chains-primary: stored chains replace typed edges; edges become a derived view

Owner rulings 2026-09-30: reasoning chains are the stored truth; the graph canvas renders a lossy derived image. No migration, no backcompat — old graph data was wiped. - contracts: GraphChain (arg_-minted id, premises, conclusion) replaces typed edges; GraphEdge survives only as the untyped derived arrow; GraphSnapshot carries stored chains; supports edges retired entirely - store: chains.jsonl ledger (edges.jsonl purged at load alongside legacy events.jsonl); readChains/appendChain seam; merge dedupes by (sorted premises, conclusion), re-assertions append under the same arg_ id - core: deriveView mints implication nodes (name ⟹, statement via formatChainLine) plus premise→imp→conclusion arrows; clusters stay proposition-only (birthSessionPartition); chainsForSelection now groups STORED chains (chain rides iff every member selected) — independent arguments for one conclusion never union; chainsToGraph/chainsToEdges die - extraction: extractor submits chains natively (expandFindings deleted); auditor receives propositions only; supports fan-out gone - deletion: full death of a proposition kills every referencing chain; arg_-prefixed node deletes kill that chain; chainsRemoved stats - UI: every arrow renders the ⟹ double shaft; supports toggle + thickness slider and detail-card edge sections deleted (card keeps name + proposition); chain table + practice pipeline read stored chains - tests: 1188 green across the new seams
2026-09-30 03:22:52 +03:00
parent a3aabb3a57
commit 4985b6f9fa
28 changed files with 669 additions and 726 deletions
@@ -68,7 +68,7 @@ import {
 	XIcon,
 } from "lucide-react";
 import { chainsForSelection, formatChainLine, fuzzyScore } from "@/src/core";
-import type { GraphEdge, GraphNode } from "@/src/core";
+import type { GraphChain, GraphNode } from "@/src/core";
 import { TopBar } from "@/components/top-bar";
 import { PracticeDialog } from "@/components/practice-dialog";
 import { DeleteNodeDialog } from "@/components/delete-node-dialog";
@@ -99,7 +99,7 @@ interface ClusterGroup {
 *  via props; the overlay wrapper below owns it. */
 export function ChainTableBody({
 	nodes,
-	edges,
+	chains: storedChains,
 	sessions,
 	fileSources,
 	query,
@@ -118,7 +118,7 @@ export function ChainTableBody({
 	onClose,
 }: {
 	nodes: GraphNode[];
-	edges: GraphEdge[];
+	chains: GraphChain[];
 	sessions: Record<string, string>;
 	fileSources: Record<string, string>;
 	query: string;
@@ -140,7 +140,7 @@ export function ChainTableBody({
 	onClose: () => void;
 }) {
 	const byId = useMemo(() => new Map(nodes.map((n) => [n.id, n])), [nodes]);
-	const chains = useMemo(() => chainsForSelection(nodes, edges), [nodes, edges]);
+	const chains = useMemo(() => chainsForSelection(nodes, storedChains), [nodes, storedChains]);
 	const searching = query.trim() !== "";

 	// The fuzzy filter: a chain is visible when ANY member matches on
@@ -223,8 +223,8 @@ export function ChainTableBody({
 	// The derived shape under the floating bar (the agents' ACTUAL input).
 	const derived = useMemo(() => {
 		const selectedNodes = [...selection].map((id) => byId.get(id)).filter((n): n is GraphNode => n !== undefined);
-		return chainsForSelection(selectedNodes, edges);
-	}, [selection, byId, edges]);
+		return chainsForSelection(selectedNodes, storedChains);
+	}, [selection, byId, storedChains]);

 	const nameOf = (id: string) => byId.get(id)?.name ?? id;
 	const dateOf = (id: string) => byId.get(id)?.createdAt.slice(0, 10) ?? "";
@@ -583,14 +583,14 @@ function RowCheckbox({
 export function ChainTableOverlay({
 	open,
 	nodes,
-	edges,
+	chains: storedChains,
 	sessions,
 	fileSources,
 	onClose,
 }: {
 	open: boolean;
 	nodes: GraphNode[];
-	edges: GraphEdge[];
+	chains: GraphChain[];
 	sessions: Record<string, string>;
 	fileSources: Record<string, string>;
 	onClose: () => void;
@@ -618,7 +618,7 @@ export function ChainTableOverlay({

 	const byId = new Map(nodes.map((n) => [n.id, n]));
 	const selectedNodes = [...selection].map((id) => byId.get(id)).filter((n): n is GraphNode => n !== undefined);
-	const derived = chainsForSelection(selectedNodes, edges);
+	const derived = chainsForSelection(selectedNodes, storedChains);
 	const nodeIds = [...selection].sort();

 	const toggleNodes = (ids: string[], next: boolean) =>
@@ -645,7 +645,7 @@ export function ChainTableOverlay({
 			>
 				<ChainTableBody
 					nodes={nodes}
-					edges={edges}
+					chains={storedChains}
 					sessions={sessions}
 					fileSources={fileSources}
 					query={query}
@@ -65,7 +65,6 @@ import {
 	sanitizeRegionTuning,
 	type PhysicsTuning,
 	type RegionTuning,
-	type EdgeType,
 	INCREMENTAL_GRAVITY,
 	LINK_DISTANCE,
 	type DepthAnchorMode,
@@ -86,14 +85,13 @@ export interface CanvasNode {
 	label: string;
 }

-/** One directed edge (follows | supports); arrow points prerequisite → dependent. */
+/** One directed edge of the DERIVED view (chains-primary, 2026-09-30):
+ *  premise → implication node → conclusion, UNTYPED — every arrow is an
+ *  implication, so every arrow renders the double-shaft glyph (⟹) +
+ *  arrowhead (DECIDED 2026-09-14, docs/vision-edge-glyph.md). */
 export interface CanvasEdge {
 	from: string;
 	to: string;
-	/** Relation type: `follows` renders the double-shaft glyph (⟹),
-	 *  `supports` the plain single line (DECIDED 2026-09-14,
-	 *  docs/vision-edge-glyph.md). */
-	type: EdgeType;
 }

 /** One cluster region: member node ids + the LLM-coined label (or null). */
@@ -623,10 +621,6 @@ export class GraphCanvasRenderer {
 	private builtVersion = -1; // version the cache was built at
 	private nodesPath: Path2D | null = null;
 	private shaftsPath: Path2D = new Path2D();
-	/** Supports shafts draw THINNER (owner, 2026-09-29): their own path +
-	 *  stroke pass at edgeWidth × supportsWidth. Arrowheads share the one
-	 *  heads path at full geometry (owner pick: shaft only). */
-	private supportsShaftsPath: Path2D = new Path2D();
 	private headsPath: Path2D = new Path2D();
 	private regionCanvas: HTMLCanvasElement | null = null;
 	/** World rect the bitmap covers (drawImage target coords). */
@@ -1237,32 +1231,26 @@ export class GraphCanvasRenderer {
 		// relation types draw the same arrow for now — the double-shaft
 		// glyph was rejected (2026-09-15); differentiation is pending a new
 		// approach. Two owner rulings 2026-09-29: the supports draw toggle
-		// (off skips the paths entirely — a draw-only hide; the sim still
-		// feels them) and the supports SHAFT thickness split (supports get
-		// their own path stroked at edgeWidth × supportsWidth; heads stay
-		// full-geometry in the one shared path).
+		// CHAINS-PRIMARY (2026-09-30): one path family — every derived arrow
+		// is an implication, double-shafted + arrowheaded uniformly.
 		const arrowLen = settings.arrowLength;
 		const shafts = new Path2D();
-		const supportsShafts = new Path2D();
 		const heads = new Path2D();
 		for (const e of data.edges) {
-			if (!settings.showSupports && e.type === "supports") continue;
 			if (!isVisible(e.from) || !isVisible(e.to)) continue;
 			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);
 			if (!g) continue;
-			const path = e.type === "supports" ? supportsShafts : shafts;
-			path.moveTo(g.shaftFrom.x, g.shaftFrom.y);
-			path.lineTo(g.shaftTo.x, g.shaftTo.y);
+			shafts.moveTo(g.shaftFrom.x, g.shaftFrom.y);
+			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.supportsShaftsPath = supportsShafts;
 		this.headsPath = heads;

 		// Cluster regions are NOT built here: they rasterize into their own
@@ -1639,10 +1627,6 @@ export class GraphCanvasRenderer {
 			ctx.lineWidth = settings.edgeWidth / k;
 			ctx.lineCap = "round";
 			ctx.stroke(this.shaftsPath);
-			if (settings.showSupports) {
-				ctx.lineWidth = Math.max(settings.edgeWidth * settings.supportsWidth, 0.5) / k;
-				ctx.stroke(this.supportsShaftsPath);
-			}
 			ctx.fill(this.headsPath);
 		}

@@ -51,10 +51,9 @@
 *
 * Rendering settings (2026-09-13): the gear in the search panel reveals
 * five sliders (node size, edge width, arrowhead length, label size, the
- * zoom threshold), the supports-edges draw toggle (2026-09-29: off hides
- * supports edges from the canvas — draw-only; physics and detail cards
- * still see them) with its shaft-thickness slider (0–1 × Edge width,
- * default 0.5; heads stay full), and the cluster-labels checkbox. SERVER-persisted
+ * zoom threshold), and the cluster-labels checkbox. (The supports-edge
+ * draw toggle + thickness slider died with supports edges themselves —
+ * chains-primary, 2026-09-30.) SERVER-persisted
 * (data/render-settings.json via /api/graph/render-settings): loaded
 * once after mount, saved debounced on every user change — one source
 * of truth shared by every browser. The label-zoom slider is log-scaled
@@ -532,36 +531,7 @@ function GraphSettingsControl({
 								onChange={(p) =>
 									changeSettings((cur) => ({ ...cur, labelZoom: fromLadderPosition(p, LABEL_ZOOM_LADDER) }))}
 							/>
-							{/* Supports draw toggle (owner, 2026-09-29): hides the single-line
-							    supports edges from the canvas — follows (⟹-meant) stay. Draw-only:
-							    physics + detail cards still see them. Last rows of the FIRST
-							    section; the border-t below starts Regions. */}
-							<label className="flex cursor-pointer items-center justify-between text-[11px] text-muted-foreground">
-								<span>Supports edges</span>
-								<input
-									type="checkbox"
-									checked={settings.showSupports}
-									onChange={(e) =>
-										changeSettings((cur) => ({ ...cur, showSupports: e.target.checked }))}
-									className="accent-primary"
-								/>
-							</label>
-							{/* Supports shaft thickness (owner, 2026-09-29): a LINEAR 0–1
-							    ratio of Edge width (not a ladder — it's a ratio; default 0.5
-							    dead-center anyway, step 0.1 = 11 stops). Grayed out by the
-							    toggle above (the Dilation pattern); 0 floors to a hairline in
-							    the renderer — arrowheads never scale (shaft-only ruling). */}
-							<SettingSlider
-								label="Supports thickness"
-								disabled={!settings.showSupports}
-								min={0}
-								max={1}
-								step={0.1}
-								value={settings.supportsWidth}
-								display={`${Math.round(settings.supportsWidth * 100) / 100}×`}
-								onChange={(v) => changeSettings((cur) => ({ ...cur, supportsWidth: v }))}
-							/>
-						{/* Regions: the blurred cluster tints. Sliders + a fixed-set
+							{/* Regions: the blurred cluster tints. Sliders + a fixed-set
 						    dropdown for the bitmap resolution (it's a discrete
 						    choice, not a free number). Server-persisted like the
 						    sizes; every range end was sweep-validated on the real
@@ -1411,7 +1381,7 @@ export function GraphView() {
 				y: positions.get(n.id)?.y ?? 0,
 				label: n.name,
 			})),
-			edges: snapshot.edges.map((e) => ({ from: e.from, to: e.to, type: e.type })),
+			edges: snapshot.edges.map((e) => ({ from: e.from, to: e.to })),
 			clusters: snapshot.clusters.map((c) => ({ id: c.id, label: c.label, members: c.members })),
 			colors: {
 				node: tokenHex(NODE_COLOR_TOKEN),
@@ -1637,53 +1607,6 @@ export function GraphView() {
 				>
 					<div className="text-sm font-medium leading-snug">{selected.node.name}</div>
 					<div className="mt-1 text-xs leading-relaxed text-muted-foreground">{selected.node.statement}</div>
-					{(() => {
-						// EDGES (owner 2026-09-27): edge classification was entirely
-						// hidden in the UI — the card now shows every edge this node
-						// participates in, grouped by direction + type, above the
-						// sessions list. Semantics (owner 2026-09-28): an edge A→B means A implies/
-						// supports B — OUTGOING edges list under "What follows from this" /
-						// "What this supports", INCOMING under "Follows from" / "Supported by".
-						// Only present groups render.
-						const id = selected.node.id;
-						const nodeById = new Map((snapshot?.nodes ?? []).map((n) => [n.id, n]));
-						const label = (nid: string) => nodeById.get(nid)?.name ?? nid;
-						const groups: { title: string; names: string[] }[] = [
-							{
-								title: "What follows from this",
-								names: (snapshot?.edges ?? []).filter((e) => e.from === id && e.type === "follows").map((e) => label(e.to)),
-							},
-							{
-								title: "What this supports",
-								names: (snapshot?.edges ?? []).filter((e) => e.from === id && e.type === "supports").map((e) => label(e.to)),
-							},
-							{
-								title: "Follows from",
-								names: (snapshot?.edges ?? []).filter((e) => e.to === id && e.type === "follows").map((e) => label(e.from)),
-							},
-							{
-								title: "Supported by",
-								names: (snapshot?.edges ?? []).filter((e) => e.to === id && e.type === "supports").map((e) => label(e.from)),
-							},
-						].filter((g) => g.names.length > 0);
-						if (groups.length === 0) return null;
-						return (
-							<div className="mt-3 flex flex-col gap-1">
-								{groups.map((g) => (
-									<div key={g.title} className="flex flex-col gap-0.5">
-										<div className="text-xs text-muted-foreground">{g.title}</div>
-										<div className="flex flex-wrap gap-1">
-											{g.names.map((name, i) => (
-												<span key={`${name}-${i}`} className="rounded-full border px-2 py-0.5 text-[11px] text-muted-foreground">
-													{name}
-												</span>
-											))}
-										</div>
-									</div>
-								))}
-							</div>
-						);
-					})()}
 					{selected.sourceIds.length > 0 ? (
 						<div className="mt-3 flex flex-col gap-1">
 							<div className="text-xs text-muted-foreground">Sessions</div>
@@ -1734,7 +1657,7 @@ export function GraphView() {
 			<ChainTableOverlay
 				open={chainsOpen && !isEmpty}
 				nodes={snapshot?.nodes ?? []}
-				edges={snapshot?.edges ?? []}
+				chains={snapshot?.chains ?? []}
 				sessions={snapshot?.sessions ?? {}}
 				fileSources={snapshot?.fileSources ?? {}}
 				onClose={() => setChainsOpen(false)}
@@ -60,11 +60,12 @@ export type ModelRole =

 /**
 * The LIVE graph store (src/store/graph.ts) — owned by the app's extraction
- * pipeline. Line shapes: src/core/contracts.ts.
+ * pipeline. Line shapes: src/core/contracts.ts. CHAINS ARE THE STORED
+ * TRUTH (owner, 2026-09-30): edges are a derived view, never stored.
 */
 export const LEDGER_FILES = {
 	nodes: path.join(PATHS.graph, "nodes.jsonl"),
-	edges: path.join(PATHS.graph, "edges.jsonl"),
+	chains: path.join(PATHS.graph, "chains.jsonl"),
 	sessions: path.join(PATHS.graph, "sessions.jsonl"),
 	/** Per-message extraction coverage (contracts/graph.ts CoverageEntry;
 	 *  the checkpoint's replacement for chat extractions — notes keep
@@ -27,7 +27,7 @@ async function main() {
 			const stats = await pipeline.runExtraction(chat.id);
 			console.log(
 				`[backfill] ${chat.id} (${chat.title.slice(0, 40)}): ` +
-					`${stats.nodes} nodes, ${stats.edges} edges in ${((Date.now() - t0) / 1000).toFixed(1)}s`,
+					`${stats.nodes} nodes, ${stats.chains ?? 0} chains in ${((Date.now() - t0) / 1000).toFixed(1)}s`,
 			);
 		} catch (err) {
 			console.error(`[backfill] ${chat.id} FAILED:`, err);
@@ -35,7 +35,7 @@ async function main() {
 	}
 	const graph = getGraph(graphStore);
 	console.log(
-		`[backfill] done: ${graph.nodes.length} nodes, ${graph.edges.length} edges`,
+		`[backfill] done: ${graph.nodes.length} nodes, ${graph.chains.length} chains`,
 	);
 }

@@ -33,7 +33,7 @@ async function main() {
 		getChunkTokens: () => effectiveSettings().graph.extractionChunkTokens,
 	});
 	const queue = [...files];
-	const totals = { nodes: 0, edges: 0, failed: 0 };
+	const totals = { nodes: 0, chains: 0, failed: 0 };
 	const workers = Array.from({ length: Math.min(limit, files.length) }, async () => {
 		for (;;) {
 			const file = queue.shift();
@@ -43,9 +43,9 @@ async function main() {
 			try {
 				const stats = await pipeline.importNotes({ filePath, text: fs.readFileSync(filePath, "utf-8") });
 				totals.nodes += stats.nodes;
-				totals.edges += stats.edges;
+				totals.chains += stats.chains ?? 0;
 				console.log(
-					`[import-notes] ${file}: ${stats.nodes} nodes, ${stats.edges} edges in ${((Date.now() - t0) / 1000).toFixed(1)}s`,
+					`[import-notes] ${file}: ${stats.nodes} nodes, ${stats.chains ?? 0} chains in ${((Date.now() - t0) / 1000).toFixed(1)}s`,
 				);
 			} catch (err) {
 				totals.failed++;
@@ -57,8 +57,8 @@ async function main() {

 	const graph = getGraph(stores.graphStore);
 	console.log(
-		`[import-notes] done: +${totals.nodes} nodes, +${totals.edges} edges, ${totals.failed} failed — ` +
-			`graph now ${graph.nodes.length} nodes, ${graph.edges.length} edges`,
+		`[import-notes] done: +${totals.nodes} nodes, +${totals.chains} chains, ${totals.failed} failed — ` +
+			`graph now ${graph.nodes.length} nodes, ${graph.chains.length} chains`,
 	);
 }

@@ -19,20 +19,28 @@ const depthMode: "off" | "vertical" | "radial" =
 	depthArg === "--depth=vertical" ? "vertical" : depthArg === "--depth=radial" ? "radial" : "off";
 import { incrementalLayout } from "../src/core/layout.ts";
 import { birthSessionPartition } from "../src/core/session-clusters.ts";
+import { deriveView, getGraph } from "../src/core/graph.ts";
 import type { GraphNode, Position } from "../src/core/contracts.ts";

 function main() {
 	const t0 = Date.now();

