diff --git a/src/agent/prompts/50-graph-context.md b/src/agent/prompts/50-graph-context.md
new file mode 100644
index 0000000..85d3ac2
--- /dev/null
+++ b/src/agent/prompts/50-graph-context.md
@@ -0,0 +1,21 @@
+# The learner's knowledge graph
+
+After these instruction fragments you may see a fenced block titled **LEARNER KNOWLEDGE GRAPH (auto-generated)**. It is the accumulated record of what this learner has actually demonstrated, across every past session — rebuilt fresh from quiz outcomes and plan trees, every turn. Each line is a proposition in its current state (in brackets), and `a → b` under **Requires** means *a* must be understood before *b*.
+
+The states, exactly:
+
+- **[missed]** — answered wrong. Treat as a live misconception site until a check proves otherwise.
+- **[dont-know]** — the learner declined to guess. Unexplored, not broken.
+- **[known]** — answered correctly. Foundation you can build on and refer to by name.
+- **[taught]** — a lesson covered it. Check that it stuck before stacking anything heavy on it.
+- **[candidate]** — asserted into a plan but never probed. Assume nothing.
+
+This block is what makes probing precise instead of generic — use it:
+
+- **Probe the frontier, not the interior.** [known] and [taught] nodes near the session's topic are the learner's foundation: reference them by name and build on them — never re-teach what the graph says he holds. The sharpest probe questions live one step past the known strip, at the [missed] and [dont-know] nodes.
+- **[missed] nodes are your first stops.** A wrong answer is a misconception until shown otherwise. Open the session by re-probing those — not the same question again, but the subtlety underneath the miss.
+- **Read the Requires chains as scaffolding.** They show what the learner's knowledge rests on. If a prerequisite under the session's topic is [missed] or [dont-know], that is where teaching starts — not at the topic itself.
+
+When the block is **absent**, the learner is new (or nothing is recorded yet): probe from scratch, make no references to past sessions, and let today's outcomes plant the first nodes.
+
+The graph is evidence, not truth — a state is only as good as its last probe. Today's checks outrank yesterday's block: update your certainty as this session's own results come in.
diff --git a/src/agent/teacher-agent.ts b/src/agent/teacher-agent.ts
index 3b43a39..6687759 100644
--- a/src/agent/teacher-agent.ts
+++ b/src/agent/teacher-agent.ts
@@ -12,6 +12,10 @@ import { createTeacherTools } from "./tools.ts";
  * The model is injectable so tests can pass a MockLanguageModelV4 and drive
  * deterministic scripted lessons (see tests/chat-flow.test.ts).
  *
+ * The optional graphContext (buildGraphContext() in src/core/graph-context.ts,
+ * wired by the chat-handler per request) is appended after the composed
+ * fragments; absent/empty means a new learner — nothing is injected.
+ *
  * The system prompt is COMPOSED: system-prompt.md is the base, then every
  * src/agent/prompts/*.md fragment in sorted filename order (workers add
  * fragments — nobody edits shared sections of the base prompt). Prefix
@@ -36,7 +40,19 @@ function composeInstructions(): string {
 
 const instructions = composeInstructions();
 
-export function createTeacherAgent(model?: LanguageModel, tools?: ToolSet) {
+/**
+ * Compose the full instruction string: base prompt + fragments, then — when
+ * the session carries graph context (W8, vision §1 "the graph as session
+ * context") — the auto-generated knowledge-graph block appended after them as
+ * a clearly-delimited section (the 50-graph-context.md fragment teaches the
+ * teacher how to read it). The fragment mechanism itself stays untouched.
+ */
+function withGraphContext(graphContext: string | null | undefined): string {
+	if (!graphContext) return instructions;
+	return `${instructions}\n\n---\n\n${graphContext}`;
+}
+
+export function createTeacherAgent(model?: LanguageModel, tools?: ToolSet, graphContext?: string | null) {
 	return new ToolLoopAgent({
 		model:
 			model ??
@@ -45,7 +61,7 @@ export function createTeacherAgent(model?: LanguageModel, tools?: ToolSet) {
 				// they stream as reasoning parts into the UI's collapsible block.
 				reasoning: { enabled: true, effort: "medium" },
 			}),
-		instructions,
+		instructions: withGraphContext(graphContext),
 		// Tools are per-request (plan tools close over chatId); chat-handler
 		// passes createTeacherTools({ chatId }). Tests pass a mock model and get
 		// the default question-only set.
diff --git a/src/core/graph-context.ts b/src/core/graph-context.ts
new file mode 100644
index 0000000..818fa11
--- /dev/null
+++ b/src/core/graph-context.ts
@@ -0,0 +1,171 @@
+/**
+ * Graph-as-context (W8; vision §1 "The graph as session context", DECIDED
+ * 2026-08-22).
+ *
+ * renderGraphContext() turns the derived graph into a compact markdown block
+ * the teacher sees as part of its instructions — this is what makes probing
+ * precise instead of generic: probe questions can target the boundary of
+ * what the learner actually holds, and personalization compounds across
+ * sessions.
+ *
+ * buildGraphContext() is the per-request entry point the chat-handler calls
+ * (stateless: it re-reads the ledgers, so it self-updates as the graph grows
+ * mid-session). An empty graph returns null — nothing is injected, and the
+ * prompt fragment (50-graph-context.md) tells the teacher how to behave when
+ * the block is absent (new learner).
