partitioner fix: chain ids lead every rendered line

The partitioner was told to reference chain ids, but no rendered line
ever showed one — chainLine emitted bare 'premises → conclusion', so
the model re-typed whole rendered lines into submit_partition and every
call failed 'unknown chain ids' validation (owner live report,
2026-09-30 evening). The generator's YOUR TARGET block had the same
blindness.

- chainLine now leads with the chain's id: [arg_x] n_a, n_b → n_c;
  a bare proposition repeats its own id ([n_y] n_y (no premises)) —
  mechanically teaching that its chain id IS its proposition id.
- PARTITIONER_INSTRUCTIONS rewritten to chains-primary vocabulary
  (was still 'follows-edges, bijective re-encoding' — pre-chains
  framing) with the id-only doctrine and singular propositions
  first-class.
- partitionSchema/problemSchema gained field descriptions: ids
  VERBATIM, never re-type, never invent.
- Generator OUTPUT bullet + target-block header say the same.

Design ruling en route: partitioner stays an LLM partitioning chains
(deterministic partitioning and propositions-as-targets both
considered and declined by the owner).

tests/practice-agents.test.ts

@@ -109,12 +109,15 @@ describe("renderParams — named levels, never a number", () => {
 });
 
 describe("rendering (the agent-facing text)", () => {
-	it("renderChains: legend with names + statements, premises → conclusion, singletons marked", () => {
+	it("renderChains: legend with names + statements, chain ids LEAD every line (the referenceable anchor)", () => {
 		const text = renderChains(chains, propositions);
 		assert.match(text, /\[n1\] Self-ownership — Each person owns themself\./);
 		assert.match(text, /\[n2\] Homesteading — Unowned goods are claimed by first use\./);
-		assert.match(text, /n1 → n3/);
-		assert.match(text, /n2 \(no premises\)/);
+		// The chain id precedes every line — the id the submit references.
+		assert.match(text, /\[n3\] n1 → n3/);
+		// A bare proposition: its own id, twice — the chain id IS the
+		// proposition id (owner fix, 2026-09-30 evening).
+		assert.match(text, /\[n2\] n2 \(no premises\)/);
 	});
 
 	it("renderPreviousProblems: numbered statements + chains; empty = first-set line", () => {

tests/practice-pipeline.test.ts

@@ -108,8 +108,11 @@ function targetOf(prompt: string): string[] {
 	const section = prompt.split("THE FULL SET")[0] ?? "";
 	const ids: string[] = [];
 	for (const line of section.split("\n")) {
-		if (line.includes("→")) ids.push(line.split("→")[1]!.trim());
-		else if (line.includes("(no premises)")) ids.push(line.replace("(no premises)", "").trim());
+		// Chain ids now LEAD every line ([arg_x] a, b → c) — strip the anchor
+		// bracket to recover the id the submit must echo.
+		const body = line.replace(/^\[[^\]]+\]\s+/, "");
+		if (body.includes("→")) ids.push(body.split("→")[1]!.trim());
+		else if (body.includes("(no premises)")) ids.push(body.replace("(no premises)", "").trim());
 	}
 	return ids;
 }