-	// Unique nodes (lines may repeat an id — first defines).
-	const seen = new Set<string>();
-	const nodes: GraphNode[] = [];
-	for (const line of graphStore.readNodes()) {
-		if (seen.has(line.id)) continue;
-		seen.add(line.id);
-		nodes.push(line);
-	}
-	const edges = graphStore.readEdges();
+	// CHAINS-PRIMARY (2026-09-30): the stored truth is nodes + chains; the
+	// replay lays out the DERIVED view (implication nodes included, untyped
+	// arrows) exactly like the real settle.
+	const graph = getGraph(graphStore);
+	const nodes = graph.nodes; // getGraph already merges lines by id
+	const view = deriveView(graph);
+	const edges = view.edges;
+	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
+	// (conclusion + every premise delivered).
+	const chainReady = (id: string): boolean => {
+		const chain = chains.find((c) => c.id === id);
+		if (!chain) return delivered.has(id);
+		return delivered.has(chain.conclusion) && chain.premises.every((p) => delivered.has(p));
+	};
 	// The cluster source (wave 7): the birth-session partition, derived on
 	// read — same as the real settle (core/layout-settle.ts).
 	const birthClusters = birthSessionPartition(nodes);
@@ -58,7 +66,7 @@ function main() {
 	const byId = new Map(nodes.map((n) => [n.id, n]));
 	const unmappedFallback = sources[sources.length - 1]?.id ?? "";

-	console.log(`[replay] ${nodes.length} unique nodes, ${edges.length} edge lines, ${sources.length} sources`);
+	console.log(`[replay] ${nodes.length} nodes, ${chains.length} chains, ${sources.length} sources`);
 	let maxOldShift = 0;
 	let shiftReport = "";
 	for (const source of sources) {
@@ -74,13 +82,18 @@ function main() {
 			}
 		}
 		for (const n of batch) delivered.add(n.id);
+		// Ready chains' implication nodes ride the same batch (they have no
+		// provenance of their own — the chain's completeness delivers them).
+		for (const chain of chains) {
+			if (chainReady(chain.id)) delivered.add(chain.id);
+		}

 		// Edges activate once BOTH endpoints exist (a later file can claim
 		// one endpoint — the edge lights up then).
 		const activeEdges = edges.filter((e) => delivered.has(e.from) && delivered.has(e.to));

 		const before = new Map(positions);
-		const batchNodes = nodes.filter((n) => delivered.has(n.id));
+		const batchNodes = view.nodes.filter((n) => delivered.has(n.id));
 		positions = incrementalLayout(batchNodes, activeEdges, positions, {
 			// The same partition the real settle would see for this batch:
 			// the birth-session clusters, filtered to delivered nodes.
@@ -28,7 +28,6 @@ import type { GraphStore } from "../../core/ports.ts";
 import { settleGraphLayout } from "../../core/layout-settle.ts";
 import { batchRuns, coverageOf, messageViewLines } from "../../core/coverage.ts";
 import { teacherProseBlocks } from "../../core/coverage.ts";
-import { chainsToEdges } from "../../core/practice.ts";
 import type { LhMessage } from "../../core/native-messages.ts";
 import { auditorGraphTools } from "../tools/graph.ts";
 import { runSubmitAgent } from "./submit-agent.ts";
@@ -266,17 +265,15 @@ function validateFindingsChains(value: FindingsSubmit): string | null {
 	return null;
 }

-/** The translation seam (extractor redesign, 2026-09-30): the wire
- *  speaks CHAINS, the pipeline speaks follows-EDGES — SessionFindings
- *  and everything downstream (auditor, resolution, merge, coverage,
- *  store) is UNCHANGED. One math, one place: chainsToEdges sits next
- *  to chainsToGraph in core/practice.ts. */
-function expandFindings(raw: FindingsSubmit): SessionFindings {
-	return {
-		propositions: raw.propositions.map((p) => ({ ...p, aliases: p.aliases ?? [] })),
-		edges: chainsToEdges(raw.chains),
-	};
-}
+/** (chains-primary, owner 2026-09-30) the wire IS the pipeline shape
+ *  now: propositions + chains, no translation — the stores keep the
+ *  chains and the derived edge view is recomputed on read. The fill
+ *  already ran inside runSubmitAgent; this only re-asserts the
+ *  aliases-filled type. */
+const asSessionFindings = (raw: FindingsSubmit): SessionFindings => ({
+	propositions: raw.propositions.map((p) => ({ ...p, aliases: p.aliases ?? [] })),
+	chains: raw.chains,
+});

 function fillAudit(raw: Static<typeof auditSchema>): AuditVerdicts {
 	return {
@@ -346,7 +343,7 @@ function runExtractor(
 		onStep,
 		neverSubmitted: "the extractor never submitted findings",
 		prepareArguments: healStringifiedArrays,
-	}).then(expandFindings);
+	}).then(asSessionFindings);
 }

 /** The extractor over ONE source of raw personal notes (the format-agnostic
@@ -371,7 +368,7 @@ function runNotesExtractor(
 		onStep,
 		neverSubmitted: "the extractor never submitted findings",
 		prepareArguments: healStringifiedArrays,
-	}).then(expandFindings);
+	}).then(asSessionFindings);
 }

 // ─── the auditor ───────────────────────────────────────────────────────────
@@ -379,7 +376,7 @@ function runNotesExtractor(

 const AUDITOR_INSTRUCTIONS = `You are the linking stage of a learning application's extraction pipeline. An extractor
 has read a source (a teaching session, or the author's personal notes) and reported findings: propositions and
-the follows edges of their reasoning chains. You NEVER see the source itself — the extractor is fully trusted, and you do not re-check
+their reasoning chains. You NEVER see the source itself — the extractor is fully trusted, and you do not re-check
 its work. Your job is IDENTITY: connecting those findings to the CURRENT knowledge graph, preparing the merge.

 You explore the graph through your tools: list_sessions, list_propositions, and find (glob over names +
@@ -406,8 +403,8 @@ IDENTITY — links, per proposition:
  propositions — different claims about the world — stay apart. You are NOT guarding against wrong merges; you are
  hunting for right ones.

-Your deliverable is ONLY the identity verdicts: "links". NEVER restate the propositions or the extractor's edges —
-the merger already has them. You NEVER create edges — relations between the new propositions come from the
+Your deliverable is ONLY the identity verdicts: "links". NEVER restate the propositions —
+the merger already has them. You NEVER create relations between propositions — they come from the
 extractor alone, and the batch connects to the existing graph ONLY through the equivalences you identify. Your
 entire deliverable is ONE submit_review call.

@@ -748,7 +745,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 		signal?.throwIfAborted(); // an abort during the extract→audit gap ends here
 		const graph = getGraph(graphStore);
 		console.info(
-			`[extraction ${jobKey}] auditor starting (${findings.propositions.length} propositions, ${findings.edges.length} edges, ` +
+			`[extraction ${jobKey}] auditor starting (${findings.propositions.length} propositions, ` +
 				`${graph.nodes.length} graph nodes)`,
 		);
 		const t0 = performance.now();
@@ -758,8 +755,8 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 		// exploration tools instead of an injected dump.
 		const auditResult = await runAuditor(
 			stageEngine("auditor", deps.auditor),
-			`Proposed findings from the extractor (the source itself is not available to you — the extractor is fully trusted):\n\n` +
-				`${JSON.stringify(findings, null, 2)}\n\n` +
+			`Proposed findings from the extractor (the source itself is not available to you — the extractor is fully trusted; the propositions only — the reasoning chains are the merger's business, owner 2026-09-30):\n\n` +
+				`${JSON.stringify({ propositions: findings.propositions }, null, 2)}\n\n` +
 				`The current knowledge graph has ${graph.nodes.length} node(s). Explore it with your tools and link what links.`,
 			signal,
 			(usage, model, step, finishReason, tools) => {
@@ -848,13 +845,13 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 	 *  per job and never throw — the source's run returns what actually
 	 *  merged. */
 	function aggregateJobs(sourceId: string, settled: PromiseSettledResult<EmissionStats>[]): EmissionStats {
-		const stats: EmissionStats = { nodes: 0, edges: 0 };
+		const stats: EmissionStats = { nodes: 0, chains: 0 };
 		let aborted = false;
 		let failed = 0;
 		for (const result of settled) {
 			if (result.status === "fulfilled") {
 				stats.nodes += result.value.nodes;
-				stats.edges += result.value.edges;
+				stats.chains! += result.value.chains ?? 0;
 				continue;
 			}
 			const err = result.reason;
@@ -874,7 +871,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 	}

 	async function runExtraction(chatId: string): Promise<EmissionStats> {
-		if (inFlight.has(chatId)) return { nodes: 0, edges: 0 };
+		if (inFlight.has(chatId)) return { nodes: 0, chains: 0 };
 		inFlight.add(chatId);
 		const t0 = performance.now();
 		// COVERAGE (vision-extraction-coverage.md, 2026-09-15): extract ONLY
@@ -895,7 +892,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 			const covered = coverageOf(record.messages, graphStore.readCoverage(), chatId);
 			if (covered.uncovered.length === 0) {
 				console.info(`[extraction ${chatId}] nothing uncovered — no-op`);
-				return { nodes: 0, edges: 0 };
+				return { nodes: 0, chains: 0 };
 			}
 			const chunkTokens = deps.getChunkTokens?.() ?? FACTORY_SETTINGS.graph.extractionChunkTokens;
 			// The batcher's one rule (owner, Wave D): a tool-call message and
@@ -960,7 +957,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 							// next snapshot fetch must already reflect the new nodes).
 							settleGraphLayout(graphStore);
 							console.info(
-								`[extraction ${jobKey}] merged: ${batchStats.nodes} nodes, ${batchStats.edges} edges`,
+								`[extraction ${jobKey}] merged: ${batchStats.nodes} nodes, ${batchStats.chains ?? 0} chains`,
 							);
 							return batchStats;
 						});
@@ -969,7 +966,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 			);
 			const stats = aggregateJobs(chatId, settled);
 			console.info(
-				`[extraction ${chatId}] merged: ${stats.nodes} nodes, ${stats.edges} edges ` +
+				`[extraction ${chatId}] merged: ${stats.nodes} nodes, ${stats.chains ?? 0} chains ` +
 					`(${Math.round(performance.now() - t0)}ms total, ${batches.length} batch job(s))`,
 			);
 			return stats;
@@ -1047,7 +1044,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti

 	async function runNotesExtraction(input: { id: string; filePath: string; text: string; importedAt: string }): Promise<EmissionStats> {
 		const { id } = input;
-		if (inFlight.has(id)) return { nodes: 0, edges: 0 };
+		if (inFlight.has(id)) return { nodes: 0, chains: 0 };
 		inFlight.add(id);
 		const t0 = performance.now();
 		try {
@@ -1098,7 +1095,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 							// The layout ledger evolves with each merge — the next
 							// snapshot fetch reflects every finished chunk.
 							settleGraphLayout(graphStore);
-							console.info(`[extraction ${jobKey}] merged: ${merged.nodes} nodes, ${merged.edges} edges`);
+							console.info(`[extraction ${jobKey}] merged: ${merged.nodes} nodes, ${merged.chains ?? 0} chains`);
 							return merged;
 						});
 					});
@@ -1106,7 +1103,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 			);
 			const stats = aggregateJobs(id, settled);
 			console.info(
-				`[extraction ${id}] merged: ${stats.nodes} nodes, ${stats.edges} edges ` +
+				`[extraction ${id}] merged: ${stats.nodes} nodes, ${stats.chains ?? 0} chains ` +
 					`(${Math.round(performance.now() - t0)}ms total, ${chunks.length} chunk job(s))`,
 			);
 			return stats;
@@ -1133,7 +1130,7 @@ export function createExtractionPipeline(deps: ExtractionPipelineDeps): Extracti
 		const contentFp = crypto.createHash("sha256").update(input.text).digest("hex").slice(0, 16);
 		if (graphStore.readSources().find((s) => s.id === id)?.contentFp === contentFp) {
 			console.info(`[extraction ${id}] re-import with unchanged content (fp match) — skipping`);
-			return { nodes: 0, edges: 0 };
+			return { nodes: 0, chains: 0 };
 		}
 		const importedAt = new Date().toISOString();
 		graphStore.upsertSource({ id, filePath: input.filePath, importedAt, contentFp });
@@ -45,6 +45,7 @@
 import type { GraphStore, PracticeStore } from "../../core/ports.ts";
 import type { Problem, ProblemSet, ReasoningChain } from "../../core/contracts.ts";
 import { chainsForSelection } from "../../core/practice.ts";
+import { getGraph } from "../../core/graph.ts";
 import {
 	createPracticeAgents,
 	type PracticeModels,
@@ -444,10 +445,10 @@ export function createPracticePipeline(deps: PracticePipelineDeps) {
 		const wanted = new Set(nodeIds);
 		const selected = deps.graphStore.readNodes().filter((n) => wanted.has(n.id));
 		const selectedIds = new Set(selected.map((n) => n.id));
-		const edges = deps
-			.graphStore.readEdges()
-			.filter((e) => e.type === "follows" && selectedIds.has(e.from) && selectedIds.has(e.to));
-		const chains = chainsForSelection(selected, edges);
+		// The STORED chains (chains-primary, owner 2026-09-30): chainsForSelection
+		// keeps a chain iff every member is selected — the same inclusion law as
+		// the pre-chains edge grouping; never the derived fan-out.
+		const chains = chainsForSelection(selected, getGraph(deps.graphStore).chains);
 		if (chains.length === 0) throw new EmptySelectionError();
 		const propositions: PropositionSnapshot = {};
 		for (const n of selected) propositions[n.id] = { name: n.name, statement: n.statement };
@@ -18,20 +18,51 @@
 */
 // ─── Knowledge graph (vision §1 — global, cross-session) ────────────────────

-/** Two relations only (DECIDED 2026-09-02): follows = b is derivable from a;
- *  supports = a grounds b without entailing it. No scalars, no encoded
- *  strength — strength is derived at read time from topology. */
 import type { CallUsage, ExtractionRunUsage } from "./chat.ts";

-export type EdgeType = "follows" | "supports";
+/** One relation of the DERIVED view — chains are the stored truth (owner,
+ *  2026-09-30: "the graph is a lossy image of what is truly stored"), and
+ *  the snapshot derives UNTYPED arrows from them: every premise → the
+ *  chain's implication node, the implication node → the conclusion.
+ *  Nothing stores or mutates these — they are rebuilt after every change
+ *  and never converted back. */
+export interface GraphEdge {
+	from: string;
+	to: string;
+}
+
+/** One stored REASONING CHAIN — an argument: premises that JOINTLY entail
+ *  the conclusion (chains-primary, owner 2026-09-30). Independent arguments
+ *  for the same conclusion are separate chains (they may share `conclusion`);
+ *  co-premises within one chain are used TOGETHER. The snapshot derives an
+ *  implication NODE per chain (id = the chain id — the arg_ namespace is its
+ *  own, collision-free with n_) plus untyped edges premises → imp →
+ *  conclusion. A chain referencing a dead node dies with it (full death
+ *  cascades through every referencing chain). */
+export interface GraphChain {
+	/** "arg_" + nanoid-like (store-assigned, the node-minting pattern). */
+	id: string;
+	/** Node ids of the argument's premises — at least one, jointly
+	 *  sufficient. Extractor-local at the wire; node ids after resolution. */
+	premises: string[];
+	/** The node id the premises jointly imply. */
+	conclusion: string;
+	/** Every (chat, message) point where this argument was asserted —
+	 *  unioned across assertion lines at read time. */
+	provenance: ProvenancePoint[];
+	createdAt: string;
+}

 /** What one extraction run merged into the graph ledgers — the merger's
- *  output, also persisted in extraction-run usage records (contracts/chat). */
+ *  output, also persisted in extraction-run usage records (contracts/chat).
+ *  `chains` is OPTIONAL IN OLD RECORDS ONLY: usage history from the
+ *  pre-chains era carries `edges` instead — tolerated at read, never
+ *  written again (no-backward-compat regime, owner 2026-09-30). */
 export interface EmissionStats {
 	/** New graph nodes appended. */
 	nodes: number;
-	/** New edge assertions appended. */
-	edges: number;
+	/** New reasoning chains appended. */
+	chains?: number;
 }

 /** One provenance point — message-granular (DECIDED 2026-09-02): nodes and
@@ -107,14 +138,6 @@ export interface GraphNode {
 	provenance: ProvenancePoint[];
 }

-export interface GraphEdge {
-	from: string;
-	to: string;
-	type: EdgeType;
-	/** Every (chat, message) point where this relation was asserted. */
-	provenance: ProvenancePoint[];
-}
-
 /** sessions.jsonl line — the emission checkpoint for one chat (which chats
 *  have been folded, and through which updatedAt — never fold twice). */
 export interface SessionCheckpoint {
@@ -143,7 +166,9 @@ export interface CoverageEntry {

 /**
 * Store format (src/store/graph.ts): JSONL ledgers at config.LEDGER_FILES
- * (nodes/edges/mappings/sessions), all append-only.
+ * (nodes/chains/sessions), all append-only. Edges are NEVER stored — the
+ * derived view (implication nodes + untyped arrows) is rebuilt from chains
+ * on every read (chains-primary, owner 2026-09-30).
 *
 *   nodes.jsonl    one line per node — the FIRST line for an id defines
 *                  name/statement/createdAt; later lines for the
@@ -151,8 +176,9 @@ export interface CoverageEntry {
 *                  their statements/aliases join `aliases`, their
 *                  provenance unions; the name stays the first line's.
 *                  getGraph merges by id.
- *   edges.jsonl    one line per edge ASSERTION; readers merge by
- *                  (from,to,type), unioning provenance.
+ *   chains.jsonl   one line per chain ASSERTION; readers merge by
+ *                  (premises, conclusion), unioning provenance — the
+ *                  first line's arg_ id is the chain's identity.
 *
 * The derived graph is rebuilt by reading the ledgers — store events,
 * derive state. sessions.jsonl is the extraction checkpoint: which chats
@@ -202,21 +228,20 @@ export interface ExtractedProposition {
 	 * + structure, nothing else. */
 }

-/** One proposed relation. Endpoints are extractor-local proposition ids
- *  ("p1", …) — the extractor is the ONLY stage that ever proposes edges
- *  (the auditor's edges argument is gone, owner 2026-09-28 evening). */
-export interface ExtractedEdge {
-	/** Proposition id that is followed / supported. */
-	from: string;
-	/** Proposition id that follows / is supported. */
-	to: string;
-	type: EdgeType;
+/** One proposed argument (extractor redesign, 2026-09-30). Endpoints are
+ *  extractor-local proposition ids ("p1", …) — the extractor is the ONLY
+ *  stage that ever proposes chains; the merger resolves them to node ids. */
+export interface ExtractedChain {
+	/** Proposition ids that JOINTLY entail the conclusion. */
+	premises: string[];
+	/** The proposition id the premises jointly imply. */
+	conclusion: string;
 }