+ *
+ * Selection strategy (§1 "the selection problem", simplest first): the WHOLE
+ * graph while it is small; past MAX_NODES, hotspots (missed / dont-know /
+ * misconception nodes) plus their 1-hop `requires` neighborhood — a live
+ * misconception is always relevant context, and the frontier is where the
+ * next session should probe.
+ */
+
+import type { GraphEdge, GraphNode } from "./contracts.ts";
+import { deriveNodeStates, getGraph, type DerivedGraph, type NodeStateClass } from "./graph.ts";
+
+/** The section header the teacher is taught to recognize (50-graph-context.md). */
+export const GRAPH_CONTEXT_HEADER = "LEARNER KNOWLEDGE GRAPH (auto-generated)";
+
+/** Above this node count only hotspots + their 1-hop neighborhood are shown. */
+export const MAX_CONTEXT_NODES = 150;
+
+/** Group order for node lines: diagnostic value first (vision §1 hotspots).
+ *  A misconception-kind node is a hotspot whatever its state — a live
+ *  misconception is always relevant context. */
+const HOTSPOT_STATES: ReadonlySet<NodeStateClass> = new Set(["missed", "dont-know"]);
+
+function groupOf(node: GraphNode, state: NodeStateClass): number {
+	if (HOTSPOT_STATES.has(state) || node.kind === "misconception") return 0;
+	if (state === "known") return 1;
+	if (state === "taught") return 2;
+	return 3; // candidate
+}
+
+const GROUP_LABELS = [
+	"Hotspots (missed / dont-know / misconceptions) — likely misconception sites and unexplored ground:",
+	"Known (answered correctly):",
+	"Taught (lessons covered them):",
+	"Candidates (never probed — assume nothing):",
+] as const;
+
+/** A hotspot is a node worth showing even under truncation (§1: diagnostic hotspots). */
+function isHotspot(node: GraphNode, state: NodeStateClass): boolean {
+	return groupOf(node, state) === 0;
+}
+
+/**
+ * Render the context block, or null when there is nothing worth injecting
+ * (no nodes; or a truncated graph whose selection came out empty).
+ *
+ * Pure: callers hand in exactly what getGraph() + deriveNodeStates() produce.
+ */
+export function renderGraphContext(
+	nodes: GraphNode[],
+	edges: GraphEdge[],
+	states: Record<string, NodeStateClass>,
+): string | null {
+	if (nodes.length === 0) return null;
+
+	// ── selection ───────────────────────────────────────────────────────────
+	const stateOf = (node: GraphNode): NodeStateClass => states[node.id] ?? "candidate";
+	let selected = nodes;
+	let truncated = false;
+	if (nodes.length > MAX_CONTEXT_NODES) {
+		truncated = true;
+		const hotspots = nodes.filter((n) => isHotspot(n, stateOf(n)));
+		const keep = new Set(hotspots.map((n) => n.id));
+		// 1-hop requires neighborhood: prerequisites AND dependents.
+		for (const edge of edges) {
+			if (edge.type !== "requires") continue;
+			if (keep.has(edge.from) || keep.has(edge.to)) {
+				keep.add(edge.from);
+				keep.add(edge.to);
+			}
+		}
+		selected = nodes.filter((n) => keep.has(n.id));
+		if (selected.length === 0) return null; // nothing diagnostic to show
+	}
+
+	// ── node lines, grouped/sorted by diagnostic priority ──────────────────────────
+	const lines: string[] = [
+		`===== ${GRAPH_CONTEXT_HEADER} =====`,
+		`${truncated ? `showing ${selected.length} of ${nodes.length} nodes (hotspots + their 1-hop neighborhood)` : `${nodes.length} nodes`}, ${edges.filter((e) => e.type === "requires").length} requires edges`,
+	];
+
+	for (const [group, label] of GROUP_LABELS.entries()) {
+		const groupNodes = selected
+			.filter((n) => groupOf(n, stateOf(n)) === group)
+			.sort((a, b) => (a.statement < b.statement ? -1 : a.statement > b.statement ? 1 : 0));
+		if (groupNodes.length === 0) continue;
+		lines.push("", label);
+		for (const node of groupNodes) {
+			const kind = node.kind === "misconception" ? " · misconception" : "";
+			lines.push(`• [${stateOf(node)}] ${node.statement} (${node.id})${kind}`);
+		}
+	}
+
+	// ── requires edges, merged into chains ──────────────────────────────────
+	const byId = new Map(selected.map((n) => [n.id, n.statement]));
+	const requires = edges.filter(
+		(e) => e.type === "requires" && byId.has(e.from) && byId.has(e.to),
+	);
+	if (requires.length > 0) {
+		lines.push("", "Requires (prerequisite → dependent):");
+		for (const chain of edgeChains(requires)) {
+			lines.push(chain.map((id) => byId.get(id) ?? id).join(" → "));
+		}
+	}
+
+	lines.push("===== end of knowledge graph =====");
+	return lines.join("\n");
+}
+
+/**
+ * Merge a set of requires edges into maximal simple chains: a→b, b→c, a→d
+ * renders as "a → b → c" and "a → d". Each edge appears in exactly one chain.
