpNodeId,
 	boxBlurRound,
 	fitTransform,
 	labelAlpha,
@@ -148,6 +149,26 @@ describe("arrowGeometry", () => {
 	test("null for coincident endpoints (never a NaN arrow)", () => {
 		assert.equal(arrowGeometry({ x: 5, y: 5 }, { x: 5, y: 5 }, 6, 6, 5), null);
 	});
+
+	// The rendering arc's geometry laws (owner, 2026-09-30): an edge INTO
+	// an imp point is drawn with toRadius 0 (headless, terminates at the
+	// center); an edge OUT of one with fromRadius 0 (starts at the center).
+	test("toRadius 0 — the tip lands exactly at the target CENTER (headless convergence)", () => {
+		const g = arrowGeometry({ x: 0, y: 0 }, { x: 100, y: 0 }, 6, 0, 5)!;
+		assert.ok(Math.abs(g.tip.x - 100) < 1e-9 && Math.abs(g.tip.y) < 1e-9, "tip = the center, past which no shaft draws");
+	});
+
+	test("fromRadius 0 — the shaft starts exactly at the source CENTER", () => {
+		const g = arrowGeometry({ x: 0, y: 0 }, { x: 100, y: 0 }, 0, 6, 5)!;
+		assert.ok(Math.abs(g.shaftFrom.x) < 1e-9 && Math.abs(g.shaftFrom.y) < 1e-9, "shaftFrom = the center");
+	});
+});
+
+describe("isImpNodeId (the pure-geometry law, rendering arc 2026-09-30)", () => {
+	test("arg_-prefixed ids are geometry; proposition ids are citizens", () => {
+		assert.equal(isImpNodeId("arg_123af5a046ba"), true);
+		assert.equal(isImpNodeId("n_abc123"), false);
+	});
 });
 
 

tests/graph.test.ts

@@ -19,11 +19,11 @@
 import assert from "node:assert/strict";
 import * as fs from "node:fs";
 import { after, describe, it } from "node:test";
-import type { AuditVerdicts, SessionFindings } from "../src/core/contracts.ts";
+import type { AuditVerdicts, GraphChain, GraphNode, SessionFindings } from "../src/core/contracts.ts";
 import type { QuestionAnswerData } from "../src/core/question-core.ts";
 import type { LhMessage } from "../src/core/native-messages.ts";
 import { projectView as projectNative } from "../src/core/view.ts";
-import { getGraph, graphSnapshot, mergeFindings, type GraphDeps } from "../src/core/graph.ts";
+import { deriveView, getGraph, graphSnapshot, mergeFindings, type GraphDeps } from "../src/core/graph.ts";
 import { coverageSlots } from "../src/core/coverage.ts";
 import { graphStore } from "../src/store/graph.ts";
 import { chatStore } from "../src/store/chats.ts";
@@ -459,18 +459,22 @@ describe("the merger (mergeFindings)", () => {
 		assert.equal(mine!.label, "/vault/cluster notes.md", "a notes file is a birth-session — the label is its path");
 
 		// Chains-primary split (owner, 2026-09-30): `nodes` is the canvas
-		// image (propositions + derived implication nodes), `propositions`
+		// image, `propositions` the stored truth alone (the chain table's
-		// is the stored truth alone — the chain table's input. The store is
+		// input). The store is shared across this suite, so assert the
-		// shared across this suite, so assert the INVARIANT, not counts:
+		// INVARIANT, not counts — and since the rendering arc
-		// image = truth + one imp node per fully-live stored chain, and the
+		// (2026-09-30), only MULTI-premise live chains mint imp nodes
-		// truth never carries an arg_ id.
+		// (this fixture's two single-premise chains collapse to direct
+		// arrows — zero imp nodes here).
 		const stored = graphStore.readChains();
 		const live = new Set(snap.propositions.map((n) => n.id));
-		const liveChains = stored.filter((c) => live.has(c.conclusion) && c.premises.every((p) => live.has(p)));
+		const impChains = stored.filter(
+			(c) => c.premises.length >= 2 && live.has(c.conclusion) && c.premises.every((p) => live.has(p)),
+		);
 		assert.ok(snap.propositions.every((n) => !n.id.startsWith("arg_")), "the stored-truth list never carries imp nodes");
-		assert.equal(snap.nodes.length, snap.propositions.length + liveChains.length, "image = truth + one imp node per live chain");
+		assert.equal(snap.nodes.length, snap.propositions.length + impChains.length, "image = truth + one imp node per MULTI-premise live chain");
 		const imp = snap.nodes.filter((n) => n.id.startsWith("arg_"));
-		assert.ok(imp.length === liveChains.length && imp.every((n) => snap.propositions.every((p) => p.id !== n.id)), "the extra nodes are exactly the derived implication nodes");
+		assert.ok(imp.length === impChains.length && imp.every((n) => snap.propositions.every((p) => p.id !== n.id)), "the extra nodes are exactly the derived implication nodes");
+		assert.equal(imp.length, 0, "this fixture's chains are single-premise — all collapsed to direct arrows");
 	});
 