 /** The extractor's output shape: the raw reasoning chains. */
 export interface SessionFindings {
 	propositions: ExtractedProposition[];
-	edges: ExtractedEdge[];
+	chains: ExtractedChain[];
 }

 /** One identity verdict: the extractor's local proposition id → the
@@ -279,8 +304,16 @@ export interface GraphClusterGroup {
 }

 export interface GraphSnapshot {
+	/** Proposition nodes + the DERIVED implication nodes (one per chain,
+	 *  id = chain id) — what the canvas renders. */
 	nodes: GraphNode[];
+	/** DERIVED untyped arrows: premise → imp → conclusion. A lossy image
+	 *  of the stored chains — rebuilt after every change, never stored. */
 	edges: GraphEdge[];
+	/** 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. */
+	chains: GraphChain[];
 	/** chatId → title, for every chat that touched the graph. */
 	sessions: Record<string, string>;
 	/** srcId → file path, for every IMPORTED NOTES file that touched the
@@ -9,11 +9,17 @@
 * orchestration) owns the cross-store choreography (chat record, jobs,
 * extraction wind-down); this module owns the LEDGERS.
 *
+ * CHAINS-PRIMARY (owner, 2026-09-30): the stored truth is propositions +
+ * reasoning chains; edges are a derived view. Deletion therefore operates
+ * on CHAIN LINES where it used to operate on edge lines — a chain dies
+ * when its provenance empties or any member node died — and the derived
+ * view follows on the next read, never rewritten here.
+ *
 * Two modes (owner-locked semantics):
 *
 *   preserve-graph  the chat's extraction bookkeeping dies — its coverage
 *                   rows and its legacy checkpoint lines — and NOTHING else:
- *                   nodes and edges stay byte-identical.
+ *                   nodes and chains stay byte-identical.
 *                   The graph keeps the session's contributions; the
 *                   snapshot simply no longer resolves the dead chatId to
 *                   a title (nodeSessions filters unknown ids at read
@@ -21,17 +27,16 @@
 *
 *   delete-nodes    "this session never happened": every trace of the
 *                   chat leaves the ledgers — its provenance points on
- *                   every node and edge line, its link lines (their
+ *                   every node and chain line, its link lines (their
 *                   phrasings die with them), its coverage/checkpoint
 *                   rows — and orphans die: a node
 *                   whose references all came from this chat disappears
- *                   entirely, pruned from the positions and embedding
- *                   ledgers too (dead members would break cluster hulls).
+ *                   entirely, pruned from the positions ledger too (dead
+ *                   members would break cluster hulls).
 *
 * Shared nodes survive automatically (the ruling): a node lives iff ANY
 * surviving reference remains — a provenance point from another chat or
- * notes source, or a surviving event (another session's quiz outcome /
- * observation) naming it. The create line of a surviving node is special:
+ * notes source. The create line of a surviving node is special:
 * name/statement/createdAt are the node's IDENTITY — the shared anchor
 * other sessions' link verdicts recognized — so they stay even when the
 * deleted chat created the node; but that session's phrasings (the line's
@@ -39,9 +44,6 @@
 * 2026-09-23: all traces, identity survives).
 *
 * Not touched, by design:
- *   - cluster-labels.jsonl — immutable history by contract, and the
- *     namer is graph-global (tied to no session); core-survival renames
- *     communities whose core shrank below half.
 *   - imported-notes sources (src_…) — a different front door with its
 *     own lifecycle (re-import dedupes by path hash); this wave deletes
 *     CHATS.
@@ -55,7 +57,7 @@

 import type {
 	CoverageEntry,
-	GraphEdge,
+	GraphChain,
 	GraphNode,
 	SessionCheckpoint,
 } from "./contracts.ts";
@@ -71,8 +73,8 @@ export type ChatDeleteMode = "preserve-graph" | "delete-nodes";
 export interface ChatDeletionStats {
 	/** Distinct nodes that died entirely (all their lines). */
 	nodesRemoved: number;
-	/** Edge assertion LINES removed (empty-provenance or dead endpoint). */
-	edgesRemoved: number;
+	/** Chain assertion LINES removed (empty-provenance or dead member). */
+	chainsRemoved: number;
 	/** Coverage rows removed. */
 	coverageRemoved: number;
 	/** Checkpoint lines removed. */
@@ -81,7 +83,7 @@ export interface ChatDeletionStats {

 const EMPTY_STATS: ChatDeletionStats = {
 	nodesRemoved: 0,
-	edgesRemoved: 0,
+	chainsRemoved: 0,
 	coverageRemoved: 0,
 	checkpointsRemoved: 0,
 };
@@ -116,7 +118,7 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C

 	// ── delete-nodes: the full purge ──────────────────────────────────────
 	const nodeLines = graphStore.readNodes();
-	const edgeLines = graphStore.readEdges();
+	const chainLines = graphStore.readChains();

 	// Does the chat touch the graph at all? (A never-extracted chat still
 	// needs its coverage rows dropped above, but no ledger rewrite — keeps
@@ -124,7 +126,7 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C
 	// changed.)
 	const touched =
 		nodeLines.some((line) => line.provenance.some((pt) => pt.chatId === chatId)) ||
-		edgeLines.some((line) => line.provenance.some((pt) => pt.chatId === chatId));
+		chainLines.some((line) => line.provenance.some((pt) => pt.chatId === chatId));
 	if (!touched) {
 		if (stats.coverageRemoved > 0 || stats.checkpointsRemoved > 0) {
 			graphStore.rewriteLedgers({ coverage, checkpoints });
@@ -133,14 +135,12 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C
 	}

 	// 1. Survival: a node lives iff a reference from ANY surviving source
-	//    remains — another chat/src's provenance point on any of its lines,
-	//    a surviving mapping line (notes-front-door nodes carry EMPTY
-	//    provenance: the file IS the anchor, recorded through the mapping
-	//    line). (Edge endpoints are deliberately
-	//    NOT survival references: an edge's asserting session always left
-	//    provenance on its endpoints, so endpoint-only liveness cannot
-	//    occur in a consistent ledger — and counting it would keep nodes
-	//    alive whose lines we would then drop, dangling the edge.)
+	//    remains — another chat/src's provenance point on any of its lines.
+	//    (Chain members are deliberately NOT survival references: a
+	//    chain's asserting session always left provenance on its endpoints,
+	//    so endpoint-only liveness cannot occur in a consistent ledger —
+	//    and counting it would keep nodes alive whose lines we would then
+	//    drop, dangling the chain.)
 	const survives = (points: ReadonlyArray<{ chatId: string }>): boolean =>
 		points.some((pt) => pt.chatId !== chatId);
 	const live = new Set<string>();
@@ -182,41 +182,49 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C
 		// else: the deleted chat's link line — dies with its phrasings.
 	}

-	// 3. Edges: strip the chat's points; an assertion dies when its
-	//    provenance empties or either endpoint died IN THIS DELETION.
-	//    (Only nodes that existed and died count — an edge whose endpoints
-	//    never resolved as nodes is foreign data the deletion leaves alone:
-	//    destructive rewriting may not exceed the deleted chat's blast
-	//    radius.)
+	// 3. Chains: strip the chat's points; an assertion dies when its
+	//    provenance empties or ANY member node (premise or conclusion)
+	//    died IN THIS DELETION. (Only nodes that existed and died count —
+	//    a chain whose members never resolved as nodes is foreign data the
+	//    deletion leaves alone: destructive rewriting may not exceed the
+	//    deleted chat's blast radius.)
 	const deadNodes = new Set([...new Set(nodeLines.map((line) => line.id))].filter((id) => !live.has(id)));
-	const outEdges: GraphEdge[] = [];
-	for (const line of edgeLines) {
-		if (deadNodes.has(line.from) || deadNodes.has(line.to)) continue;
+	const outChains: GraphChain[] = [];
+	for (const line of chainLines) {
+		if (deadNodes.has(line.conclusion) || line.premises.some((premise) => deadNodes.has(premise))) continue;
 		const points = line.provenance.filter((pt) => pt.chatId !== chatId);
 		// An assertion dies when THIS deletion empties its provenance — a
 		// line that already had no points is foreign/legacy data, not this
 		// chat's trace; it rides untouched.
 		if (line.provenance.length > 0 && points.length === 0) continue;
-		outEdges.push(points.length === line.provenance.length ? line : { ...line, provenance: points });
+		outChains.push(points.length === line.provenance.length ? line : { ...line, provenance: points });
 	}

 	stats.nodesRemoved = [...new Set(nodeLines.map((line) => line.id))].filter((id) => !live.has(id)).length;
-	stats.edgesRemoved = edgeLines.length - outEdges.length;
+	stats.chainsRemoved = chainLines.length - outChains.length;

 	graphStore.rewriteLedgers({
 		nodes: outNodes,
-		edges: outEdges,
+		chains: outChains,
 		coverage,
 		checkpoints,
 	});

-	// 5. Positions: prune dead nodes (stale resting spots would pin
-	//    nothing — but pruning keeps the ledger honest and the revision
-	//    moving for exactly the right reason).
+	// 4. Positions: prune dead nodes AND dead chains (an argument's derived
+	//    implication node carries the chain's arg_ id — stale resting spots
+	//    would pin nothing; pruning keeps the ledger honest and the
+	//    revision moving for exactly the right reason).
+	const deadChainIds = new Set(
+		chainLines
+			.filter((line) => !outChains.includes(line))
+			.map((line) => line.id),
+	);
 	const positions = graphStore.readPositions();
 	const knownNodeIds = new Set(nodeLines.map((line) => line.id));
 	const prunedPositions = Object.fromEntries(
-		Object.entries(positions).filter(([id]) => live.has(id) || !knownNodeIds.has(id)),
+		Object.entries(positions).filter(
+			([id]) => (live.has(id) || !knownNodeIds.has(id)) && !deadChainIds.has(id),
+		),
 	);
 	if (Object.keys(prunedPositions).length !== Object.keys(positions).length) {
 		graphStore.writePositions(prunedPositions);
@@ -224,6 +232,7 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C

 	return stats;
 }
+
 // ─── single-node deletion (node interlude, owner-locked full-death) ───────────

 /**
@@ -236,13 +245,15 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C
 * one deletes a NODE and takes its every trace —
 *
 *   - every line of the node (create + link lines)
- *   - every EDGE touching it (from or to), whatever session asserted it
- *   - every mapping line that anchored it (the audit trail; for a
- *     notes-born node the file IS the anchor — its mapping line is the
- *     only one)
- *   - its resting position
+ *   - every CHAIN referencing it (as premise or conclusion), whatever
+ *     session asserted it — a chain with a dead member is not a chain
+ *   - its resting position (and every dead chain's)
 *
- * The blast radius is exactly the rows naming the node id: other nodes'
+ * An ARGUMENT deletion is the same call with an arg_-prefixed id (owner,
+ * 2026-09-30: the chain table's fenced delete kills chains): the "node"
+ * is the derived implication node whose id IS the chain's id.
+ *
+ * The blast radius is exactly the rows naming the id: other nodes'
 * provenance, aliases, and sessions are untouched (full death is
 * NODE-scoped, not session-scoped), and the source records of notes
 * imports stay (the import's bookkeeping; deleting one proposition is not
@@ -256,43 +267,68 @@ export function deleteChatTraces(graphStore: GraphStore, chatId: string, mode: C
 * second run finds no lines and changes nothing.
 */
 export interface NodeDeletionStats {
-	/** Edge assertion LINES removed (every edge touching the node). */
-	edgesRemoved: number;
+	/** Chain assertion LINES removed (every chain referencing the node). */
+	chainsRemoved: number;
 }

 function nodeLinesOf(graphStore: GraphStore, nodeId: string): GraphNode[] {
 	return graphStore.readNodes().filter((line) => line.id === nodeId);
 }

+function chainLinesOf(graphStore: GraphStore, chainId: string): GraphChain[] {
+	return graphStore.readChains().filter((line) => line.id === chainId);
+}
+
 /**
- * Full-death one node. Returns null when no such node exists (the
- * orchestration maps that to 404); rewrites only the ledgers that
- * changed (unchanged files keep their mtimes — the version stamp moves
- * only when something really did).
+ * Full-death one node (or one argument, by its arg_ id). Returns null
+ * when no such node/chain exists (the orchestration maps that to 404);
+ * rewrites only the ledgers that changed (unchanged files keep their
+ * mtimes — the version stamp moves only when something really did).
 */
 export function deleteNodeTraces(graphStore: GraphStore, nodeId: string): NodeDeletionStats | null {
+	const chainLines = graphStore.readChains();
+
+	// The argument branch: an arg_ id names a CHAIN, not a proposition —
+	// its lines die, and that is the whole death (the member propositions
+	// survive: deleting an argument spares its premises/conclusion).
+	if (nodeId.startsWith("arg_")) {
+		const outChains = chainLines.filter((line) => line.id !== nodeId);
+		if (outChains.length === chainLines.length) return null; // unknown argument
+		graphStore.rewriteLedgers({ chains: outChains });
+		const positions = graphStore.readPositions();
+		if (positions[nodeId] !== undefined) {
+			const { [nodeId]: _dead, ...rest } = positions;
+			graphStore.writePositions(rest);
+		}
+		return { chainsRemoved: chainLines.length - outChains.length };
+	}
+
 	const nodeLines = nodeLinesOf(graphStore, nodeId);
 	if (nodeLines.length === 0) return null;

-	const edgeLines = graphStore.readEdges();
-	const outEdges = edgeLines.filter((line) => line.from !== nodeId && line.to !== nodeId);
+	const outChains = chainLines.filter(
+		(line) => line.conclusion !== nodeId && !line.premises.includes(nodeId),
+	);

 	// Only the touched ledgers: the node's own lines always die (its file
 	// must move), everything else rewrites only when rows actually drop.
 	const outNodes = graphStore.readNodes().filter((line) => line.id !== nodeId);
 	graphStore.rewriteLedgers({
 		nodes: outNodes,
-		...(outEdges.length !== edgeLines.length ? { edges: outEdges } : {}),
+		...(outChains.length !== chainLines.length ? { chains: outChains } : {}),
 	});

-	// The resting position dies with the node.
+	// The resting positions die with the node and every dead chain.
+	const deadChainIds = new Set(chainLines.filter((line) => !outChains.includes(line)).map((line) => line.id));
 	const positions = graphStore.readPositions();
-	if (positions[nodeId] !== undefined) {
-		const { [nodeId]: _dead, ...rest } = positions;
-		graphStore.writePositions(rest);
+	const prunedPositions = Object.fromEntries(
+		Object.entries(positions).filter(([id]) => id !== nodeId && !deadChainIds.has(id)),
+	);
+	if (Object.keys(prunedPositions).length !== Object.keys(positions).length) {
+		graphStore.writePositions(prunedPositions);
 	}

 	return {
-		edgesRemoved: edgeLines.length - outEdges.length,
+		chainsRemoved: chainLines.length - outChains.length,
 	};
 }
@@ -45,7 +45,8 @@ import { randomBytes } from "node:crypto";
 import type { CoverageEntry } from "./contracts/graph.ts";
 import type {
 	AuditVerdicts,
-	ExtractedEdge,
+	ExtractedChain,
+	GraphChain,
 	SessionFindings,
 	Cluster,
 	EmissionStats,
@@ -56,6 +57,7 @@ import type {
 } from "./contracts.ts";
 import { MIN_CLUSTER_SIZE } from "./clusters.ts";
 import { birthSessionOf, birthSessionPartition } from "./session-clusters.ts";
+import { formatChainLine } from "./practice.ts";
 import type { ChatStore, GraphStore } from "./ports.ts";

 /** The storage ports every graph operation needs, passed explicitly. */
@@ -69,6 +71,18 @@ function newGraphNodeId(): string {
 	return `n_${randomBytes(6).toString("hex")}`;
 }

+/** "arg_" + 12 hex chars — the implication-node namespace (a chain's id
+ *  IS its derived node's id; collision-free with n_ by construction). */
+function newGraphChainId(): string {
+	return `arg_${randomBytes(6).toString("hex")}`;
+}
+
+/** A chain's merge key: sorted premises + conclusion — the identity an
+ *  assertion re-stating the same argument merges under. */
+function chainKey(premises: ReadonlyArray<string>, conclusion: string): string {
+	return `${[...premises].sort().join("+")}>${conclusion}`;
+}
+
 /** What one merge run merges FROM (the caller supplies it — the merger never
 *  reads the chat store): the coverage checkpoint for a session batch, or —
 *  for the format-agnostic notes front door (2026-09-13) — no coverage at
@@ -127,7 +141,7 @@ export function mergeFindings(
 	source: MergeSource,
 ): EmissionStats {
 	const { graphStore: ledgers } = deps;
-	const stats: EmissionStats = { nodes: 0, edges: 0 };
+	const stats: EmissionStats = { nodes: 0, chains: 0 };

 	// 1. Resolution: THIS job's propositions → graph node ids, built
 	//    in-memory as the propositions resolve (owner, 2026-09-29: the
@@ -180,31 +194,41 @@ export function mergeFindings(
 		mapping.set(p.id, graphNodeId);
 	}

-	// 2. Edges — the extractor's own, the ONLY edge source (the auditor's
-	//    edges argument is gone, owner 2026-09-28 evening). Endpoints are
-	//    this job's local proposition ids and resolve through the job-local
-	//    map; edges carry the run's chat-level provenance point and dedupe
-	//    by (from,to,type) already asserted by THIS chat — an assertion by
-	//    another chat stays untouched (provenance unions at read time).
+	// 2. Chains — the extractor's own, the ONLY chain source; the stored
+	//    truth (chains-primary, owner 2026-09-30). Endpoints are this
+	//    job's local proposition ids and resolve through the job-local
+	//    map; chains carry the run's chat-level provenance point and
+	//    dedupe by (premises, conclusion) already asserted by THIS chat —
+	//    an assertion by another chat stays untouched (provenance unions
+	//    at read time; a known argument re-stated appends under the SAME
+	//    arg_ id — link-style, exactly like node link-appends; the first
+	//    line's premises/createdAt stand at read time).
 	const assertedByChat = new Set<string>();
-	for (const line of ledgers.readEdges()) {
-		const key = `${line.from}\u0000${line.to}\u0000${line.type}`;
+	const idOfKey = new Map<string, string>();
+	for (const line of ledgers.readChains()) {
+		const key = chainKey(line.premises, line.conclusion);
+		if (!idOfKey.has(key)) idOfKey.set(key, line.id);
 		if (line.provenance.some((pt) => pt.chatId === chatId)) assertedByChat.add(key);
 	}
-	const emitEdge = (edge: ExtractedEdge): void => {
-		// Extractor-local ids only — the auditor's bridging edges are gone
-		// (owner, 2026-09-28 evening), so raw node-id endpoints no longer occur.
+	const emitChain = (chain: ExtractedChain): void => {
 		const resolve = (endpoint: string): string | undefined => mapping.get(endpoint);
-		const from = resolve(edge.from);
-		const to = resolve(edge.to);
-		if (!from || !to || from === to) return; // unresolvable endpoint — skip
-		const key = `${from}\u0000${to}\u0000${edge.type}`;
-		if (assertedByChat.has(key)) return;
-		ledgers.appendEdge({ from, to, type: edge.type, provenance: pointOf(chatId) });
+		const conclusion = resolve(chain.conclusion);
+		if (conclusion === undefined) return; // unresolvable endpoint — skip
+		// Duplicate local ids resolving to one node (two phrasings of one
+		// premise) collapse; a premise equal to the conclusion is dropped.
+		const premises = [...new Set(chain.premises.map(resolve))].filter(
+			(p): p is string => p !== undefined && p !== conclusion,
+		);
+		if (premises.length === 0) return; // a chain IS an argument — bare propositions ride the node ledger alone
+		const key = chainKey(premises, conclusion);
+		if (assertedByChat.has(key)) return; // this chat already asserted this argument
+		const id = idOfKey.get(key) ?? newGraphChainId();
+		ledgers.appendChain({ id, premises, conclusion, createdAt: now, provenance: pointOf(chatId) });
+		idOfKey.set(key, id);
 		assertedByChat.add(key);
-		stats.edges++;
+		stats.chains!++;
 	};
-	for (const edge of findings.edges) emitEdge(edge); // the extractor's edges — the ONLY edge source
+	for (const chain of findings.chains) emitChain(chain); // the extractor's chains — the ONLY chain source // the extractor's edges — the ONLY edge source