+ */
+function edgeChains(edges: GraphEdge[]): string[][] {
+	const chains: string[][] = [];
+	const used = new Set<GraphEdge>();
+
+	const sorted = [...edges].sort((a, b) =>
+		`${a.from}\u0000${a.to}` < `${b.from}\u0000${b.to}` ? -1 : 1,
+	);
+	for (const edge of sorted) {
+		if (used.has(edge)) continue;
+		used.add(edge);
+		let chain = [edge.from, edge.to];
+		// Extend forward along unused outgoing edges (branching yields sibling
+		// chains; a cycle stops the walk).
+		for (;;) {
+			const tail = chain[chain.length - 1]!;
+			const next = sorted.find((e) => !used.has(e) && e.from === tail);
+			if (!next || chain.includes(next.to)) break; // branching or a cycle — stop
+			used.add(next);
+			chain.push(next.to);
+		}
+		// Extend backward along unused incoming edges, symmetrically.
+		for (;;) {
+			const head = chain[0]!;
+			const prev = sorted.find((e) => !used.has(e) && e.to === head);
+			if (!prev || chain.includes(prev.from)) break;
+			used.add(prev);
+			chain.unshift(prev.from);
+		}
+		chains.push(chain);
+	}
+	return chains;
+}
+
+// ─── the per-request entry point ─────────────────────────────────────────────
+
+/**
+ * Build the graph context block for one request. Stateless — re-reads the
+ * ledgers every call, so it self-updates as the graph grows mid-session.
+ * Accepts an injected derived graph (tests); defaults to the live one.
+ */
+export function buildGraphContext(graph: DerivedGraph = getGraph()): string | null {
+	const states = deriveNodeStates(graph.nodes, graph.events);
+	return renderGraphContext(graph.nodes, graph.edges, states);
+}
diff --git a/src/core/graph.ts b/src/core/graph.ts
index 5c88cd5..df7a2b8 100644
--- a/src/core/graph.ts
+++ b/src/core/graph.ts
@@ -4,7 +4,10 @@
  *
  * emitChat(chatId) folds ONE chat into the global graph — naive union,
  * deterministic, no LLM:
- *   plan-tree nodes   → GraphNodes (statement = title, aliases empty)
+ *   plan-tree nodes   → GraphNodes (statement = title, aliases empty;
+ *                       W8: a title exactly matching an existing statement
+ *                       or alias — case-insensitive, trimmed — maps onto the
+ *                       existing node instead of appending a duplicate)
  *   plan-tree edges   → `requires` GraphEdges (from = prerequisite)
  *   answered quizzes  → ledger events (probe-* before the first plan_init
  *                       output, check / dont-know after; ref = toolCallId)
@@ -23,6 +26,11 @@ import type { QuestionAnswerData } from "./question-core.ts";
 import { getChat, listChats } from "../store/chats.ts";
 import { graphLedgers, newGraphNodeId } from "../store/graph.ts";
 
+/** The ledger surface emitChat needs (the real one is src/store/graph.ts).
+ *  Injectable so tests can fold fixtures into an in-memory ledger instead of
+ *  the live data/graph files. */
+export type GraphLedgers = typeof graphLedgers;
+
 // ─── transcript scanning ─────────────────────────────────────────────────────
 
 /** A flattened, order-preserving view of every tool part in a transcript. */
@@ -91,8 +99,11 @@ export interface EmissionStats {
  * Fold one chat into the graph ledgers. Idempotent — safe to call after every
  * turn (chat-handler onFinish) and again on catch-up (GET /api/graph). Sync
  * and fast: a handful of small-file reads plus one append per new record.
+ *
+ * `ledgers` is injectable for tests (in-memory ledger); production always
+ * uses the live store.
  */
-export function emitChat(chatId: string): EmissionStats {
+export function emitChat(chatId: string, ledgers: GraphLedgers = graphLedgers): EmissionStats {
 	const record = getChat(chatId);
 	if (!record) return { nodes: 0, edges: 0, events: 0 };
 	const stats: EmissionStats = { nodes: 0, edges: 0, events: 0 };
@@ -100,7 +111,7 @@ export function emitChat(chatId: string): EmissionStats {
 	// 1. This chat's existing mappings — the identity map is per-chat (v1 is
 	// naive union: two sessions' tree nodes never merge into one graph node).
 	const mapping = new Map<string, string>();
-	for (const m of graphLedgers.readMappings()) {
+	for (const m of ledgers.readMappings()) {
 		if (m.chatId === chatId) mapping.set(m.treeNodeId, m.graphNodeId);
 	}
 
@@ -112,10 +123,33 @@ export function emitChat(chatId: string): EmissionStats {
 	const tree =
 		record.tree && record.tree.nodes.length > 0 ? record.tree : replayFinalTree(record.messages);
 
-	// 3. Tree nodes without a mapping → GraphNode + mapping.
+	// 3. Tree nodes without a mapping → GraphNode + mapping. W8 merge
+	// improvement: a title that EXACTLY matches (case-insensitive, trimmed) an
+	// existing node's statement or alias maps onto that node instead of
+	// appending a duplicate — the mapping line is still appended so provenance
+	// stays honest. Fuzzy/embedding matching stays deferred (vision §1
+	// consolidation pipeline).