 	it("derives the sessions index in graphSnapshot", () => {
@@ -996,3 +1000,66 @@ describe("session coverage read (extraction-UX redesign, 2026-09-24)", () => {
 		assert.equal(sessionCoverage("chat_never_was"), null);
 	});
 });
+
+// ─── deriveView (the rendering arc, owner 2026-09-30) ────────────────────────
+
+describe("deriveView (the argument's geometry)", () => {
+	const prop = (id: string): GraphNode => ({
+		id,
+		name: id.toUpperCase(),
+		statement: `${id} statement`,
+		aliases: [],
+		createdAt: "2026-09-30T00:00:00.000Z",
+		provenance: [],
+	});
+	const chain = (id: string, premises: string[], conclusion: string): GraphChain => ({
+		id,
+		premises,
+		conclusion,
+		provenance: [],
+		createdAt: "2026-09-30T00:00:00.000Z",
+	});
+
+	it("a SINGLE-premise chain collapses to ONE direct arrow — no imp node", () => {
+		const view = deriveView({ nodes: [prop("a"), prop("b")], chains: [chain("arg_ab", ["a"], "b")] });
+		assert.deepEqual(view.nodes.map((n) => n.id), ["a", "b"], "no arg_ node minted");
+		assert.deepEqual(view.edges, [{ from: "a", to: "b" }], "the argument IS a plain arrow");
+	});
+
+	it("a MULTI-premise chain keeps the imp node + fan (premises in, conclusion out)", () => {
+		const view = deriveView({
+			nodes: [prop("a"), prop("b"), prop("c")],
+			chains: [chain("arg_ab", ["a", "b"], "c")],
+		});
+		assert.deepEqual(view.nodes.map((n) => n.id).sort(), ["a", "arg_ab", "b", "c"]);
+		assert.deepEqual(
+			[...view.edges].sort((x, y) => (x.from < y.from ? -1 : x.from > y.from ? 1 : x.to < y.to ? -1 : 1)),
+			[
+				{ from: "a", to: "arg_ab" },
+				{ from: "arg_ab", to: "c" },
+				{ from: "b", to: "arg_ab" },
+			],
+		);
+		const imp = view.nodes.find((n) => n.id === "arg_ab")!;
+		assert.equal(imp.name, "\u27f9");
+	});
+
+	it("two chains SHARING a conclusion stay distinct — two geometry points, never a unioned fan", () => {
+		const view = deriveView({
+			nodes: [prop("a"), prop("b"), prop("c"), prop("d"), prop("e")],
+			chains: [chain("arg_e1", ["a", "b"], "e"), chain("arg_e2", ["c", "d"], "e")],
+		});
+		assert.deepEqual(
+			view.nodes.map((n) => n.id).sort(),
+			["a", "arg_e1", "arg_e2", "b", "c", "d", "e"],
+		);
+		assert.ok(view.edges.some((x) => x.from === "arg_e1" && x.to === "e"));
+		assert.ok(view.edges.some((x) => x.from === "arg_e2" && x.to === "e"));
+	});
+
+	it("dangling chains drop (missing member — the honest belt)", () => {
+		const view = deriveView({ nodes: [prop("a")], chains: [chain("arg_ghost", ["a"], "gone"), chain("arg_gone", ["ghost"], "a")] });
+		assert.deepEqual(view.nodes.map((n) => n.id), ["a"]);
+		assert.deepEqual(view.edges, []);
+	});
+});

tests/layout.test.ts

@@ -106,16 +106,18 @@ describe("incrementalLayout", () => {
 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("a")]; // "a" appended twice
+		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")],
+			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);
-		assert.deepEqual(Object.keys(written[0]!).sort(), ["a", "arg_ab", "b"], "one position per unique node AND the derived implication node");
+		// 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", () => {
@@ -129,6 +131,32 @@ describe("settleGraphLayout", () => {
 		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.