 	// 3. Checkpoint — THE COVERAGE DISCIPLINE (vision-extraction-coverage.md):
 	//    only now, after every append succeeded, is the batch covered. The
@@ -222,21 +246,26 @@ export function mergeFindings(

 // ─── derivation (reads only — everything below is recomputable) ─────────────

+/** The merged STORED truth: propositions + chains (chains-primary, owner
+ *  2026-09-30). `nodes` are PROPOSITIONS ONLY — no derived implication
+ *  nodes; the auditor's and prober's views see the world, not the
+ *  rendering. The canvas-facing VIEW (implication nodes + untyped
+ *  arrows) is deriveView() below — the lossy image. */
 export interface DerivedGraph {
 	nodes: GraphNode[];
-	edges: GraphEdge[];
+	chains: GraphChain[];
 }

 /**
 * The whole graph from the ledgers. Node LINES may repeat an id (link-
 * appends): the FIRST line defines name/statement/createdAt; later
 * lines' statements and aliases join `aliases`, provenance unions — the
- * name never changes after creation. Edge
- * LINES are assertions, merged by (from,to,type) with unioned provenance,
- * first-seen order. `store events, derive state` — this is the only reader
- * that matters.
+ * name never changes after creation. Chain LINES are assertions, merged
+ * by (premises, conclusion) with unioned provenance; the first line's
+ * arg_ id / premises / createdAt are the chain's identity.
+ * `store events, derive state` — this is the only reader that matters.
 */
-export function getGraph(graphStore: GraphStore): DerivedGraph {
+export function getGraph(graphStore: Pick<GraphStore, "readNodes" | "readChains">): DerivedGraph {
 	// Merge node lines by id (first line defines; later lines add phrasings).
 	const byId = new Map<string, GraphNode>();
 	for (const line of graphStore.readNodes()) {
@@ -254,29 +283,68 @@ export function getGraph(graphStore: GraphStore): DerivedGraph {
 		}
 	}

-	const merged: GraphEdge[] = [];
-	const byKey = new Map<string, GraphEdge>();
-	for (const line of graphStore.readEdges()) {
-		const key = `${line.from}\u0000${line.to}\u0000${line.type}`;
+	// Merge chain assertion lines by (premises, conclusion): the first
+	// line's id/premises/createdAt stand, provenance unions.
+	const chains: GraphChain[] = [];
+	const byKey = new Map<string, GraphChain>();
+	for (const line of graphStore.readChains()) {
+		const key = chainKey(line.premises, line.conclusion);
 		const existing = byKey.get(key);
 		if (existing) {
 			for (const pt of line.provenance) {
 				if (!existing.provenance.some((q) => samePoint(q, pt))) existing.provenance.push(pt);
 			}
 		} else {
-			const edge: GraphEdge = { ...line, provenance: [...line.provenance] };
-			byKey.set(key, edge);
-			merged.push(edge);
+			const chain: GraphChain = { ...line, premises: [...line.premises], provenance: [...line.provenance] };
+			byKey.set(key, chain);
+			chains.push(chain);
 		}
 	}
-	return { nodes: [...byId.values()], edges: merged };
+	return { nodes: [...byId.values()], chains };
+}
+
+/** The DERIVED view — what the canvas renders. One implication NODE per
+ *  chain (id = the chain's arg_ id; name "⟹"; statement = the chain
+ *  line; the chain's provenance/createdAt) plus UNTYPED arrows: each
+ *  premise → the implication node, the implication node → the
+ *  conclusion. Rendering specialization (invisible / physics-free)
+ *  comes later (owner, 2026-09-30: physics is fine with imp nodes as
+ *  regular nodes for now). 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 };
+	const live = new Set(graph.nodes.map((node) => node.id));
+	const impNodes: GraphNode[] = [];
+	const edges: GraphEdge[] = [];
+	for (const chain of graph.chains) {
+		if (!live.has(chain.conclusion) || !chain.premises.every((premise) => live.has(premise))) continue;
+		impNodes.push({
+			id: chain.id,
+			name: "⟹",
+			statement: formatChainLine(chain, names),
+			aliases: [],
+			createdAt: chain.createdAt,
+			provenance: [...chain.provenance],
+		});
+		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 };
 }

 // ─── the /api/graph payload ──────────────────────────────────────────────────

 /** Everything the home graph view needs, in one fetch (shape: contracts). */
 export function graphSnapshot(deps: GraphDeps): GraphSnapshot {
-	const { nodes, edges } = getGraph(deps.graphStore);
+	const graph = getGraph(deps.graphStore);
+	// The canvas-facing lossy image: propositions + derived implication
+	// nodes, untyped arrows. `chains` (the stored truth) ride along for
+	// the chain table and the practice pipeline — they read the truth,
+	// never the derived fan-out.
+	const view = deriveView(graph);
+	const nodes = view.nodes;

 	const nodeChats = new Map<string, Set<string>>();
 	const touch = (nodeId: string, chatId: string): void => {
@@ -290,13 +358,6 @@ export function graphSnapshot(deps: GraphDeps): GraphSnapshot {
 	for (const node of nodes) {
 		for (const pt of node.provenance) touch(node.id, pt.chatId);
 	}
-	for (const edge of edges) {
-		for (const pt of edge.provenance) {
-			touch(edge.from, pt.chatId);
-			touch(edge.to, pt.chatId);
-		}
-	}
-
 	// Labels for every source the graph can point back at: real chats
 	// (title, deep-linkable) and imported notes files (path, static — the
 	// format-agnostic front door's provenance).
@@ -330,7 +391,9 @@ export function graphSnapshot(deps: GraphDeps): GraphSnapshot {
 	// presentation rule (a region needs >= 3 propositions for a hull). A
 	// birth session whose record is gone (deleted chat) keeps its members
 	// but renders unlabeled — honest, never guessed.
-	const communities = birthSessionPartition(nodes);
+	// PROPOSITIONS ONLY (owner, 2026-09-30): derived implication nodes
+	// never partition — the stored world clusters, its image follows.
+	const communities = birthSessionPartition(graph.nodes);
 	const clusters: Cluster[] = communities
 		.filter((community) => community.members.length >= MIN_CLUSTER_SIZE)
 		.map((community) => ({
@@ -346,7 +409,8 @@ export function graphSnapshot(deps: GraphDeps): GraphSnapshot {

 	return {
 		nodes,
-		edges,
+		edges: view.edges,
+		chains: graph.chains,
 		sessions,
 		fileSources,
 		nodeSessions,
@@ -1,6 +1,7 @@
-import type { GraphEdge, GraphNode, Position } from "./contracts.ts";
+import type { GraphChain, GraphNode, Position } from "./contracts.ts";
 import { incrementalLayout } from "./layout.ts";
 import { birthSessionPartition } from "./session-clusters.ts";
+import { deriveView, getGraph } from "./graph.ts";

 /**
 * The merge-time settle: recompute the resting layout from the CURRENT
@@ -10,6 +11,12 @@ import { birthSessionPartition } from "./session-clusters.ts";
 * commit (client positions become the anchor set). Synchronous — it must
 * finish before the next /api/graph fetch reflects the change.
 *
+ * CHAINS-PRIMARY (owner, 2026-09-30): the settle lays out the DERIVED
+ * view — propositions AND the derived implication nodes (one per chain,
+ * arg_ ids) over the derived untyped arrows — so positions exist for
+ * every node the canvas renders. Implication nodes participate in the
+ * physics as regular nodes (rendering specialization comes later).
+ *
 * SPLIT FROM layout.ts deliberately (2026-09-13): layout.ts is in the
 * browser barrel, and the settle needs the cluster partition for the
 * cluster centroid pull — this module must not ship in the client bundle.
@@ -18,27 +25,20 @@ import { birthSessionPartition } from "./session-clusters.ts";
 */
 export function settleGraphLayout(graphStore: {
 	readNodes(): GraphNode[];
-	readEdges(): GraphEdge[];
+	readChains(): GraphChain[];
 	readPositions(): Record<string, Position>;
 	writePositions(positions: Record<string, Position>): void;
 }): void {
-	const nodes = graphStore.readNodes();
-	if (nodes.length === 0) return;
-	// Node LINES may repeat an id (link-appends) — dedupe, first defines.
-	const seen = new Set<string>();
-	const unique = nodes.filter((n) => {
-		if (seen.has(n.id)) return false;
-		seen.add(n.id);
-		return true;
-	});
-	const edges = graphStore.readEdges();
+	const graph = getGraph(graphStore);
+	if (graph.nodes.length === 0) return;
+	const view = deriveView(graph);
 	const previous = new Map(Object.entries(graphStore.readPositions()));
 	// The cluster partition for the centroid pull: the SAME birth-session
 	// partition the snapshot renders (derived from provenance on read —
 	// core/session-clusters.ts, wave 7) — one cluster concept everywhere.
-	// The unique list is the deduped set the partition needs (lines may
-	// repeat an id — first defines).
-	const communities = birthSessionPartition(unique);
-	const next = incrementalLayout(unique, edges, previous, { clusters: communities });
+	// PROPOSITIONS ONLY (owner, 2026-09-30): implication nodes never
+	// partition; the stored world clusters, its image follows.
+	const communities = birthSessionPartition(graph.nodes);
+	const next = incrementalLayout(view.nodes, view.edges, previous, { clusters: communities });
 	graphStore.writePositions(Object.fromEntries(next));
-}
+}
@@ -14,7 +14,7 @@ import type {
 	ChatRecord,
 	ChatSettings,
 	ChatSummary,
-	GraphEdge,
+	GraphChain,
 	GraphNode,
 	JobKind,
 	JobRecord,
@@ -65,11 +65,12 @@ export interface ChatStore {
 }

 // ─── GraphStore — the append-only evidence ledgers (data/graph) ──────────────
-// v1 surface = the five JSONL ledgers (nodes / edges / events / mappings /
-// sessions). Reads return the raw append-order lines; merging edge assertions
-// by (from, to, type) is DERIVED in core/graph.ts — the store never decides.
-// The extraction pipeline (next stage) becomes the sole writer; this read
-// surface stays.
+// Chains are the stored truth (owner, 2026-09-30): nodes + reasoning
+// chains; edges are a DERIVED view (core/graph.ts) and never touch this
+// seam. Reads return the raw append-order lines; merging chain assertions
+// by (premises, conclusion) is DERIVED in core/graph.ts — the store never
+// decides. The extraction pipeline is the sole writer; this read surface
+// stays.

 export interface GraphStore {
 	/** Append one GraphNode (ids are unique — no merging needed). */
@@ -77,12 +78,10 @@ export interface GraphStore {
 	/** Raw node lines in append order. */
 	readNodes(): GraphNode[];

-	/** Append one edge ASSERTION (a second session asserting the same
-	 *  (from, to, type) appends another line; readers merge). */
-	appendEdge(assertion: GraphEdge): void;
-	readEdges(): GraphEdge[];
-
-	/** Append one quiz outcome / understanding observation. */
+	/** Append one chain ASSERTION (a second session asserting the same
+	 *  (premises, conclusion) appends another line; readers merge). */
+	appendChain(assertion: GraphChain): void;
+	readChains(): GraphChain[];

 	/** Append one emission checkpoint. */
 	appendCheckpoint(checkpoint: SessionCheckpoint): void;
@@ -122,7 +121,7 @@ export interface GraphStore {
 	 *  replacement atomic. */
 	rewriteLedgers(next: {
 		nodes?: GraphNode[];
-		edges?: GraphEdge[];
+		chains?: GraphChain[];
 		coverage?: CoverageEntry[];
 		checkpoints?: SessionCheckpoint[];
 	}): void;
@@ -2,16 +2,15 @@
 * Practice-module core — the chain bijection + coverage (slice 1 of the
 * 2026-09-29 plan). Pure, no I/O.
 *
- * chainsForSelection(): the graph → chains translation — group by
- * conclusion over FOLLOWS edges only (supports are invisible to practice,
- * owner 2026-09-29: "no edges"). chainsToGraph(): the exact inverse — the
- * bijection the chain notation promises (renderable back to the graph
- * with no information loss; the round-trip is pinned in
- * tests/practice.test.ts). chainCoverage(): the set's completeness law —
- * the union of the problems' chains must equal the set's chains; the
- * partitioner's submit is validated against it.
+ * chainsForSelection(): the stored CHAINS (chains-primary, owner
+ *  2026-09-30) filtered to a selection — a chain rides along iff ALL of
+ *  its members are selected; nodes in no surviving chain become singleton
+ *  chains. formatChainLine(): one world-facing line per chain.
+ *  chainCoverage(): the set's completeness law — the union of the
+ *  problems' chains must equal the set's chains; the partitioner's submit
+ *  is validated against it.
 */
-import type { CueDistance, GraphEdge, GraphNode, LadderRung, Presentation, Problem, ReasoningChain } from "./contracts.ts";
+import type { CueDistance, GraphChain, GraphNode, LadderRung, Presentation, Problem, ReasoningChain } from "./contracts.ts";

 /** The named levels (owner-approved 2026-09-29) — definitions verbatim
 *  from the ladder doctrine / the contract's tables. The UI's stepped
@@ -36,81 +35,34 @@ export const PRESENTATIONS: Record<Presentation, { name: string; definition: str
 	application: { name: "Application", definition: "a concrete worldly affair — a case, episode, system, or story — in which the proposition's structure appears in the wild." },
 };

-/** The selection's follows-edges as chains: every edge into a node joins
- *  that node's (one) chain; a node with no in- AND no out-follows-edge in
- *  the selection is a singleton chain. Premise-only nodes are NOT separate
- *  chains — they are covered inside the chains they feed. Deterministic:
- *  chains sorted by id, premises sorted. */
+/** The stored chains filtered to a selection (chains-primary, owner
+ *  2026-09-30): a chain rides along iff its conclusion AND every premise
+ *  are selected; a node in no surviving chain is a singleton chain
+ *  (premises: []). Premise-only nodes whose chain was excluded are
+ *  singletons — the same inclusion law as the pre-chains edge grouping.
+ *  Every stored chain keeps its OWN id (arg_…) — two independent
+ *  arguments for one conclusion stay distinct. Deterministic: chains
+ *  sorted by id, premises sorted. */
 export function chainsForSelection(
 	nodes: ReadonlyArray<Pick<GraphNode, "id">>,
-	edges: ReadonlyArray<Pick<GraphEdge, "from" | "to" | "type">>,
+	chains: ReadonlyArray<Pick<GraphChain, "id" | "premises" | "conclusion">>,
 ): ReasoningChain[] {
 	const selected = new Set(nodes.map((n) => n.id));
-	const premisesByConclusion = new Map<string, Set<string>>();
-	for (const edge of edges) {
-		if (edge.type !== "follows") continue; // supports are NO edges here (owner, 2026-09-29)
-		if (!selected.has(edge.from) || !selected.has(edge.to)) continue;
-		const premises = premisesByConclusion.get(edge.to) ?? new Set<string>();
-		premises.add(edge.from);
-		premisesByConclusion.set(edge.to, premises);
-	}
 	const chained = new Set<string>();
-	const chains: ReasoningChain[] = [];
-	for (const [conclusion, premises] of premisesByConclusion) {
-		chains.push({ id: conclusion, premises: [...premises].sort(), conclusion });
-		chained.add(conclusion);
-		for (const premise of premises) chained.add(premise);
+	const included: ReasoningChain[] = [];
+	for (const chain of chains) {
+		if (!selected.has(chain.conclusion)) continue;
+		if (!chain.premises.every((premise) => selected.has(premise))) continue;
+		included.push({ id: chain.id, premises: [...chain.premises].sort(), conclusion: chain.conclusion });
+		chained.add(chain.conclusion);
+		for (const premise of chain.premises) chained.add(premise);
 	}
 	for (const node of nodes) {
 		if (!chained.has(node.id)) {
-			chains.push({ id: node.id, premises: [], conclusion: node.id });
+			included.push({ id: node.id, premises: [], conclusion: node.id });
 		}
 	}
-	return chains.sort((a, b) => (a.id < b.id ? -1 : a.id > b.id ? 1 : 0));
-}
-
-/** The exact inverse of chainsForSelection: node ids = every chain member,
- *  edges = one follows-edge per (premise, conclusion) pair. Deterministic:
- *  node ids sorted, edges sorted by (from, to). */
-export function chainsToGraph(
-	chains: ReadonlyArray<Pick<ReasoningChain, "premises" | "conclusion">>,
-): {
-	nodeIds: string[];
-	edges: Array<{ from: string; to: string; type: "follows" }>;
-} {
-	const nodeIds = new Set<string>();
-	const edges: Array<{ from: string; to: string; type: "follows" }> = [];
-	for (const chain of chains) {
-		nodeIds.add(chain.conclusion);
-		for (const premise of chain.premises) {
-			nodeIds.add(premise);
-			edges.push({ from: premise, to: chain.conclusion, type: "follows" });
-		}
-	}
-	edges.sort((a, b) => (a.from !== b.from ? (a.from < b.from ? -1 : 1) : a.to < b.to ? -1 : 1));
-	return { nodeIds: [...nodeIds].sort(), edges };
-}
-
-/** The extraction seam's chain→edge expansion (extractor redesign,
- *  2026-09-30): the extractor SUBMITS chains (premises + conclusion);
- *  the pipeline's internal findings carry follows-EDGES downstream
- *  (auditor, merger, coverage — all unchanged). Each premise becomes
- *  one edge into the conclusion — chainsToGraph's edge law, shared
- *  (one math, one place). Identical (premise-set, conclusion) chains
- *  dedupe SILENTLY here: the model restating an argument is a no-op,
- *  never an error (validation errors are the loud channel; see the
- *  extractor's validate hook). */
-export function chainsToEdges(
-	chains: ReadonlyArray<Pick<ReasoningChain, "premises" | "conclusion">>,
-): Array<{ from: string; to: string; type: "follows" }> {
-	const seen = new Set<string>();
-	const deduped = chains.filter((chain) => {
-		const key = `${[...chain.premises].sort().join("+")}>${chain.conclusion}`;
-		if (seen.has(key)) return false;
-		seen.add(key);
-		return true;
-	});
-	return chainsToGraph(deduped).edges;
+	return included.sort((a, b) => (a.id < b.id ? -1 : a.id > b.id ? 1 : 0));
 }