+	const norm = (s: string): string => s.trim().toLowerCase();
+	const existingByTitle = new Map<string, string>();
+	for (const node of ledgers.readNodes()) {
+		const statementKey = norm(node.statement);
+		if (statementKey && !existingByTitle.has(statementKey)) existingByTitle.set(statementKey, node.id);
+		for (const alias of node.aliases) {
+			const aliasKey = norm(alias);
+			if (aliasKey && !existingByTitle.has(aliasKey)) existingByTitle.set(aliasKey, node.id);
+		}
+	}
 	const now = new Date().toISOString();
 	for (const node of tree.nodes) {
 		if (mapping.has(node.id)) continue;
+		const titleKey = norm(node.title);
+		const existingId = titleKey ? existingByTitle.get(titleKey) : undefined;
+		if (existingId !== undefined) {
+			// Exact match: reuse the node, record the mapping, append nothing.
+			ledgers.appendMapping({ chatId, treeNodeId: node.id, graphNodeId: existingId });
+			mapping.set(node.id, existingId);
+			continue;
+		}
 		const graphNode: GraphNode = {
 			id: newGraphNodeId(),
 			// statement is the title; the summary stays out (contracts).
@@ -124,8 +158,9 @@ export function emitChat(chatId: string): EmissionStats {
 			kind: "truth",
 			createdAt: now,
 		};
-		graphLedgers.appendNode(graphNode);
-		graphLedgers.appendMapping({ chatId, treeNodeId: node.id, graphNodeId: graphNode.id });
+		ledgers.appendNode(graphNode);
+		ledgers.appendMapping({ chatId, treeNodeId: node.id, graphNodeId: graphNode.id });
+		existingByTitle.set(titleKey, graphNode.id);
 		mapping.set(node.id, graphNode.id);
 		stats.nodes++;
 	}
@@ -134,7 +169,7 @@ export function emitChat(chatId: string): EmissionStats {
 	// whole ledger: an existing assertion just gains this chatId as
 	// provenance (appended as a new line; reads merge).
 	const asserted = new Map<string, Set<string>>();
-	for (const line of graphLedgers.readEdges()) {
+	for (const line of ledgers.readEdges()) {
 		const key = `${line.from}\u0000${line.to}\u0000${line.type}`;
 		let provenance = asserted.get(key);
 		if (!provenance) {
@@ -150,7 +185,7 @@ export function emitChat(chatId: string): EmissionStats {
 		const key = `${from}\u0000${to}\u0000requires`;
 		const provenance = asserted.get(key);
 		if (provenance?.has(chatId)) continue; // already asserted by this chat
-		graphLedgers.appendEdge({ from, to, type: "requires", provenance: [chatId] });
+		ledgers.appendEdge({ from, to, type: "requires", provenance: [chatId] });
 		if (provenance) provenance.add(chatId);
 		else asserted.set(key, new Set([chatId]));
 		stats.edges++;
@@ -161,7 +196,7 @@ export function emitChat(chatId: string): EmissionStats {
 	// chat-scoped (a quiz toolCallId or taught:<treeNodeId>) — a ref already
 	// in the ledger means this turn was folded before.
 	const seenRefs = new Set<string>();
-	for (const event of graphLedgers.readEvents()) {
+	for (const event of ledgers.readEvents()) {
 		if (event.chatId === chatId && event.ref) seenRefs.add(event.ref);
 	}
 	let planSeen = false;
@@ -173,7 +208,7 @@ export function emitChat(chatId: string): EmissionStats {
 		if (part.name === "quiz" && part.state === "output-available") {
 			const event = quizEvent(part, chatId, mapping, planSeen, now);
 			if (event?.ref !== undefined && !seenRefs.has(event.ref)) {
-				graphLedgers.appendEvent(event);
+				ledgers.appendEvent(event);
 				seenRefs.add(event.ref);
 				stats.events++;
 			}
@@ -185,7 +220,7 @@ export function emitChat(chatId: string): EmissionStats {
 			if (result?.ok && typeof input?.id === "string") {
 				const ref = `taught:${input.id}`;
 				if (!seenRefs.has(ref)) {
-					graphLedgers.appendEvent({
+					ledgers.appendEvent({
 						nodeId: mapping.get(input.id) ?? null,
 						kind: "taught",
 						chatId,
@@ -200,7 +235,7 @@ export function emitChat(chatId: string): EmissionStats {
 	}
 
 	// 6. Checkpoint: this chat is folded through its current updatedAt.
-	graphLedgers.appendCheckpoint({ chatId, foldedAt: record.updatedAt });
+	ledgers.appendCheckpoint({ chatId, foldedAt: record.updatedAt });
 	return stats;
 }
 
diff --git a/src/server/chat-handler.ts b/src/server/chat-handler.ts
index ef3a7b6..d171224 100644
--- a/src/server/chat-handler.ts
+++ b/src/server/chat-handler.ts
@@ -3,6 +3,7 @@ import { createTeacherAgent, type TeacherAgent } from "../agent/teacher-agent.ts
 import { createTeacherTools } from "../agent/tools.ts";
 import { spawnPendingJobs } from "../agent/subagents/runner.ts";
 import { emitChat } from "../core/graph.ts";
+import { buildGraphContext } from "../core/graph-context.ts";
 import { getChat, saveMessages } from "../store/chats.ts";
 
 /**
@@ -29,8 +30,20 @@ export async function handleChatRequest(req: Request, agent?: TeacherAgent): Pro
 		return Response.json({ error: "messages must be an array" }, { status: 400 });
 	}
 
+	// W8 (vision §1 "the graph as session context"): the learner's knowledge
+	// graph rides along as part of the teacher's instructions. Built per
+	// request — stateless, and self-updating as the graph grows mid-session
+	// (the emission hook below folds each turn). A read failure must never
+	// take the lesson down: the block is context, not a dependency.