 /** A chain as one world-facing line — the propositions' NAMES joined
@@ -54,19 +54,6 @@ export interface GraphRenderSettings {
 	labelZoom: number;
 	/** Node + hover label font size, WORLD units (scales with camera). */
 	labelSize: number;
-	/** Draw `supports` edges at all (owner, 2026-09-29): off hides them
-	 *  from the canvas — a DRAW toggle only. The physics sim still feels
-	 *  them (settings never shift the graph: camera, one frame), and node
-	 *  detail cards still list them. */
-	showSupports: boolean;
-	/** Relative SHAFT thickness of supports edges (owner, 2026-09-29):
-	 *  a 0–1 multiplier of edgeWidth — default 0.5, the single-line
-	 *  relation reads as the lighter one. SHAFT ONLY: arrowheads keep
-	 *  full Arrowhead-size geometry (owner pick). Linear, not a ladder —
-	 *  it's a ratio; exactly 0 floors to a hairline in the renderer
-	 *  (canvas cannot stroke a true 0-width line; hiding is the toggle's
-	 *  job). */
-	supportsWidth: number;
 	/** Toggle for the cluster region labels (hulls always draw). */
 	clusterLabels: boolean;
 	/** Cluster label font size, px on screen (camera-compensated —
@@ -108,14 +95,6 @@ export function sanitizeRenderSettings(raw: unknown): GraphRenderSettings {
 		arrowLength: legacySizes ? DEFAULT_RENDER_SETTINGS.arrowLength : ladd(r.arrowLength, ARROW_LENGTH_LADDER, DEFAULT_RENDER_SETTINGS.arrowLength),
 		labelZoom: ladd(r.labelZoom, LABEL_ZOOM_LADDER, DEFAULT_RENDER_SETTINGS.labelZoom),
 		labelSize: legacySizes ? DEFAULT_RENDER_SETTINGS.labelSize : ladd(r.labelSize, LABEL_SIZE_LADDER, DEFAULT_RENDER_SETTINGS.labelSize),
-		showSupports:
-			typeof r.showSupports === "boolean" ? r.showSupports : DEFAULT_RENDER_SETTINGS.showSupports,
-		// Linear ratio, not a ladder: real numbers clamp to [0, 1]; anything
-		// else resets to the default.
-		supportsWidth:
-			typeof r.supportsWidth === "number" && Number.isFinite(r.supportsWidth)
-				? clamp(r.supportsWidth, 0, 1)
-				: DEFAULT_RENDER_SETTINGS.supportsWidth,
 		clusterLabels:
 			typeof r.clusterLabels === "boolean" ? r.clusterLabels : DEFAULT_RENDER_SETTINGS.clusterLabels,
 		clusterLabelSize: ladd(
@@ -283,8 +262,6 @@ export const DEFAULT_RENDER_SETTINGS: GraphRenderSettings = {
 	arrowLength: 2,
 	labelZoom: 4,
 	labelSize: 3,
-	showSupports: true,
-	supportsWidth: 0.5,
 	clusterLabels: true,
 	clusterLabelSize: 14,
 	regions: DEFAULT_REGION_TUNING,
@@ -75,7 +75,7 @@ export function graphRevision(): number {
 	let revision = 0;
 	for (const file of [
 		LEDGER_FILES.nodes,
-		LEDGER_FILES.edges,
+		LEDGER_FILES.chains,
 		LEDGER_FILES.sessions,
 		LEDGER_FILES.coverage,
 		POSITIONS_FILE,
@@ -1,5 +1,5 @@
 /**
- * GraphStore — the fs JSONL adapter: four append-only ledgers at
+ * GraphStore — the fs JSONL adapter: the append-only ledgers at
 * config.LEDGER_FILES (contracts.ts "v1 emission").
 *   nodes.jsonl     GraphNode        — one line per node write: the FIRST
 *                                      line for an id defines it; a later
@@ -7,10 +7,18 @@
 *                                      link-append (session phrasings join
 *                                      aliases, provenance unions); reads
 *                                      merge by id (core/graph.ts getGraph)
- *   edges.jsonl    GraphEdge        — one line per edge ASSERTION (a second
- *                                      session asserting the same (from,to,type)
- *                                      appends another line; reads merge)
+ *   chains.jsonl    GraphChain       — one line per chain ASSERTION (a second
+ *                                      session asserting the same
+ *                                      (premises, conclusion) appends
+ *                                      another line; readers merge)
 *   sessions.jsonl  SessionCheckpoint— emission checkpoints (foldedAt)
+ *   coverage.jsonl  CoverageEntry    — per-message extraction coverage
+ *
+ * CHAINS-PRIMARY (owner, 2026-09-30): there is NO edges ledger — the edge
+ * view (implication nodes + untyped arrows) is derived in core/graph.ts on
+ * every read and never persisted. A stale edges.jsonl left by a pre-chains
+ * build is deleted once, here, at adapter load (same doctrine as the
+ * events-ledger purge below).
 *
 * Plus config.SOURCES_FILE (sources.json): the imported-notes bookkeeping
 * (NOT a ledger) — one JSON map, src-id → NotesSource, read-modify-write
@@ -28,7 +36,7 @@ import * as fs from "node:fs";
 import * as path from "node:path";
 import { LEDGER_FILES, POSITIONS_FILE, SOURCES_FILE } from "../../config.ts";
 import type {
-	GraphEdge,
+	GraphChain,
 	GraphNode,
 	ExtractionRunUsage,
 	NotesSource,
@@ -94,15 +102,20 @@ const isGraphNode = (v: unknown): v is GraphNode =>
 	Array.isArray(v.provenance) &&
 	v.provenance.every(isProvenancePoint);

-const EDGE_TYPES = ["follows", "supports"] as const;
-
-const isGraphEdge = (v: unknown): v is GraphEdge =>
+/** A chain line: premises ≥ 1 (a chain IS an argument — bare propositions
+ *  ride the node ledger alone), every member a string, conclusion a string.
+ *  Endpoint EXISTENCE is the derivation's concern (it drops dangling
+ *  chains); the store only shapes. */
+const isGraphChain = (v: unknown): v is GraphChain =>
 	isRecord(v) &&
-	isString(v.from) &&
-	isString(v.to) &&
-	(EDGE_TYPES as readonly string[]).includes(v.type as string) &&
+	isString(v.id) &&
+	Array.isArray(v.premises) &&
+	v.premises.length > 0 &&
+	v.premises.every(isString) &&
+	isString(v.conclusion) &&
 	Array.isArray(v.provenance) &&
-	v.provenance.every(isProvenancePoint);
+	v.provenance.every(isProvenancePoint) &&
+	isString(v.createdAt);

 const isCheckpoint = (v: unknown): v is SessionCheckpoint =>
 	isRecord(v) && isString(v.chatId) && isString(v.foldedAt);
@@ -123,12 +136,13 @@ export const graphStore: GraphStore = {
 		return readValid(LEDGER_FILES.nodes, isGraphNode);
 	},

-	/** Append one edge ASSERTION; readers merge lines by (from,to,type). */
-	appendEdge(assertion: GraphEdge): void {
-		appendLine(LEDGER_FILES.edges, assertion);
+	/** Append one chain ASSERTION; readers merge lines by (premises,
+	 *  conclusion). */
+	appendChain(assertion: GraphChain): void {
+		appendLine(LEDGER_FILES.chains, assertion);
 	},
-	readEdges(): GraphEdge[] {
-		return readValid(LEDGER_FILES.edges, isGraphEdge);
+	readChains(): GraphChain[] {
+		return readValid(LEDGER_FILES.chains, isGraphChain);
 	},

 	appendCheckpoint(checkpoint: SessionCheckpoint): void {
@@ -184,13 +198,13 @@ export const graphStore: GraphStore = {
 	 *  as "nothing yet", same as never-emitted. */
 	rewriteLedgers(next: {
 		nodes?: GraphNode[];
-		edges?: GraphEdge[];
+		chains?: GraphChain[];
 		coverage?: CoverageEntry[];
 		checkpoints?: SessionCheckpoint[];
 	}): void {
 		const files = {
 			nodes: LEDGER_FILES.nodes,
-			edges: LEDGER_FILES.edges,
+			chains: LEDGER_FILES.chains,
 			coverage: LEDGER_FILES.coverage,
 			checkpoints: LEDGER_FILES.sessions,
 		} as const;
@@ -290,20 +304,21 @@ function writeSourceMap(map: Record<string, NotesSource>): void {
 	fs.writeFileSync(SOURCES_FILE, JSON.stringify(map, null, "\t"), "utf-8");
 }

-// ─── one-way migration: the events ledger is gone (2026-09-27) ────────────────
-// Quiz outcomes and understanding observations are no longer formalized in
-// the graph — the pipeline writes nodes + edges only. A stale events.jsonl
-// left by an earlier build is deleted once, here, at adapter load: dead
-// ledgers are exactly the confusion the cleanup removes (owner ruling).
+// ─── one-way purges at adapter load: dead ledgers are exactly the confusion
+// the cleanup removes (owner doctrine — nothing reads them, nothing writes
+// them, a stale file lying around is a lie). ────────────────────────────────
 {
-	const legacyEvents = path.join(path.dirname(LEDGER_FILES.nodes), "events.jsonl");
-	try {
-		if (fs.existsSync(legacyEvents)) {
-			fs.rmSync(legacyEvents);
-			console.info(`[graph-store] purged legacy events ledger: ${legacyEvents}`);
+	const graphDir = path.dirname(LEDGER_FILES.nodes);
+	for (const legacy of ["edges.jsonl", "events.jsonl"]) {
+		const file = path.join(graphDir, legacy);
+		try {
+			if (fs.existsSync(file)) {
+				fs.rmSync(file);
+				console.info(`[graph-store] purged legacy ledger: ${file}`);
+			}
+		} catch (err) {
+			console.warn(`[graph-store] could not purge legacy ledger ${file}:`, err);
 		}
-	} catch (err) {
-		console.warn(`[graph-store] could not purge legacy events ledger:`, err);
 	}
 }

@@ -33,7 +33,7 @@ import type {
 	AuditVerdicts,
 	CoverageEntry,
 	ExtractionRunUsage,
-	GraphEdge,
+	GraphChain,
 	GraphNode,

 	NotesSource,
@@ -74,7 +74,7 @@ function fauxEngine(steps: FauxResponseStep[]): PiEngine {
 /** An in-memory GraphStore (core/ports.ts) — this suite never touches data/graph. */
 function memoryLedgers() {
 	const nodes: GraphNode[] = [];
-	const edges: GraphEdge[] = [];
+	const chains: GraphChain[] = [];
 	const checkpoints: SessionCheckpoint[] = [];
 	const coverage: CoverageEntry[] = [];
 	const sources = new Map<string, NotesSource>();
@@ -82,8 +82,8 @@ function memoryLedgers() {
 		return {
 		appendNode: (n: GraphNode) => void nodes.push(n),
 		readNodes: () => nodes.map((n) => ({ ...n })),
-		appendEdge: (e: GraphEdge) => void edges.push(e),
-		readEdges: () => edges.map((e) => ({ ...e })),
+		appendChain: (c: GraphChain) => void chains.push(c),
+		readChains: () => chains.map((c) => ({ ...c, premises: [...c.premises], provenance: [...c.provenance] })),
 		appendCheckpoint: (c: SessionCheckpoint) => void checkpoints.push(c),
 		readCheckpoints: () => checkpoints.map((c) => ({ ...c })),
 		// Extraction coverage (vision-extraction-coverage.md) — append-only;
@@ -114,7 +114,7 @@ function memoryLedgers() {
 		// store: replace the provided ledgers' full contents.
 		rewriteLedgers: (next) => {
 			if (next.nodes) nodes.splice(0, nodes.length, ...next.nodes.map((n) => ({ ...n, provenance: [...n.provenance], aliases: [...n.aliases] })));
-			if (next.edges) edges.splice(0, edges.length, ...next.edges.map((e) => ({ ...e, provenance: [...e.provenance] })));
+			if (next.chains) chains.splice(0, chains.length, ...next.chains.map((c) => ({ ...c, premises: [...c.premises], provenance: [...c.provenance] })));
 			if (next.coverage) coverage.splice(0, coverage.length, ...next.coverage.map((c) => ({ ...c })));
 			if (next.checkpoints) checkpoints.splice(0, checkpoints.length, ...next.checkpoints.map((c) => ({ ...c })));
 		},
@@ -386,7 +386,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {

 		const pipeline = createExtractionPipeline({ chatStore, graphStore: ledgers, extractor, auditor: submitModel("submit_review", verdict) });
 		const stats = await pipeline.runExtraction(chatId);
-		assert.deepEqual(stats, { nodes: 2, edges: 1 });
+		assert.deepEqual(stats, { nodes: 2, chains: 1 });
 	});

 	it("stringified-payload heal: the CHAINS array arriving as ONE JSON string still validates (redesign, 2026-09-30)", async () => {
@@ -402,7 +402,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 			extractor,
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, edges: 1 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, chains: 1 });
 	});

 	it("runs end to end: findings → audit verdict (identity) → deterministic merge + checkpoint", async () => {
@@ -436,7 +436,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 		// p1 creates no node, p2 creates one, and the extractor's edge
 		// resolves through them. (The old echo form could silently drop
 		// content by omitting it; that accidental drop channel is gone.)
-		assert.deepEqual(stats, { nodes: 1, edges: 1 });
+		assert.deepEqual(stats, { nodes: 1, chains: 1 });

 		// Link-append: the phrasing joined the existing node's aliases and
 		// the provenance unioned; p2's create line is its own node.
@@ -544,7 +544,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 			auditor: submitModel("submit_review", verdict),
 		});
 		const stats = await pipeline.runExtraction(chatId);
-		assert.deepEqual(stats, { nodes: 2, edges: 1 }); // full findings merge (verdicts-only)
+		assert.deepEqual(stats, { nodes: 2, chains: 1 }); // full findings merge (verdicts-only)
 		// Wave 7 (950ddfd): birth-session clusters carry session-name labels,
 		// so the post-merge naming garnish is gone — no model spend, no
 		// naming-run records, no label writes.
@@ -609,7 +609,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 		});
 		// The old run-level throw is gone: one failed job is absorbed at
 		// the fan-out — the run resolves with what actually merged (zeros).
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 0, edges: 0 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 0, chains: 0 });
 		assert.equal(ledgers.readNodes().length, 0);
 		assert.equal(ledgers.readCheckpoints().length, 0, "no checkpoint — the next trigger re-runs");
 		assert.equal(ledgers.readCoverage().length, 0);
@@ -620,7 +620,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 			extractor: silentModel(),
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await failingExtractor.runExtraction(chatId), { nodes: 0, edges: 0 });
+		assert.deepEqual(await failingExtractor.runExtraction(chatId), { nodes: 0, chains: 0 });
 		assert.equal(ledgers.readCheckpoints().length, 0);

 		// THE isolation pin: a two-batch chat whose SECOND extractor call
@@ -642,7 +642,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 			engineFor: (role) =>
 				role === "extractor" ? fauxEngine([countingStep]) : submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await mixed.runExtraction(chunkyId), { nodes: 2, edges: 1 }, "batch 1's merge survives batch 2's failure");
+		assert.deepEqual(await mixed.runExtraction(chunkyId), { nodes: 2, chains: 1 }, "batch 1's merge survives batch 2's failure");
 		assert.equal(invocations, 2);
 		assert.equal(ledgers.readCoverage().length, 3, "batch 1 checkpointed its three messages");
 		assert.equal(
@@ -731,8 +731,8 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 		assert.equal(extractionStatuses().find((r) => r.chatId === a.chatId)?.phase, "auditing", "A still audits while B waits");

 		gateOpen();
-		assert.deepEqual(await runA, { nodes: 1, edges: 0 });
-		assert.deepEqual(await runB, { nodes: 1, edges: 0 });
+		assert.deepEqual(await runA, { nodes: 1, chains: 0 });
+		assert.deepEqual(await runB, { nodes: 1, chains: 0 });
 		assert.ok(bAuditorCalled);
 		assert.ok(bSawAlphasMerge, "B's auditor saw A's merged node — audit serialized after merge");
 		assert.equal(extractionStatuses().length, 0, "both runs left the registry");
@@ -774,7 +774,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {

 		// The dock's abort button, pressed while B queues.
 		assert.equal(abortExtraction(b.chatId), true);
-		assert.deepEqual(await runB, { nodes: 0, edges: 0 }, "aborted before auditing — zero emissions");
+		assert.deepEqual(await runB, { nodes: 0, chains: 0 }, "aborted before auditing — zero emissions");
 		assert.ok(!bAuditorCalled, "B's auditor was never invoked");
 		assert.ok(!extractionStatuses().some((r) => r.chatId === b.chatId), "B left the registry");
 		assert.equal(ledgers.readCoverage().some((row) => row.chatId === b.chatId), false, "B checkpointed nothing");
@@ -782,14 +782,14 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 		// The chain link B abandoned still resolved: A finishes, and a
 		// THIRD run audits normally — no deadlock residue.
 		gateOpen();
-		assert.deepEqual(await runA, { nodes: 1, edges: 0 });
+		assert.deepEqual(await runA, { nodes: 1, chains: 0 });
 		const pipelineC = createExtractionPipeline({
 			chatStore,
 			graphStore: ledgers,
 			extractor: submitModel("submit_findings", single("pc", "Gamma claim", "Gamma statement")),
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await pipelineC.runExtraction(c.chatId), { nodes: 1, edges: 0 });
+		assert.deepEqual(await pipelineC.runExtraction(c.chatId), { nodes: 1, chains: 0 });
 	});

 	it("captures per-stage usage live, persists the run's usage into the chat record", async () => {
@@ -862,7 +862,7 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 		const stats = await runPromise;

 		// A deliberate stop, not a failure: zero emissions, no throw.
-		assert.deepEqual(stats, { nodes: 0, edges: 0 });
+		assert.deepEqual(stats, { nodes: 0, chains: 0 });
 		assert.equal(extractionStatuses().length, 0, "the registry clears");
 		assert.equal(ledgers.readNodes().length, 0, "nothing merged");
 		assert.equal(ledgers.readCheckpoints().length, 0, "nothing checkpointed — the next trigger re-runs");
@@ -907,13 +907,13 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {

 		const first = pipeline.runExtraction(chatId);
 		const second = await pipeline.runExtraction(chatId); // in-flight → zeros
-		assert.deepEqual(second, { nodes: 0, edges: 0 });
+		assert.deepEqual(second, { nodes: 0, chains: 0 });

 		release();
 		// The gated extractor never submits — an ISOLATED job failure now
 		// (per-chunk jobs, owner 2026-09-28): the run resolves with zeros
 		// instead of throwing.
-		assert.deepEqual(await first, { nodes: 0, edges: 0 });
+		assert.deepEqual(await first, { nodes: 0, chains: 0 });
 	});

 	it("registers runs on the process-wide registry (route-instance safety): a second pipeline instance sees the same single-flight state", async () => {
@@ -959,10 +959,10 @@ describe("the extraction pipeline (extractor → auditor → merger)", () => {
 		);
 		const g = globalThis as { __lhExtractionRuns?: { running: Map<string, unknown> } };
 		assert.ok(g.__lhExtractionRuns?.running.has(chatId), "the registry lives on globalThis — no module-instance split can hide runs");
-		assert.deepEqual(await observer.runExtraction(chatId), { nodes: 0, edges: 0 }, "single-flight spans pipeline instances");
+		assert.deepEqual(await observer.runExtraction(chatId), { nodes: 0, chains: 0 }, "single-flight spans pipeline instances");

 		release();
-		assert.deepEqual(await first, { nodes: 0, edges: 0 }, "isolated job failure — the run resolves zeros");
+		assert.deepEqual(await first, { nodes: 0, chains: 0 }, "isolated job failure — the run resolves zeros");
 		assert.ok(!extractionStatuses().some((run) => run.chatId === chatId), "the registry entry clears when the run ends (however it ends)");
 		assert.ok(!g.__lhExtractionRuns?.running.has(chatId), "nothing leaks into the global registry");
 	});
@@ -1027,7 +1027,7 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 		]);
 	}

-	it("co-premises fan out at the seam: ONE chain with two premises becomes TWO follows-edges into the conclusion", async () => {
+	it("co-premises ride as ONE stored argument — the fan-out to arrows is the derived view, not the store", async () => {
 		const { chatId } = fixtureChat();
 		const ledgers = memoryLedgers();
 		const extractor = submitModel("submit_findings", {
@@ -1044,16 +1044,16 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 			extractor,
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 3, edges: 2 });
-		// Both edges point INTO the conclusion's resolved node; the two
-		// from-ends are exactly the two premises (node ids are random —
-		// assert set-wise, never by ledger order).
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 3, chains: 1 });
+		// The stored chain's premises are exactly the two premises; the
+		// conclusion is C's resolved node (ids are random — assert
+		// set-wise, never by ledger order).
 		const byName = new Map(ledgers.readNodes().map((n) => [n.name, n.id]));
 		const conclusion = byName.get("C")!;
-		const edges = ledgers.readEdges();
-		assert.ok(edges.every((e) => e.to === conclusion), "both edges point INTO the conclusion");
+		const chains = ledgers.readChains();
+		assert.ok(chains.every((c) => c.conclusion === conclusion), "chains point INTO the conclusion");
 		assert.deepEqual(
-			edges.map((e) => e.from).sort(),
+			chains.flatMap((c) => c.premises).sort(),
 			[byName.get("A")!, byName.get("B")!].sort(),
 		);
 	});
@@ -1079,11 +1079,11 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 			extractor,
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		// Independent arguments for the same conclusion are separate chains
-		// → two edges into C; the bare p4 rides the propositions list alone.
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 4, edges: 2 });
+		// Independent arguments for the same conclusion are separate chains;
+		// the bare p4 rides the propositions list alone.
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 4, chains: 2 });
 		const lonely = ledgers.readNodes().find((n) => n.name === "Lonely")!;
-		assert.ok(ledgers.readEdges().every((e) => e.from !== lonely.id && e.to !== lonely.id));
+		assert.ok(ledgers.readChains().every((c) => !c.premises.includes(lonely.id) && c.conclusion !== lonely.id));
 	});

 	it("identical chains dedupe SILENTLY at the expansion — restating an argument is a no-op, not an error", async () => {
@@ -1099,7 +1099,7 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 			extractor,
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, edges: 1 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, chains: 1 });
 	});

 	it("the OLD wire shape (an edges array, no chains) is dead: validation fails every turn — nothing merges", async () => {
@@ -1127,7 +1127,7 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 			graphStore: ledgers,
 			engineFor: (role) => (role === "extractor" ? oldShape() : submitModel("submit_review", { links: [] })),
 		});
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 0, edges: 0 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 0, chains: 0 });
 	});

 	it("validate error-back: a chain referencing an UNKNOWN id is rejected, the model re-submits clean", async () => {
@@ -1145,7 +1145,7 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 		});
 		// The first submit was schema-VALID — only the chain law caught it;
 		// the retry merges in full.
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, edges: 1 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, chains: 1 });
 	});

 	it("validate error-back: a conclusion in its OWN premises is rejected, the model re-submits clean", async () => {
@@ -1161,7 +1161,7 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 			extractor: retryEngine(bad, FINDINGS),
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, edges: 1 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, chains: 1 });
 	});

 	it("empty premises never pass: the schema's minItems rejects, the model re-submits clean", async () => {
@@ -1177,7 +1177,7 @@ describe("the extractor redesign (owner, 2026-09-30): chains are the deliverable
 			extractor: retryEngine(bad, FINDINGS),
 			auditor: submitModel("submit_review", { links: [] }),
 		});
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, edges: 1 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 2, chains: 1 });
 	});

 	it("the system prompt is goal-first: ONE shared core, both preambles assembled onto it", () => {
@@ -1226,7 +1226,7 @@ describe("the notes front door (importNotes — format-agnostic)", () => {
 		});
 		const stats = await pipeline.importNotes({ filePath: "/vault/learn vim.md", text: NOTES_TEXT });

-		assert.deepEqual(stats, { nodes: 1, edges: 0 });
+		assert.deepEqual(stats, { nodes: 1, chains: 0 });
 		// The run surfaced as a NOTES run labeled with the file path.
 		assert.deepEqual(seen, [{ kind: "notes", label: "/vault/learn vim.md" }]);
 		assert.equal(extractionStatuses().length, 0, "the registry clears when the run ends");
@@ -1290,7 +1290,7 @@ describe("the notes front door (importNotes — format-agnostic)", () => {
 		// independently (owner, 2026-09-29 — the mappings ledger is gone);
 		// cross-chunk identity is the auditor's linkTo verdict, and these
 		// fixtures submit none.
-		assert.deepEqual(stats, { nodes: calls, edges: 0 });
+		assert.deepEqual(stats, { nodes: calls, chains: 0 });
 		assert.equal(ledgers.readNodes().length, calls);
 	});

@@ -1319,7 +1319,7 @@ describe("the notes front door (importNotes — format-agnostic)", () => {
 		});
 		// Isolated job failure (per-chunk jobs, owner 2026-09-28): the run
 		// resolves zeros — no throw — and still nothing merged.
-		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 0, edges: 0 });
+		assert.deepEqual(await pipeline.runExtraction(chatId), { nodes: 0, chains: 0 });
 		assert.equal(ledgers.readNodes().length, 0);
 		assert.equal(ledgers.readCoverage().length, 0, "nothing checkpointed — the messages stay re-runnable");
 	});
@@ -1334,13 +1334,13 @@ describe("the notes front door (importNotes — format-agnostic)", () => {
 				auditor: submitModel("submit_review", NOTES_VERDICT),
 			});
 		const first = await mk().importNotes({ filePath: "/vault/learn vim.md", text: NOTES_TEXT });
-		assert.deepEqual(first, { nodes: 1, edges: 0 });
+		assert.deepEqual(first, { nodes: 1, chains: 0 });

 		// Unchanged text: the content fingerprint matches — no extraction
 		// at all (no model calls, no usage record; the mappings ledger
 		// used to give this no-op at merge time by accident).
 		const second = await mk().importNotes({ filePath: "/vault/learn vim.md", text: NOTES_TEXT });
-		assert.deepEqual(second, { nodes: 0, edges: 0 }, "unchanged content is a true no-op");
+		assert.deepEqual(second, { nodes: 0, chains: 0 }, "unchanged content is a true no-op");

 		assert.equal(ledgers.readSources().length, 1, "one source identity — the path hashes to the same id");
 		assert.equal(ledgers.readSources()[0]!.extractions?.length, 1, "only the real run billed its usage");
@@ -1350,7 +1350,7 @@ describe("the notes front door (importNotes — format-agnostic)", () => {
 		// whole file re-runs (fresh merge; the auditor's links would dedupe
 		// identity on a real model).
 		const third = await mk().importNotes({ filePath: "/vault/learn vim.md", text: `${NOTES_TEXT}\nA new closing line.` });
-		assert.deepEqual(third, { nodes: 1, edges: 0 }, "changed content re-extracts");
+		assert.deepEqual(third, { nodes: 1, chains: 0 }, "changed content re-extracts");
 		assert.equal(ledgers.readSources()[0]!.extractions?.length, 2, "the re-run bills its usage");
 		assert.equal(ledgers.readNodes().length, 2);
 	});
@@ -1367,7 +1367,7 @@ describe("the notes front door (importNotes — format-agnostic)", () => {

 		const srcId = extractionStatuses().find((r) => r.chatId.startsWith("src_"))!.chatId;
 		assert.equal(abortExtraction(srcId), true);
-		assert.deepEqual(await runPromise, { nodes: 0, edges: 0 });
+		assert.deepEqual(await runPromise, { nodes: 0, chains: 0 });
 		assert.equal(ledgers.readNodes().length, 0, "nothing merged");
 		assert.equal(ledgers.readCheckpoints().length, 0, "nothing checkpointed");
 		assert.equal(ledgers.readSources()[0]!.extractions?.length, 1, "partial usage still persisted");
@@ -1462,7 +1462,7 @@ describe("the chunked pipeline (extraction coverage)", () => {
 		// SEPARATE job's namespace (owner, 2026-09-29 — no mapping table)
 		// — its propositions merge again as fresh nodes. Cross-batch
 		// identity is the auditor's linkTo verdict, never the merger's.
-		assert.deepEqual(stats, { nodes: 4, edges: 2 });
+		assert.deepEqual(stats, { nodes: 4, chains: 2 });

 		// Per-batch coverage: every message checkpointed, nothing legacy.
 		const coverage = ledgers.readCoverage();
@@ -1474,7 +1474,7 @@ describe("the chunked pipeline (extraction coverage)", () => {
 		// new usage entry (no money spent on covered ground).
 		const before = views.length;
 		const again = await pipeline.runExtraction(chatId);
-		assert.deepEqual(again, { nodes: 0, edges: 0 });
+		assert.deepEqual(again, { nodes: 0, chains: 0 });
 		assert.equal(views.length, before);
 		// PER-CHUNK JOBS (owner 2026-09-28): one usage record per batch job
 		// (two), and the no-op run adds none.
@@ -1521,7 +1521,7 @@ describe("the chunked pipeline (extraction coverage)", () => {
 		const stats = await runPromise;

 		// Batch 1's emissions are kept and its messages stay covered.
-		assert.deepEqual(stats, { nodes: 2, edges: 1 });
+		assert.deepEqual(stats, { nodes: 2, chains: 1 });
 		assert.equal(ledgers.readCoverage().length, 3, "batch 1 checkpointed its three messages");
 		const cov = coverageOf(record.messages, ledgers.readCoverage(), chatId);
 		assert.equal(cov.uncoveredCount, 2, "the in-flight batch's messages stay uncovered");
@@ -1654,7 +1654,7 @@ describe("per-chunk parallel jobs (owner, 2026-09-28)", () => {

 		// SOURCE-WIDE abort: every chunk job of the fan-out dies together.
 		assert.equal(abortExtraction(srcId), true);
-		assert.deepEqual(await runPromise, { nodes: 0, edges: 0 });
+		assert.deepEqual(await runPromise, { nodes: 0, chains: 0 });
 		assert.equal(extractionStatuses().filter((r) => r.chatId === srcId).length, 0, "all rows leave the registry");
 		assert.equal(ledgers.readNodes().length, 0, "nothing merged");
 		// Per-job usage: all 8 chunk jobs persisted their (failed) spend.
@@ -1706,7 +1706,7 @@ describe("per-chunk parallel jobs (owner, 2026-09-28)", () => {
 		// Identical findings in every chunk, one merge PER chunk (jobs are
 		// independent — owner, 2026-09-29): 8 chunks × 2 propositions,
 		// 8 × 1 edge. The auditor's links, not the merger, dedupe identity.
-		assert.deepEqual(stats, { nodes: 16, edges: 8 });
+		assert.deepEqual(stats, { nodes: 16, chains: 8 });
 		assert.equal(ledgers.readNodes().length, 16);
 	});
 });
@@ -1730,12 +1730,12 @@ describe("the session-deletion guard (chat deleted mid-run)", () => {
 		// emissions (stats present but empty — nothing merged).
 		assert.ok(stats);
 		assert.equal(stats.nodes, 0);
-		assert.equal(stats.edges, 0);
+		assert.equal(stats.chains, 0);

 		// Nothing merged, nothing checkpointed — the deleted chat leaves no
 		// trace for a later snapshot to resurrect.
 		assert.equal(ledgers.readNodes().length, 0);
-		assert.equal(ledgers.readEdges().length, 0);
+		assert.equal(ledgers.readChains().length, 0);
 		assert.equal(ledgers.readCoverage().length, 0);
 		assert.equal(ledgers.readCheckpoints().length, 0);

@@ -15,7 +15,7 @@ import { createProberTools } from "../src/agent/tools.ts";
 import { auditorGraphTools } from "../src/agent/tools/graph.ts";
 import type { ChatStore, GraphStore, JobStore } from "../src/core/ports.ts";
 import type { ChatSummary } from "../src/core/contracts/chat.ts";
-import type { GraphEdge, GraphNode } from "../src/core/contracts/graph.ts";
+import type { GraphChain, GraphNode } from "../src/core/contracts/graph.ts";

 // ─── fixtures ────────────────────────────────────────────────────────────────

@@ -39,10 +39,10 @@ function fakeStores(
 		chats?: Array<Pick<ChatSummary, "id" | "title" | "createdAt" | "updatedAt">>;
 	} = {},
 ): { chatStore: ChatStore; graphStore: GraphStore } {
-	const edges: GraphEdge[] = [];
+	const chains: GraphChain[] = [];
 	const graphStore: GraphStore = {
 		readNodes: () => nodes,
-		readEdges: () => edges,
+		readChains: () => chains,
 		readCheckpoints: () => [],
 		readCoverage: () => [],
 		readSources: () => [],
@@ -243,11 +243,10 @@ function fixtureFindings(): SessionFindings {
 				aliases: [],
 			},
 		],
-		edges: [
+		chains: [
 			{
-				from: "p1",
-				to: "p2",
-				type: "follows",
+				premises: ["p1"],
+				conclusion: "p2",
 			},
 		],
 	};
@@ -274,14 +273,14 @@ function scopedGraph(chatIds: string[]) {
 	const graph = getGraph(graphStore);
 	return {
 		nodes: graph.nodes.filter((n) => n.provenance.some((pt) => chatIds.includes(pt.chatId))),
-		edges: graph.edges.filter((e) => e.provenance.some((pt) => chatIds.includes(pt.chatId))),
+		chains: graph.chains.filter((c) => c.provenance.some((pt) => chatIds.includes(pt.chatId))),
 	};
 }

 describe("the merger (mergeFindings)", () => {
 	it("creates nodes from the verdicts with chat-level provenance", () => {
 		const stats = mergeFindings(chat1.id, fixtureFindings(), fixtureVerdicts(), graphDeps, sessionSource(chat1.id));
-		assert.deepEqual(stats, { nodes: 3, edges: 1 });
+		assert.deepEqual(stats, { nodes: 3, chains: 1 });

 		const graph = scopedGraph([chat1.id]);
 		assert.equal(graph.nodes.length, 3);
@@ -298,13 +297,13 @@ describe("the merger (mergeFindings)", () => {
 		const alpha = graph.nodes.find((n) => n.statement === "Alpha intuition")!;
 		assert.deepEqual(alpha.provenance, [{ chatId: chat1.id, messageId: "" }]);

-		// The follows edge, provenance attached.
-		assert.equal(graph.edges.length, 1);
-		const edge = graph.edges[0]!;
-		assert.equal(edge.from, idByStatement.get("Alpha intuition"));
-		assert.equal(edge.to, idByStatement.get("Beta rule"));
-		assert.equal(edge.type, "follows");
-		assert.deepEqual(edge.provenance, [{ chatId: chat1.id, messageId: "" }]);
+		// The stored chain, provenance attached.
+		assert.equal(graph.chains.length, 1);
+		const chain = graph.chains[0]!;
+		assert.match(chain.id, /^arg_/, "store-minted argument id");
+		assert.deepEqual(chain.premises, [idByStatement.get("Alpha intuition")]);
+		assert.equal(chain.conclusion, idByStatement.get("Beta rule"));
+		assert.deepEqual(chain.provenance, [{ chatId: chat1.id, messageId: "" }]);

 	});