+	let graphContext: string | null = null;
+	try {
+		graphContext = buildGraphContext();
+	} catch (err) {
+		console.error(`[chat ${chatId}] graph context build failed:`, err);
+	}
+
 	return createAgentUIStreamResponse({
-		agent: agent ?? createTeacherAgent(undefined, createTeacherTools({ chatId })),
+		agent: agent ?? createTeacherAgent(undefined, createTeacherTools({ chatId }), graphContext),
 		uiMessages: body.messages as UIMessage[],
 		onFinish: ({ messages, isAborted }) => {
 			// Persist even when aborted: the partial transcript (including any
diff --git a/tests/graph-context.test.ts b/tests/graph-context.test.ts
new file mode 100644
index 0000000..13ac07a
--- /dev/null
+++ b/tests/graph-context.test.ts
@@ -0,0 +1,416 @@
+/**
+ * Graph-as-context tests (W8; vision §1 "the graph as session context").
+ *
+ *   renderGraphContext  — pure: empty / small / cap-truncation rendering
+ *   buildGraphContext   — per-request entry point (derived-graph → block)
+ *   injection plumbing  — chat-flow style: the teacher's instructions carry
+ *                         the block (MockLanguageModelV4 captures the prompt)
+ *   exact-match merge   — emitChat dedupes case/whitespace-identical titles
+ *                         onto existing nodes (no fuzzy matching)
+ *
+ * Ledger isolation: NONE needed for the merge tests — emitChat's ledger is
+ * injectable (in-memory), so the live data/graph files are only ever READ
+ * here (tests/graph.test.ts owns the backup-and-clear dance; both suites run
+ * concurrently as separate processes). Chat fixtures are real ChatRecords,
+ * created and deleted by this suite like tests/chat-flow.test.ts does.
+ */
+
+import assert from "node:assert/strict";
+import * as fs from "node:fs";
+import * as path from "node:path";
+import { after, describe, it } from "node:test";
+import { MockLanguageModelV4, simulateReadableStream } from "ai/test";
+import type { LanguageModelV4StreamPart } from "@ai-sdk/provider";
+import type { GraphEdge, GraphNode, LedgerEvent } from "../src/core/contracts.ts";
+import type { NodeStateClass } from "../src/core/graph.ts";
+import { emitChat, type GraphLedgers } from "../src/core/graph.ts";
+import {
+	buildGraphContext,
+	GRAPH_CONTEXT_HEADER,
+	MAX_CONTEXT_NODES,
+	renderGraphContext,
+} from "../src/core/graph-context.ts";
+import { createTeacherAgent } from "../src/agent/teacher-agent.ts";
+import { handleChatRequest } from "../src/server/chat-handler.ts";
+import { createChat, getChat, saveMessages, saveTree } from "../src/store/chats.ts";
+import { type NodeMapping, type SessionCheckpoint } from "../src/store/graph.ts";
+import { createTree } from "../src/core/plan-tree.ts";
+import { PATHS } from "../config.ts";
+
+// ─── fixtures ────────────────────────────────────────────────────────────────
+
+function node(id: string, statement: string, over: Partial<GraphNode> = {}): GraphNode {
+	return { id, statement, aliases: [], kind: "truth", createdAt: "2026-08-22T00:00:00.000Z", ...over };
+}
+
+function edge(from: string, to: string): GraphEdge {
+	return { from, to, type: "requires", provenance: ["chat_x"] };
+}
+
+function states(...entries: [string, NodeStateClass][]): Record<string, NodeStateClass> {
+	return Object.fromEntries(entries);
+}
+
+// ─── renderGraphContext (pure) ───────────────────────────────────────────────
+
+describe("renderGraphContext (pure)", () => {
+	it("returns null for an empty graph (inject nothing)", () => {
+		assert.equal(renderGraphContext([], [], {}), null);
+	});
+
+	it("renders a header, state-grouped node lines (hotspots first), and chained requires edges", () => {
+		const nodes = [
+			node("n_a", "Chain rule intuition"),
+			node("n_b", "Quotient rule"),
+			node("n_c", "Product rule"),
+			node("n_d", "Composite functions"),
+		];
+		const edges = [edge("n_a", "n_b"), edge("n_b", "n_c"), edge("n_d", "n_a")];
+		const st = states(
+			["n_a", "known"],
+			["n_b", "missed"],
+			["n_c", "candidate"],
+			["n_d", "taught"],
+		);
+		const out = renderGraphContext(nodes, edges, st)!;
+
+		assert.ok(out.includes(GRAPH_CONTEXT_HEADER), "header line present");
+		assert.match(out, /4 nodes, 3 requires edges/);
+
+		// Node lines: "• [state] statement (id)".
+		assert.ok(out.includes("• [missed] Quotient rule (n_b)"));
+		assert.ok(out.includes("• [known] Chain rule intuition (n_a)"));
+		assert.ok(out.includes("• [taught] Composite functions (n_d)"));
+		assert.ok(out.includes("• [candidate] Product rule (n_c)"));
+
+		// Groups in the decided order: hotspots, known, taught, candidates.
+		const order = ["Hotspots", "Known", "Taught", "Candidates"].map((g) => out.indexOf(g));
+		assert.deepEqual([...order].sort((a, b) => a - b), order, "groups appear in priority order");
+
+		// Edges merged into chains: d → a → b → c (one line, three arrows).
+		assert.ok(out.includes("Composite functions → Chain rule intuition → Quotient rule → Product rule"));
+		assert.ok(out.includes("Requires (prerequisite → dependent)"));
+		assert.ok(out.includes("===== end of knowledge graph ====="), "clear end delimiter");
+	});
+
+	it("renders branching edges as sibling chains, not one false chain", () => {
+		const nodes = [node("n_a", "A"), node("n_b", "B"), node("n_c", "C")];
+		const out = renderGraphContext(nodes, [edge("n_a", "n_b"), edge("n_a", "n_c")], states())!;
+		assert.ok(out.includes("A → B"));
+		assert.ok(out.includes("A → C"));
+		assert.ok(!out.includes("B → C"), "no edge was invented between siblings");
+	});
+
+	it("marks misconception-kind nodes as hotspots even when their state is candidate", () => {
+		const nodes = [node("n_m", "Division by zero is fine", { kind: "misconception" })];
+		const out = renderGraphContext(nodes, [], states(["n_m", "candidate"]))!;
+		assert.match(out, /• \[candidate\] Division by zero is fine \(n_m\) · misconception/);
+		assert.ok(out.includes("Hotspots"), "misconception nodes join the hotspot group");
+	});
+
+	it("caps at MAX_CONTEXT_NODES: hotspots + their 1-hop requires neighborhood only, with a truncation note", () => {
+		// 3 hotspots, each with a prerequisite and a dependent (1-hop), plus a
+		// long tail of disconnected candidates that must drop out.
+		const nodes: GraphNode[] = [];
+		const edges: GraphEdge[] = [];
+		const st: Record<string, NodeStateClass> = {};
+		const hotspot = (i: number) => {
+			const h = `n_h${i}`;
+			const pre = `n_p${i}`;
+			const dep = `n_d${i}`;
+			nodes.push(node(pre, `Prerequisite ${i}`), node(h, `Hotspot ${i}`), node(dep, `Dependent ${i}`));
+			edges.push(edge(pre, h), edge(h, dep));
+			st[pre] = "known";
+			st[h] = "missed";
+			st[dep] = "candidate";
+		};
+		hotspot(1);
+		hotspot(2);
+		hotspot(3);
+		for (let i = 0; i < MAX_CONTEXT_NODES; i++) {
+			const id = `n_f${i}`;
+			nodes.push(node(id, `Far away ${i}`));
+			st[id] = "candidate";
+		}
+		assert.ok(nodes.length > MAX_CONTEXT_NODES, "fixture exceeds the cap");
+
+		const out = renderGraphContext(nodes, edges, st)!;
+		assert.ok(out.includes("• [missed] Hotspot 1 (n_h1)"), "hotspots stay");
+		assert.ok(out.includes("• [known] Prerequisite 1 (n_p1)"), "1-hop prerequisites stay");
+		assert.ok(out.includes("• [candidate] Dependent 1 (n_d1)"), "1-hop dependents stay");
+		assert.ok(!out.includes("Far away"), "disconnected nodes drop out");
+		assert.match(out, new RegExp(`showing 9 of ${nodes.length} nodes`), "truncation is noted");
+		assert.ok(out.includes(", 6 requires edges"), "edges among the selected nodes stay");
+	});
+
+	it("keeps the full graph at exactly the cap (no truncation note)", () => {
+		const nodes = Array.from({ length: MAX_CONTEXT_NODES }, (_, i) => node(`n_${i}`, `Node ${i}`));
+		const out = renderGraphContext(nodes, [], {})!;
+		assert.ok(out.includes(`• [candidate] Node ${MAX_CONTEXT_NODES - 1}`));
+		assert.ok(!out.includes("showing"), "at the cap nothing is dropped");
+	});
+
+	it("returns null when a too-large graph has no hotspots at all", () => {
+		const nodes = Array.from({ length: MAX_CONTEXT_NODES + 1 }, (_, i) => node(`n_${i}`, `Node ${i}`));
+		assert.equal(renderGraphContext(nodes, [], {}), null);
+	});
+});
+
+// ─── buildGraphContext (the per-request entry point) ────────────────────────
+
+describe("buildGraphContext", () => {
+	it("returns null for an empty derived graph", () => {
+		assert.equal(buildGraphContext({ nodes: [], edges: [], events: [] }), null);
+	});
+
+	it("derives states from events and renders the block", () => {
+		const nodes = [node("n_a", "Solo node"), node("n_b", "Checked node")];
+		const events: LedgerEvent[] = [
+			{ nodeId: "n_b", kind: "check-correct", chatId: "c1", at: "2026-08-22T00:00:00.000Z", ref: "r1" },
+		];
+		const out = buildGraphContext({ nodes, edges: [], events })!;
+		assert.ok(out.includes(GRAPH_CONTEXT_HEADER));
+		assert.ok(out.includes("• [known] Checked node (n_b)"), "check-correct → known");
+		assert.ok(out.includes("• [candidate] Solo node (n_a)"), "no events → candidate");
+	});
+
+	it("reads the live ledgers without throwing (read-only integration)", () => {
+		// Other suites (graph.test.ts) mutate data/graph concurrently, so only
+		// assert the shape of the result, never its content. Read-only is
+		// structural: buildGraphContext only ever calls getGraph().