@@ -321,15 +320,15 @@ describe("the merger (mergeFindings)", () => {
 				{ id: "p1", name: "Rep one", statement: "Independence one statement", aliases: [] },
 				{ id: "p2", name: "Rep two", statement: "Independence two statement", aliases: [] },
 			],
-			edges: [{ from: "p1", to: "p2", type: "follows" }],
+			chains: [{ premises: ["p1"], conclusion: "p2" }],
 		};
 		const first = mergeFindings(rep.id, findings, { links: [] }, graphDeps, sessionSource(rep.id));
-		assert.deepEqual(first, { nodes: 2, edges: 1 });
+		assert.deepEqual(first, { nodes: 2, chains: 1 });
 		const second = mergeFindings(rep.id, findings, { links: [] }, graphDeps, sessionSource(rep.id));
-		assert.deepEqual(second, { nodes: 2, edges: 1 }, "nothing remembered — everything re-creates");
+		assert.deepEqual(second, { nodes: 2, chains: 1 }, "nothing remembered — everything re-creates");
 		const graph = scopedGraph([rep.id]);
 		assert.equal(graph.nodes.length, 4, "the propositions merge again as fresh nodes");
-		assert.equal(graph.edges.length, 2, "fresh endpoints — fresh edge assertions");
+		assert.equal(graph.chains.length, 2, "fresh endpoints — fresh chain assertions");
 		// exactly one checkpoint line per merge, though — checkpoints are a log
 		assert.equal(graphStore.readCheckpoints().filter((c) => c.chatId === rep.id).length, 2);
 	});
@@ -341,10 +340,10 @@ describe("the merger (mergeFindings)", () => {
 				{ id: "p1", name: "Dup", statement: "Dup statement", aliases: [] },
 				{ id: "p1", name: "Dup", statement: "Dup statement", aliases: [] },
 			],
-			edges: [],
+			chains: [],
 		};
 		const stats = mergeFindings(dup.id, findings, { links: [] }, graphDeps, sessionSource(dup.id));
-		assert.deepEqual(stats, { nodes: 1, edges: 0 }, "the duplicate id is skipped — first resolution stands");
+		assert.deepEqual(stats, { nodes: 1, chains: 0 }, "the duplicate id is skipped — first resolution stands");
 	});

 	it("applies a linkTo verdict: phrasings join aliases, provenance unions, no duplicate node", () => {
@@ -373,7 +372,7 @@ describe("the merger (mergeFindings)", () => {
 						aliases: ["alpha intuition"],
 					},
 				],
-				edges: [],
+				chains: [],
 			},
 			// VERDICTS-ONLY: the identity call is a link entry, not a field
 			// on the proposition (owner, 2026-09-28).
@@ -381,7 +380,7 @@ describe("the merger (mergeFindings)", () => {
 			graphDeps,
 			sessionSource(chat2.id),
 		);
-		assert.deepEqual(stats, { nodes: 0, edges: 0 });
+		assert.deepEqual(stats, { nodes: 0, chains: 0 });

 		const after = scopedGraph([chat1.id, chat2.id]);
 		assert.equal(after.nodes.length, 3, "no duplicate node");
@@ -410,7 +409,7 @@ describe("the merger (mergeFindings)", () => {
 						aliases: [],
 					},
 				],
-				edges: [],
+				chains: [],
 			},
 			{ links: [] },
 			graphDeps,
@@ -439,10 +438,9 @@ describe("the merger (mergeFindings)", () => {
 					statement,
 					aliases: [],
 				})),
-				edges: [
-					{ from: "p1", to: "p2", type: "follows", },
-					{ from: "p2", to: "p3", type: "follows", },
-					{ from: "p1", to: "p3", type: "follows", },
+				chains: [
+					{ premises: ["p1"], conclusion: "p2", },
+					{ premises: ["p2"], conclusion: "p3", },
 				],
 			},
 			{ links: [] },
@@ -494,7 +492,7 @@ describe("the merger (mergeFindings)", () => {
 						aliases: [],
 					},
 				],
-				edges: [],
+				chains: [],
 			},
 			// empty verdicts — identity is the auditor's call alone
 			{ links: [] },
@@ -519,13 +517,13 @@ describe("the merger (mergeFindings)", () => {
 						aliases: [],
 					},
 				],
-				edges: [],
+				chains: [],
 			},
 			{ links: [] },
 			graphDeps,
 			{ foldedAt: "2026-09-13T00:00:00.000Z" },
 		);
-		assert.deepEqual(stats, { nodes: 1, edges: 0 });
+		assert.deepEqual(stats, { nodes: 1, chains: 0 });

 		const node = getGraph(graphStore).nodes.find((n) => n.statement.startsWith("Vim starts"))!;
 		assert.deepEqual(node.provenance, [{ chatId: "src_notesfixture", messageId: "" }], "one chat-level point — the source key, no message anchors");
@@ -617,7 +615,7 @@ describe("session deletion (deleteChatTraces + deleteChatSession, wave 6)", () =
 				{ id: "p1", name: "Shared core", statement: "Shared core statement", aliases: ["shared feel"], },
 				{ id: "p2", name: "Solo fact", statement: "Solo fact statement", aliases: ["solo feel"], },
 			],
-			edges: [{ from: "p1", to: "p2", type: "follows", }],
+			chains: [{ premises: ["p1"], conclusion: "p2", }],
 		};
 		mergeFindings(dA.id, findingsA, { links: [] }, graphDeps, sessionSource(dA.id));
 		// Resolve through THIS session's provenance — the shared ledger
@@ -642,7 +640,7 @@ describe("session deletion (deleteChatTraces + deleteChatSession, wave 6)", () =
 				{ id: "q1", name: "Shared again", statement: "Shared core, rephrased", aliases: ["B phrasing"] },
 				{ id: "q2", name: "B extra", statement: "B extra statement", aliases: ["b extra feel"], },
 			],
-			edges: [{ from: "q1", to: "q2", type: "follows", }],
+			chains: [{ premises: ["q1"], conclusion: "q2", }],
 		};
 		mergeFindings(dB.id, findingsB, { links: [{ id: "q1", linkTo: xId }] }, graphDeps, sessionSource(dB.id));
 		const zId = bornOf(dB.id, "B extra statement");
@@ -665,7 +663,7 @@ describe("session deletion (deleteChatTraces + deleteChatSession, wave 6)", () =
 		const stats = deleteChatTraces(graphStore, dA.id, "delete-nodes");
 		assert.deepEqual(stats, {
 			nodesRemoved: 1,
-			edgesRemoved: 1,
+			chainsRemoved: 1,
 			coverageRemoved: 2,
 			checkpointsRemoved: 1,
 		} satisfies ChatDeletionStats);
@@ -684,9 +682,12 @@ describe("session deletion (deleteChatTraces + deleteChatSession, wave 6)", () =
 		assert.equal(graphStore.readNodes().some((n) => n.id === yId), false);
 		// Z (dB-only) is untouched, byte-identical.
 		assert.equal(JSON.stringify(graphStore.readNodes().find((n) => n.id === zId)), zLineBefore);
-		// Edges: dA's assertion X→Y died; dB's X→Z survived.
+		// Chains: dA's argument X⇒Y died (Y died); dB's X⇒Z survived.
 		const scoped = scopedGraph([dA.id, dB.id]);
-		assert.deepEqual(scoped.edges, [{ from: xId, to: zId, type: "follows", provenance: [{ chatId: dB.id, messageId: "" }] }]);
+		assert.equal(scoped.chains.length, 1);
+		assert.deepEqual(scoped.chains[0]!.premises, [xId]);
+		assert.equal(scoped.chains[0]!.conclusion, zId);
+		assert.deepEqual(scoped.chains[0]!.provenance, [{ chatId: dB.id, messageId: "" }]);
 		// Positions: the orphan pruned.
 		const positions = graphStore.readPositions();
 		assert.equal(positions[yId], undefined);
@@ -703,25 +704,25 @@ describe("session deletion (deleteChatTraces + deleteChatSession, wave 6)", () =
 		graphStore.appendNode({ id: "n_del_append_probe", name: "Probe", statement: "Probe statement", aliases: [], createdAt: "2026-09-23T00:04:00.000Z", provenance: [{ chatId: "chat_foreign_probe", messageId: "" }] });
 		assert.equal(graphStore.readNodes().length, nodesBefore + 1);
 		// Idempotent: a second run finds nothing.
-		assert.deepEqual(deleteChatTraces(graphStore, dA.id, "delete-nodes"), { ...stats, nodesRemoved: 0, edgesRemoved: 0, coverageRemoved: 0, checkpointsRemoved: 0 } satisfies ChatDeletionStats);
+		assert.deepEqual(deleteChatTraces(graphStore, dA.id, "delete-nodes"), { ...stats, nodesRemoved: 0, chainsRemoved: 0, coverageRemoved: 0, checkpointsRemoved: 0 } satisfies ChatDeletionStats);
 	});

 	it("preserve-graph: only the extraction bookkeeping dies — the graph ledgers are byte-identical", () => {
 		const { dA, dB, xId, yId, zId } = buildTwoSessionScenario();
 		const before = {
 			nodes: graphStore.readNodes(),
-			edges: graphStore.readEdges(),
+			chains: graphStore.readChains(),
 			positions: graphStore.readPositions(),
 		};
 		const stats = deleteChatTraces(graphStore, dA.id, "preserve-graph");
 		assert.deepEqual(stats, {
 			nodesRemoved: 0,
-			edgesRemoved: 0,
+			chainsRemoved: 0,
 			coverageRemoved: 2,
 			checkpointsRemoved: 1,
 		} satisfies ChatDeletionStats);
 		assert.deepEqual(graphStore.readNodes(), before.nodes);
-		assert.deepEqual(graphStore.readEdges(), before.edges);
+		assert.deepEqual(graphStore.readChains(), before.chains);
 		assert.deepEqual(graphStore.readPositions(), before.positions);
 		assert.equal(graphStore.readCoverage().some((row) => row.chatId === dA.id), false);
 		assert.equal(graphStore.readCoverage().some((row) => row.chatId === dB.id), true);
@@ -769,12 +770,12 @@ describe("single-node deletion (deleteNodeTraces + deleteGraphNode, node interlu
 	/** The full-death scenario: node X is born in a notes file (EMPTY
 	 *  provenance — a legacy line; the mappings anchor is gone, owner
 	 *  2026-09-29), re-encountered by a chat (link line: alias +
-	 *  provenance), and asserted in edges by two sessions. */
+	 *  provenance), and asserted in chains by two sessions. */
 	function buildNodeScenario() {
 		// Clean slate per test: each test in this describe builds its own
 		// scenario from empty ledgers (the suite's isolation covers the
 		// whole file; this covers describe-internal stacking).
-		graphStore.rewriteLedgers({ nodes: [], edges: [] });
+		graphStore.rewriteLedgers({ nodes: [], chains: [] });
 		graphStore.writePositions({});
 		graphStore.appendNode({
 			id: "n_dead",
@@ -802,18 +803,20 @@ describe("single-node deletion (deleteNodeTraces + deleteGraphNode, node interlu
 			createdAt: "2026-09-23T00:00:00.000Z",
 			provenance: [{ chatId: "chat_node_a", messageId: "m2" }],
 		});
-		graphStore.appendEdge({ from: "n_dead", to: "n_keep", type: "follows", provenance: [{ chatId: "chat_node_a", messageId: "m1" }] });
-		graphStore.appendEdge({ from: "n_keep", to: "n_dead", type: "supports", provenance: [{ chatId: "chat_node_b", messageId: "m3" }] });
-		graphStore.appendEdge({ from: "n_keep", to: "n_other", type: "follows", provenance: [{ chatId: "chat_node_b", messageId: "m3" }] });
-		// Resting positions for both.
-		graphStore.writePositions({ n_dead: { x: 1, y: 1 }, n_keep: { x: 2, y: 2 } });
+		graphStore.appendChain({ id: "arg_dead_keep", premises: ["n_dead"], conclusion: "n_keep", createdAt: "2026-09-23T00:00:00.000Z", provenance: [{ chatId: "chat_node_a", messageId: "m1" }] });
+		graphStore.appendChain({ id: "arg_keep_dead", premises: ["n_keep"], conclusion: "n_dead", createdAt: "2026-09-23T00:00:00.000Z", provenance: [{ chatId: "chat_node_b", messageId: "m3" }] });
+		// A FOREIGN chain the deletion must not touch (destructive rewriting
+		// may not exceed the blast radius — foreign data rides untouched).
+		graphStore.appendChain({ id: "arg_keep_other", premises: ["n_keep"], conclusion: "n_other", createdAt: "2026-09-23T00:00:00.000Z", provenance: [{ chatId: "chat_node_b", messageId: "m3" }] });
+		// Resting positions for both nodes and both dying chains' imp nodes.
+		graphStore.writePositions({ n_dead: { x: 1, y: 1 }, n_keep: { x: 2, y: 2 }, arg_dead_keep: { x: 1.5, y: 1.5 }, arg_keep_dead: { x: 2.5, y: 2.5 } });
 	}

 	it("deleteNodeTraces: FULL DEATH — the node, its edges, its evidence, its anchors, its position", () => {
 		buildNodeScenario();
 		const keepLineBefore = JSON.stringify(graphStore.readNodes().find((n) => n.id === "n_keep"));
 		const stats = deleteNodeTraces(graphStore, "n_dead");
-		assert.deepEqual(stats, { edgesRemoved: 2 } satisfies NodeDeletionStats);
+		assert.deepEqual(stats, { chainsRemoved: 2 } satisfies NodeDeletionStats);

 		// The node's EVERY line is gone; the neighbor is byte-identical
 		// (full death is node-scoped — other nodes' sessions keep their
@@ -824,15 +827,17 @@ describe("single-node deletion (deleteNodeTraces + deleteGraphNode, node interlu
 			keepLineBefore,
 			"the untouched node is byte-identical",
 		);
-		// Only the edge to nowhere rode along; the foreign edge X→Z stays.
+		// Only the chains referencing X died; the foreign chain stays.
 		assert.deepEqual(
-			graphStore.readEdges().map((e) => [e.from, e.to]),
-			[["n_keep", "n_other"]],
+			graphStore.readChains().map((c) => [c.premises, c.conclusion]),
+			[[["n_keep"], "n_other"]],
 		);
 		// The resting position died with the node.
 		const positions = graphStore.readPositions();
 		assert.equal(positions["n_dead"], undefined);
 		assert.deepEqual(positions["n_keep"], { x: 2, y: 2 });
+		assert.equal(positions["arg_dead_keep"], undefined, "the dying chains' imp-node positions die too");
+		assert.equal(positions["arg_keep_dead"], undefined);
 		// Atomic rewrites left no temp files.
 		assert.equal(fs.readdirSync(PATHS.graph).filter((f) => f.includes(".tmp-")).length, 0);
 		// Idempotent: a second run finds no node — null.
@@ -849,7 +854,7 @@ describe("single-node deletion (deleteNodeTraces + deleteGraphNode, node interlu
 			provenance: [{ chatId: "chat_node_solo", messageId: "m1" }],
 		});
 		const stats = deleteNodeTraces(graphStore, "n_solo");
-		assert.deepEqual(stats, { edgesRemoved: 0 } satisfies NodeDeletionStats);
+		assert.deepEqual(stats, { chainsRemoved: 0 } satisfies NodeDeletionStats);
 		assert.equal(graphStore.readNodes().some((n) => n.id === "n_solo"), false);
 	});

@@ -899,7 +904,7 @@ describe("single-node deletion (deleteNodeTraces + deleteGraphNode, node interlu
 		const revisionBefore = graphRevision();
 		const outcome = deleteGraphNode("n_orch");
 		assert.ok(outcome.ok);
-		assert.deepEqual(outcome.stats, { edgesRemoved: 0 });
+		assert.deepEqual(outcome.stats, { chainsRemoved: 0 });
 		assert.ok(outcome.graphRevision > 0);
 		assert.ok(outcome.graphRevision >= revisionBefore, "the version stamp moved");
 		assert.equal(graphStore.readNodes().some((n) => n.id === "n_orch"), false);
@@ -8,7 +8,7 @@ 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 { GraphNode, GraphEdge, Position } from "../src/core/contracts.ts";
+import type { GraphChain, GraphNode, Position } from "../src/core/contracts.ts";

 const node = (id: string): GraphNode => ({
 	id,
@@ -18,7 +18,9 @@ const node = (id: string): GraphNode => ({
 	createdAt: "2026-09-13T00:00:00.000Z",
 	provenance: [],
 });
-const edge = (from: string, to: string): GraphEdge => ({ from, to, type: "supports", 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,
@@ -107,20 +109,20 @@ describe("settleGraphLayout", () => {
 		const lines = [node("a"), node("b"), node("a")]; // "a" appended twice
 		const store = {
 			readNodes: () => lines.map((l) => ({ ...l })),
-			readEdges: () => [edge("a", "b")],
+			readChains: () => [chain("arg_ab", ["a"], "b")],
 			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", "b"], "one position per UNIQUE node");
+		assert.deepEqual(Object.keys(written[0]!).sort(), ["a", "arg_ab", "b"], "one position per unique node AND the derived implication node");
 	});

 	it("does nothing on an empty graph", () => {
 		const written: Record<string, Position>[] = [];
 		settleGraphLayout({
 			readNodes: () => [],
-			readEdges: () => [],
+			readChains: () => [],
 			readPositions: () => ({} as Record<string, Position>),
 			writePositions: (p) => void written.push(p),
 		});
@@ -27,18 +27,18 @@ import {
 	type RunningPractice,
 } from "../src/agent/subagents/practice-pipeline.ts";
 import { chainCoverage } from "../src/core/practice.ts";
-import type { GraphEdge, GraphNode, ProblemSet } from "../src/core/contracts.ts";
+import type { GraphChain, GraphNode, ProblemSet } from "../src/core/contracts.ts";
 import type { ChatStore, GraphStore, PracticeStore } from "../src/core/ports.ts";
 import { ModelsNotConfiguredError } from "../src/core/settings.ts";

 // ─── in-memory stores ────────────────────────────────────────────────────────

-function memoryGraph(nodes: GraphNode[], edges: GraphEdge[]): GraphStore {
+function memoryGraph(nodes: GraphNode[], chains: GraphChain[]): GraphStore {
 	return {
 		appendNode: () => {},
 		readNodes: () => nodes.map((n) => ({ ...n, provenance: [...n.provenance], aliases: [...n.aliases] })),
-		appendEdge: () => {},
-		readEdges: () => edges.map((e) => ({ ...e, provenance: [...e.provenance] })),
+		appendChain: () => {},
+		readChains: () => chains.map((c) => ({ ...c, premises: [...c.premises], provenance: [...c.provenance] })),
 		appendCheckpoint: () => {},
 		readCheckpoints: () => [],
 		appendCoverage: () => {},
@@ -284,15 +284,16 @@ function diamondGraph(): GraphStore {
 		createdAt: NOW,
 		provenance: pt("chat_1"),
 	});
-	const edge = (from: string, to: string, type: "follows" | "supports" = "follows"): GraphEdge => ({
-		from,
-		to,
-		type,
+	const chain = (from: string, to: string): GraphChain => ({
+		id: to, // fixture id = conclusion id (the form the generator prompt renders)
+		premises: [from],
+		conclusion: to,
 		provenance: pt("chat_1"),
+		createdAt: NOW,
 	});
 	return memoryGraph(
 		[node("a", "A"), node("b", "B"), node("c", "C"), node("d", "D"), node("e", "E")],
-		[edge("a", "b"), edge("a", "c"), edge("b", "d"), edge("c", "d")],
+		[chain("a", "b"), chain("a", "c"), { id: "d", premises: ["b", "c"], conclusion: "d", provenance: pt("chat_1"), createdAt: NOW }],
 	);
 }

@@ -372,7 +373,7 @@ describe("createProblemSet (generation)", () => {

 		assert.match(set.id, /^ps_/);
 		assert.equal(set.status, "partitioning");
-		assert.equal(set.title, "Practice — 2026-09-29"); // nodeIds path: dated fallback title
+		assert.equal(set.title, `Practice — ${new Date().toISOString().slice(0, 10)}`); // nodeIds path: dated fallback title