+		const out = buildGraphContext();
+		assert.ok(out === null || out.includes(GRAPH_CONTEXT_HEADER));
+	});
+});
+
+// ─── injection plumbing (chat-flow style) ───────────────────────────────────
+
+function usage() {
+	return {
+		inputTokens: { total: 10, noCache: 10, cacheRead: 0, cacheWrite: 0 },
+		outputTokens: { total: 5, text: 5, reasoning: 0 },
+	};
+}
+
+/** A model that records every prompt it is given and replies with plain text. */
+function capturingModel(prompts: string[]) {
+	return new MockLanguageModelV4({
+		doStream: async (options) => {
+			prompts.push(JSON.stringify(options.prompt));
+			const chunks: LanguageModelV4StreamPart[] = [
+				{ type: "stream-start", warnings: [] },
+				{ type: "text-start", id: "t1" },
+				{ type: "text-delta", id: "t1", delta: "Where shall we begin?" },
+				{ type: "text-end", id: "t1" },
+				{ type: "finish", finishReason: { unified: "stop", raw: "stop" }, usage: usage() },
+			];
+			return { stream: simulateReadableStream({ chunks, initialDelayInMs: 0, chunkDelayInMs: 0 }) };
+		},
+	});
+}
+
+async function drain(res: Response): Promise<void> {
+	if (res.status !== 200) {
+		assert.fail(`expected 200, got ${res.status}: ${await res.text()}`);
+	}
+	await res.text(); // consumes the SSE stream to completion (fires onFinish)
+}
+
+function post(chatId: string, messages: unknown[]): Request {
+	return new Request("http://test/api/chat", {
+		method: "POST",
+		headers: { "Content-Type": "application/json" },
+		body: JSON.stringify({ chatId, messages }),
+	});
+}
+
+const createdChats: string[] = [];
+after(() => {
+	for (const id of createdChats) {
+		try {
+			fs.unlinkSync(path.join(PATHS.chats, `${id}.json`));
+		} catch {
+			/* already gone */
+		}
+	}
+});
+
+describe("graph-context injection (chat-flow style)", () => {
+	it("the teacher's instructions carry the block after the composed fragments", async () => {
+		const graph = {
+			nodes: [node("n_ctx", "Chain rule intuition"), node("n_ctx2", "Derivative as a limit")],
+			edges: [edge("n_ctx2", "n_ctx")],
+			events: [
+				{ nodeId: "n_ctx2", kind: "check-correct", chatId: "c1", at: "2026-08-22T00:00:00.000Z", ref: "r1" },
+			] as LedgerEvent[],
+		};
+		const context = buildGraphContext(graph);
+		assert.ok(context, "fixture graph renders a block");
+
+		// Exactly what chat-handler does per request when no agent is passed:
+		// createTeacherAgent(model, tools, buildGraphContext()).
+		const prompts: string[] = [];
+		const agent = createTeacherAgent(capturingModel(prompts), undefined, context);
+		const chat = createChat("Test: graph context injection");
+		createdChats.push(chat.id);
+
+		await drain(
+			await handleChatRequest(
+				post(chat.id, [{ id: "u1", role: "user", parts: [{ type: "text", text: "teach me calculus" }] }]),
+				agent,
+			),
+		);
+
+		assert.equal(prompts.length, 1, "one model call");
+		const system = prompts[0]!;
+		assert.ok(system.includes(GRAPH_CONTEXT_HEADER), "the block reached the model");
+		assert.ok(system.includes("Chain rule intuition"), "fixture node reached the model");
+		// The block sits AFTER the composed fragments (the phases fragment is
+		// part of the static instructions), and the fragment teaching the
+		// teacher to read it is present too.
+		const fragmentIdx = system.indexOf("The two phases");
+		const graphFragIdx = system.indexOf("The learner's knowledge graph");
+		const blockIdx = system.indexOf(GRAPH_CONTEXT_HEADER);
+		assert.ok(fragmentIdx !== -1 && graphFragIdx !== -1, "prompt fragments composed");
+		assert.ok(graphFragIdx > fragmentIdx, "50-graph-context.md sorts after 30-phases.md");
+		assert.ok(blockIdx > graphFragIdx, "the block is appended after the fragments");
+	});
+
+	it("no block is injected when the context is null (new learner)", async () => {
+		const prompts: string[] = [];
+		const agent = createTeacherAgent(capturingModel(prompts));
+		const chat = createChat("Test: no graph context");
+		createdChats.push(chat.id);
+		await drain(
+			await handleChatRequest(
+				post(chat.id, [{ id: "u1", role: "user", parts: [{ type: "text", text: "hi" }] }]),
+				agent,
+			),
+		);
+		const system = prompts[0]!;
+		assert.ok(system.includes("The learner's knowledge graph"), "the fragment is always composed");
+		assert.ok(!system.includes("===== LEARNER KNOWLEDGE GRAPH"), "no auto-generated block");
+	});
+});
+
+// ─── exact-match merge (emitChat dedup) ─────────────────────────────────────
+
+/** An in-memory stand-in for the five ledgers (see GraphLedgers in graph.ts). */
+function memoryLedgers() {
+	const nodes: GraphNode[] = [];
+	const edges: GraphEdge[] = [];
+	const events: LedgerEvent[] = [];
+	const mappings: NodeMapping[] = [];
+	const checkpoints: SessionCheckpoint[] = [];
+	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 })),
+		appendEvent: (e: LedgerEvent) => void events.push(e),
+		readEvents: () => events.map((e) => ({ ...e })),
+		appendMapping: (m: NodeMapping) => void mappings.push(m),
+		readMappings: () => mappings.map((m) => ({ ...m })),
+		appendCheckpoint: (c: SessionCheckpoint) => void checkpoints.push(c),
+		readCheckpoints: () => checkpoints.map((c) => ({ ...c })),
+		// Test accessors (not part of the GraphLedgers surface).
+		counts: { get nodes() { return nodes.length; }, get mappings() { return mappings.length; } },
+	} satisfies GraphLedgers & { counts: { nodes: number; mappings: number } };
+}
+
+/** A real chat record with a stored tree (emitChat reads the real chat store). */
+function fixtureChat(title: string, tree: ReturnType<typeof createTree>) {
+	const chat = createChat(title);
+	createdChats.push(chat.id);
+	saveTree(chat.id, tree);
+	saveMessages(chat.id, [{ id: "u1", role: "user", parts: [{ type: "text", text: "go" }] }]);
+	return getChat(chat.id)!;
+}
+
+describe("exact-match merge (emitChat)", () => {
+	it("maps a case/whitespace-identical title onto the existing node instead of duplicating", () => {
+		const ledgers = memoryLedgers();
+		const chat1 = fixtureChat("Merge A", createTree([{ id: "cr", title: "Chain rule intuition" }], []));
+		let stats = emitChat(chat1.id, ledgers);
+		assert.deepEqual(stats, { nodes: 1, edges: 0, events: 0 });
+		const firstId = ledgers.readNodes()[0]!.id;
+
+		// Second session, same proposition: different casing + padding.
+		const chat2 = fixtureChat("Merge B", createTree([{ id: "cr2", title: "  chain Rule INTUITION " }], []));
+		stats = emitChat(chat2.id, ledgers);
+		assert.deepEqual(stats, { nodes: 0, edges: 0, events: 0 }, "no duplicate node appended");
+
+		assert.equal(ledgers.counts.nodes, 1, "still exactly one graph node");
+		assert.equal(ledgers.readNodes()[0]!.id, firstId);
+		// Provenance stays honest: one mapping line per (chat, treeNodeId).
+		assert.equal(ledgers.counts.mappings, 2);
+		assert.deepEqual(ledgers.readMappings()[1], { chatId: chat2.id, treeNodeId: "cr2", graphNodeId: firstId });
+	});
+
+	it("matches aliases too (exact, case-insensitive)", () => {
+		const ledgers = memoryLedgers();
+		ledgers.appendNode({
+			id: "n_alias",
+			statement: "Differentiation basics",
+			aliases: ["the derivative"],
+			kind: "truth",
+			createdAt: "2026-08-22T00:00:00.000Z",
+		});
+		const chat = fixtureChat("Merge alias", createTree([{ id: "d", title: "The Derivative" }], []));
+		const stats = emitChat(chat.id, ledgers);
+		assert.deepEqual(stats, { nodes: 0, edges: 0, events: 0 }, "alias match → no new node");
+		assert.deepEqual(ledgers.readMappings(), [{ chatId: chat.id, treeNodeId: "d", graphNodeId: "n_alias" }]);
+	});
+
+	it("does NOT fuzzy-match near-identical titles (that stays deferred)", () => {
+		const ledgers = memoryLedgers();
+		const chat1 = fixtureChat("Fuzzy A", createTree([{ id: "cr", title: "Chain rule intuition" }], []));
+		emitChat(chat1.id, ledgers);
+		const chat2 = fixtureChat(
+			"Fuzzy B",
+			createTree([{ id: "cr2", title: "Chain rules intuition" }], []),
+		);
+		const stats = emitChat(chat2.id, ledgers);
+		assert.equal(stats.nodes, 1, "near-miss titles stay separate nodes");
+		assert.equal(ledgers.counts.nodes, 2);
+	});
+
+	it("merged nodes unify the second chat's edges onto the existing graph node", () => {
+		const ledgers = memoryLedgers();
+		const chat1 = fixtureChat(
+			"Edge A",
+			createTree(
+				[
+					{ id: "base", title: "Derivative as a limit" },
+					{ id: "chain", title: "Chain rule intuition" },
+				],
+				[{ from: "base", to: "chain" }],
+			),
+		);
+		emitChat(chat1.id, ledgers);
+
+		// Second session re-teaches the same two propositions (exact titles)
+		// and asserts the same edge — it must dedupe onto the existing nodes.
+		const chat2 = fixtureChat(
+			"Edge B",
+			createTree(
+				[
+					{ id: "base", title: "derivative as a limit" },
+					{ id: "chain", title: "chain rule intuition" },
+				],
+				[{ from: "base", to: "chain" }],
+			),
+		);
+		const stats = emitChat(chat2.id, ledgers);
+		// A new ASSERTION line is appended (provenance is honest) — reads merge
+		// by (from,to,type), so the derived graph still has one edge with both
+		// sessions in its provenance.
+		assert.deepEqual(stats, { nodes: 0, edges: 1, events: 0 }, "no new nodes, one re-assertion line");
+		assert.equal(ledgers.counts.nodes, 2);
+		const lines = ledgers.readEdges();
+		assert.equal(lines.length, 2, "two assertion lines for the same edge");
+		assert.equal(lines[0]!.from, lines[1]!.from);
+		assert.equal(lines[0]!.to, lines[1]!.to);
+		assert.deepEqual(lines.map((l) => l.provenance), [[chat1.id], [chat2.id]]);
+	});
+});