 		// Stubs appear the moment the partition lands — numbered, generating.
 		await until(() => f.practice.store.getSet(set.id)?.status === "generating");
@@ -1,115 +1,107 @@
 /**
- * PRACTICE-MODULE CORE (slice 1, 2026-09-29 plan): the chain bijection —
- * chainsForSelection (group by conclusion, FOLLOWS ONLY — supports are
- * invisible to practice, owner ruling) / chainsToGraph (the exact inverse,
- * round-trip pinned) — and chainCoverage (the set's completeness law:
- * union of the problems' chains must equal the set's chains).
+ * PRACTICE-MODULE CORE: chainsForSelection over the STORED chains
+ * (chains-primary, owner 2026-09-30: a chain rides along iff every member
+ * is selected; nodes in no surviving chain are singletons) and
+ * chainCoverage (the set's completeness law: union of the problems' chains
+ * must equal the set's chains).
 */

 import assert from "node:assert/strict";
 import { describe, it } from "node:test";
-import type { EdgeType } from "../src/core/contracts.ts";
-import { chainCoverage, chainsForSelection, chainsToEdges, chainsToGraph, formatChainLine } from "../src/core/practice.ts";
+import type { GraphChain } from "../src/core/contracts.ts";
+import { chainCoverage, chainsForSelection, formatChainLine } from "../src/core/practice.ts";

 // ─── fixtures ────────────────────────────────────────────────────────────────

 const n = (id: string) => ({ id });
-const e = (from: string, to: string, type: EdgeType = "follows") => ({ from, to, type });
+const arg = (id: string, premises: string[], conclusion: string): GraphChain => ({
+	id,
+	premises,
+	conclusion,
+	provenance: [],
+	createdAt: "2026-09-30T00:00:00.000Z",
+});

-/** The plan's canonical shape: diamond a→b, a→c, b→d, c→d. */
-const diamond = {
-	nodes: [n("a"), n("b"), n("c"), n("d")],
-	edges: [e("a", "b"), e("a", "c"), e("b", "d"), e("c", "d")],
-};
-const diamondChains = [
-	{ id: "b", premises: ["a"], conclusion: "b" },
-	{ id: "c", premises: ["a"], conclusion: "c" },
-	{ id: "d", premises: ["b", "c"], conclusion: "d" },
-];
+/** The plan's canonical shape: diamond a→b, a→c, b∧c→d — three stored
+ *  arguments (each its own arg_ id, conclusion ids may repeat). */
+const diamondNodes = [n("a"), n("b"), n("c"), n("d")];
+const diamondArgs = [arg("arg_b", ["a"], "b"), arg("arg_c", ["a"], "c"), arg("arg_d", ["b", "c"], "d")];

 // ─── chainsForSelection ──────────────────────────────────────────────────────

 describe("chainsForSelection", () => {
-	it("groups by conclusion: the diamond a→b, a→c, b→d, c→d is three chains", () => {
-		assert.deepEqual(chainsForSelection(diamond.nodes, diamond.edges), diamondChains);
+	it("keeps every fully-selected stored argument, each under its own id", () => {
+		assert.deepEqual(chainsForSelection(diamondNodes, diamondArgs), [
+			{ id: "arg_b", premises: ["a"], conclusion: "b" },
+			{ id: "arg_c", premises: ["a"], conclusion: "c" },
+			{ id: "arg_d", premises: ["b", "c"], conclusion: "d" },
+		]);
 	});

-	it("a premise-only node is NOT its own chain — it lives inside the chains it feeds", () => {
-		const ids = chainsForSelection(diamond.nodes, diamond.edges).map((c) => c.id);
+	it("a premise-only node is NOT its own chain — it lives inside the arguments it feeds", () => {
+		const ids = chainsForSelection(diamondNodes, diamondArgs).map((c) => c.id);
 		assert.ok(!ids.includes("a")); // a is only ever a premise
 	});

 	it("an isolated node becomes a singleton chain", () => {
-		const chains = chainsForSelection([...diamond.nodes, n("z")], diamond.edges);
+		const chains = chainsForSelection([...diamondNodes, n("z")], diamondArgs);
 		assert.deepEqual(chains.at(-1), { id: "z", premises: [], conclusion: "z" });
 	});

-	it("supports edges are NO edges — nodes joined only by supports are singletons", () => {
-		const chains = chainsForSelection([n("x"), n("y")], [e("x", "y", "supports")]);
+	it("two independent arguments for one conclusion stay DISTINCT chains", () => {
+		// The bijection problem that killed edge-grouping (owner, 2026-09-30):
+		// A∧B⇒E and C∧D⇒E must never union into A∧B∧C∧D⇒E.
+		const chains = chainsForSelection(
+			[n("a"), n("b"), n("c"), n("d"), n("e")],
+			[arg("arg_e1", ["a", "b"], "e"), arg("arg_e2", ["c", "d"], "e")],
+		);
 		assert.deepEqual(chains, [
-			{ id: "x", premises: [], conclusion: "x" },
-			{ id: "y", premises: [], conclusion: "y" },
+			{ id: "arg_e1", premises: ["a", "b"], conclusion: "e" },
+			{ id: "arg_e2", premises: ["c", "d"], conclusion: "e" },
 		]);
 	});

-	it("an edge with an endpoint outside the selection is excluded entirely", () => {
-		// a→out would chain a; out is not selected, so the edge is gone and
+	it("an argument with ANY member outside the selection is excluded entirely", () => {
+		// arg_ab needs b; b is not selected, so the argument is gone and
 		// a (nothing else left) falls back to a singleton.
-		const chains = chainsForSelection([n("a")], [e("a", "out"), e("in", "a")]);
+		const chains = chainsForSelection([n("a")], [arg("arg_ab", ["a"], "b"), arg("arg_ia", ["in"], "a")]);
 		assert.deepEqual(chains, [{ id: "a", premises: [], conclusion: "a" }]);
 	});

-	it("duplicate edge assertions collapse into one premise", () => {
-		const chains = chainsForSelection([n("a"), n("b")], [e("a", "b"), e("a", "b")]);
-		assert.deepEqual(chains, [{ id: "b", premises: ["a"], conclusion: "b" }]);
+	it("a chain referencing unknown node ids simply never applies", () => {
+		const chains = chainsForSelection([n("a"), n("b")], [arg("arg_ghost", ["ghost"], "b")]);
+		assert.deepEqual(chains, [
+			{ id: "a", premises: [], conclusion: "a" },
+			{ id: "b", premises: [], conclusion: "b" },
+		]);
 	});

-	it("is deterministic — chains and premises sorted by id", () => {
+	it("is deterministic — chains sorted by id, premises sorted", () => {
 		const shuffled = chainsForSelection(
 			[n("d"), n("c"), n("b"), n("a")],
-			[e("c", "d"), e("a", "c"), e("a", "b"), e("b", "d")],
+			[arg("arg_d", ["c", "b"], "d"), arg("arg_c", ["a"], "c"), arg("arg_b", ["a"], "b")],
 		);
-		assert.deepEqual(shuffled, diamondChains);
-	});
-});
-
-// ─── chainsToGraph — the bijection ───────────────────────────────────────────
-
-describe("chainsToGraph (the inverse)", () => {
-	it("reproduces exactly the selection's follows-edges (both ends selected)", () => {
-		const supportsNoise = e("x", "y", "supports");
-		const outside = e("a", "out");
-		const { edges } = chainsToGraph(chainsForSelection(diamond.nodes, [...diamond.edges, supportsNoise, outside]));
-		assert.deepEqual(edges, [...diamond.edges]);
-	});
-
-	it("round-trips a canonical chain list — singletons survive only for edge-less nodes", () => {
-		// NOTE: the bijection is over chainsForSelection's IMAGE — lists where a
-		// singleton's node never also appears as a premise/conclusion elsewhere.
-		// (A "singleton + premise elsewhere" list is degenerate: not something
-		// the translation ever produces.)
-		const canonical = [
-			{ id: "p1", premises: ["a", "b"], conclusion: "p1" },
-			{ id: "p9", premises: [], conclusion: "p9" },
-			{ id: "c1", premises: ["p1"], conclusion: "c1" },
-		];
-		const nodeIds = [...new Set(canonical.flatMap((c) => [c.conclusion, ...c.premises]))];
-		const roundTripped = chainsForSelection(nodeIds.map(n), chainsToGraph(canonical).edges);
-		assert.deepEqual(roundTripped, [
-			{ id: "c1", premises: ["p1"], conclusion: "c1" },
-			{ id: "p1", premises: ["a", "b"], conclusion: "p1" },
-			{ id: "p9", premises: [], conclusion: "p9" },
+		assert.deepEqual(shuffled, [
+			{ id: "arg_b", premises: ["a"], conclusion: "b" },
+			{ id: "arg_c", premises: ["a"], conclusion: "c" },
+			{ id: "arg_d", premises: ["b", "c"], conclusion: "d" },
 		]);
 	});
 });

 // ─── chainCoverage ───────────────────────────────────────────────────────────

+const diamondChains = [
+	{ id: "arg_b", premises: ["a"], conclusion: "b" },
+	{ id: "arg_c", premises: ["a"], conclusion: "c" },
+	{ id: "arg_d", premises: ["b", "c"], conclusion: "d" },
+];
+
 describe("chainCoverage", () => {
 	it("complete cover: every chain exercised, no missing", () => {
 		const set = {
 			chains: diamondChains,
-			problems: [{ chains: ["b", "c"] }, { chains: ["d"] }],
+			problems: [{ chains: ["arg_b", "arg_c"] }, { chains: ["arg_d"] }],
 		};
 		assert.deepEqual(chainCoverage(set), { missing: [], duplicated: [] });
 	});
@@ -117,23 +109,23 @@ describe("chainCoverage", () => {
 	it("missing: a chain no problem exercises", () => {
 		const set = {
 			chains: diamondChains,
-			problems: [{ chains: ["d"] }],
+			problems: [{ chains: ["arg_d"] }],
 		};
-		assert.deepEqual(chainCoverage(set), { missing: ["b", "c"], duplicated: [] });
+		assert.deepEqual(chainCoverage(set), { missing: ["arg_b", "arg_c"], duplicated: [] });
 	});

 	it("duplicated is informational — a chain exercised twice is allowed", () => {
 		const set = {
 			chains: diamondChains,
-			problems: [{ chains: ["b", "c", "d"] }, { chains: ["b", "d"] }],
+			problems: [{ chains: ["arg_b", "arg_c", "arg_d"] }, { chains: ["arg_b", "arg_d"] }],
 		};
-		assert.deepEqual(chainCoverage(set), { missing: [], duplicated: ["b", "d"] });
+		assert.deepEqual(chainCoverage(set), { missing: [], duplicated: ["arg_b", "arg_d"] });
 	});

 	it("problems claiming chain ids outside the set neither cover nor fail anything", () => {
 		const set = {
-			chains: [{ id: "b" }] as Array<{ id: string }>,
-			problems: [{ chains: ["b", "ghost"] }],
+			chains: [{ id: "arg_b" }] as Array<{ id: string }>,
+			problems: [{ chains: ["arg_b", "ghost"] }],
 		};
 		assert.deepEqual(chainCoverage(set), { missing: [], duplicated: [] });
 	});
@@ -159,38 +151,3 @@ describe("formatChainLine (the chain table's one-line shape, 2026-09-29)", () =>
 		assert.equal(formatChainLine({ premises: ["ghost"], conclusion: "c1" }, props), "ghost → Conclusion");
 	});
 });
-
-// ─── chainsToEdges — the extraction seam's expansion (2026-09-30) ────────────
-
-describe("chainsToEdges (the extractor redesign's translation seam)", () => {
-	it("each premise becomes ONE follows-edge into the conclusion", () => {
-		const edges = chainsToEdges([{ premises: ["p1", "p2"], conclusion: "c1" }]);
-		assert.deepEqual(edges, [
-			{ from: "p1", to: "c1", type: "follows" },
-			{ from: "p2", to: "c1", type: "follows" },
-		]);
-	});
-
-	it("chains sharing a conclusion union their premises; the result stays sorted", () => {
-		const edges = chainsToEdges([
-			{ premises: ["p2"], conclusion: "c1" },
-			{ premises: ["p1"], conclusion: "c1" },
-		]);
-		assert.deepEqual(edges, [
-			{ from: "p1", to: "c1", type: "follows" },
-			{ from: "p2", to: "c1", type: "follows" },
-		]);
-	});
-
-	it("identical (premise-set, conclusion) chains dedupe silently — restating is a no-op", () => {
-		const chain = { premises: ["p1", "p2"], conclusion: "c1" };
-		assert.deepEqual(chainsToEdges([chain, chain, { premises: ["p2", "p1"], conclusion: "c1" }]), [
-			{ from: "p1", to: "c1", type: "follows" },
-			{ from: "p2", to: "c1", type: "follows" },
-		]);
-	});
-
-	it("empty in, empty out — bare propositions ride the propositions list alone", () => {
-		assert.deepEqual(chainsToEdges([]), []);
-	});
-});
@@ -29,7 +29,7 @@ import { renderToStaticMarkup } from "react-dom/server";
 import { describe, it } from "node:test";
 import { ChainTableBody } from "../components/chain-table.tsx";
 import type { ChainSort } from "../components/chain-table.tsx";
-import type { GraphEdge, GraphNode } from "../src/core/contracts.ts";
+import type { GraphChain, GraphNode } from "../src/core/contracts.ts";

 /** The fixture graph — two follows-chains + one standalone:
 *  a → c1 ← b  (chain one, conclusion born chat1), d → e (chain two,
@@ -58,15 +58,14 @@ const NODES: GraphNode[] = [
 	node("orphan", "Orphan", "Statement O.", null),
 ];

-const EDGES: GraphEdge[] = [
-	{ from: "a", to: "c1", type: "follows" },
-	{ from: "b", to: "c1", type: "follows" },
-	{ from: "d", to: "e", type: "follows" },
-] as GraphEdge[];
+const CHAINS: GraphChain[] = [
+	{ id: "c1", premises: ["a", "b"], conclusion: "c1", provenance: [], createdAt: "2026-09-20T10:00:00.000Z" },
+	{ id: "e", premises: ["d"], conclusion: "e", provenance: [], createdAt: "2026-09-20T10:00:00.000Z" },
+];

 const BASE = {
 	nodes: NODES,
-	edges: EDGES,
+	chains: CHAINS,
 	sessions: { chat1: "Ethics lesson", chat2: "Second chat" },
 	fileSources: { notes1: "notes/raw/ethics.md" },
 	query: "",
@@ -118,8 +118,6 @@ describe("sanitizeRenderSettings", () => {
 			arrowLength: 3,
 			labelZoom: 2,
 			labelSize: 4,
-			showSupports: false,
-			supportsWidth: 0.3,
 			clusterLabels: false,
 			clusterLabelSize: 20,
 			regions: DEFAULT_REGION_TUNING,
@@ -128,27 +126,13 @@ describe("sanitizeRenderSettings", () => {
 		assert.deepEqual(sanitizeRenderSettings(valid), valid); // every value a ladder member
 	});

-	test("showSupports (2026-09-29): boolean-only, default on — the draw toggle", () => {
-		// A render-only hide for supports edges: anything but a real boolean
-		// (missing key, legacy file, garbage) loads as ON (today's look); a
-		// real false round-trips untouched.
-		assert.equal(sanitizeRenderSettings({}).showSupports, true);
-		assert.equal(sanitizeRenderSettings({ showSupports: false }).showSupports, false);
-		assert.equal(sanitizeRenderSettings({ showSupports: "no" }).showSupports, true);
-		assert.equal(sanitizeRenderSettings({ showSupports: 0 }).showSupports, true);
-	});
-
-	test("supportsWidth (2026-09-29): linear 0–1 ratio of edgeWidth, default 0.5", () => {
-		// The supports shaft-thickness multiplier: LINEAR (not a ladder —
-		// it's a ratio), real numbers clamp to [0, 1], anything else resets
-		// to the default. The 0 end floors to a hairline in the renderer.
-		assert.equal(sanitizeRenderSettings({}).supportsWidth, 0.5);
-		assert.equal(sanitizeRenderSettings({ supportsWidth: 0 }).supportsWidth, 0);
-		assert.equal(sanitizeRenderSettings({ supportsWidth: 1 }).supportsWidth, 1);
-		assert.equal(sanitizeRenderSettings({ supportsWidth: 0.37 }).supportsWidth, 0.37);
-		assert.equal(sanitizeRenderSettings({ supportsWidth: 1.7 }).supportsWidth, 1);
-		assert.equal(sanitizeRenderSettings({ supportsWidth: -0.3 }).supportsWidth, 0);
-		assert.equal(sanitizeRenderSettings({ supportsWidth: "thick" }).supportsWidth, 0.5);
+	test("supports settings are GONE (chains-primary, 2026-09-30): stale keys silently drop", () => {
+		// Supports edges were retired; showSupports/supportsWidth no longer
+		// exist. A legacy file carrying them loads without the keys — the
+		// sanitizer drops unknown fields by construction.
+		const cleaned = sanitizeRenderSettings({ showSupports: false, supportsWidth: 0.9 } as never);
+		assert.equal("showSupports" in cleaned, false);
+		assert.equal("supportsWidth" in cleaned, false);
 	});

 	test("the pre-2026-09-13 stored shape (flat, no regions/physics) still loads", () => {
@@ -11,7 +11,7 @@

 import assert from "node:assert/strict";
 import { describe, it } from "node:test";
-import type { GraphEdge, GraphNode, NotesSource, ChatSummary } from "../src/core/contracts.ts";
+import type { GraphChain, GraphNode, NotesSource, ChatSummary } from "../src/core/contracts.ts";
 import type { ChatStore, GraphStore } from "../src/core/ports.ts";
 import {
 	graphSessionIndex,
@@ -40,10 +40,10 @@ function fakeStores(
 		sources?: Array<Pick<NotesSource, "id" | "filePath" | "importedAt">>;
 	} = {},
 ): GraphDeps {
-	const edges: GraphEdge[] = [];
+	const chains: GraphChain[] = [];
 	const graphStore: GraphStore = {
 		readNodes: () => nodes,
-		readEdges: () => edges,
+		readChains: () => chains,
 		readCheckpoints: () => [],
 		readCoverage: () => [],
 		readSources: () =>
@@ -244,7 +244,7 @@ test("appendExtractionUsage: appends, idempotent per startedAt, not in list payl
 		startedAt,
 		at: "2026-09-09T00:00:00Z",
 		durationMs: 42_000,
-		stats: { nodes: 1, edges: 2 },
+		stats: { nodes: 1, chains: 2 },
 		stages: {
 			extractor: { model: "openrouter:z-ai/glm-5.3-flash", steps: [call({ inputTokens: 100, outputTokens: 10 })] },
 			auditor: { model: "openrouter:z-ai/glm-5.3-flash", steps: [call({ inputTokens: 50, outputTokens: 5 })] },
@@ -281,7 +281,7 @@ test("appendSourceUsage: appends to the source record, idempotent per startedAt,
 			startedAt,
 			at: "2026-09-13T00:00:00Z",
 			durationMs: 42_000,
-			stats: { nodes: 1, edges: 2 },
+			stats: { nodes: 1, chains: 2 },
 			stages: {
 				extractor: { model: "openrouter:z-ai/glm-5.3-flash", steps: [call({ inputTokens: 100, outputTokens: 10 })] },
 				auditor: { model: "openrouter:z-ai/glm-5.3-flash", steps: [call({ inputTokens: 50, outputTokens: 5 })] },