practice fix follow-up — the picker lists EVERY birth-session group (owner ruling)

Owner escalation on deviation 1: practice availability must not
inherit a visual-rendering threshold. graphClusters() now runs
birthSessionPartition(snap.nodes) directly (same size-desc/id-asc
ordering) instead of reading the snapshot's MIN_CLUSTER_SIZE-filtered
clusters array — MIN_CLUSTER_SIZE stays a hull-drawing rule only.
Label join mirrors the snapshot's (chat title / notes path, null when
the naming record is gone). Contract doc + architecture.md sentence
corrected to match; empty-picker copy reworded ('once a session births
its first proposition' — no 3+ mechanics). Render pins: new empty line
+ a 1- and 2-proposition group listing pin. 1130/1130, tsc 0, lint 0,
build 0.

docs/architecture.md

@@ -380,7 +380,7 @@ Practice turns the graph into problem sets the learner reasons through out loud.
 
 **The jobs pattern — registry, not JobRecords.** Practice runs are NOT Workbench jobs: no `JobStore` records, no steer messages, nothing ever wakes the teacher — a practice run isn't chat-scoped (a set outlives its birth session and has no lesson to re-enter; its result is itself, persisted in its own store and read by its own page). What it shares with the Workbench is the observability surface: a `globalThis` run registry (the module-instance idiom — `__lhPracticeRuns`), one row per set-phase (`setId:generation`, `setId:grading`), feeding the activity dock (GraduationCap rows; abort is set-scoped and idempotent; a boot sweep marks orphaned `partitioning`/`generating` sets as `error "Interrupted (server restarted)"` — the job runner's crash-honesty at set grain). Store writes serialize behind a per-set mutex; the pipeline is the sole writer of `data/practice`.
 
-**API + UI.** Creation is GRAPH-DOMAIN, not chat-domain (owner ruling 2026-09-29: "problem sets always take in nodes — graph objects"): `POST /api/practice/sets` takes `{nodeIds, params, title?}` ONLY — no chatId, no clusterId; the UI resolves a picked cluster to its member node ids and passes the cluster's label as the title. `GET /api/graph/clusters` serves the picker: the birth-session clusters the graph view renders (`graphSnapshot`'s clusters verbatim — same ordering, same MIN_CLUSTER_SIZE presentation filter), each as `{key, kind: "chat"|"notes", label, nodeIds, nodeCount}`; a cluster whose naming record is gone keeps `label: null` — honest, never guessed. 202 `{id}` with generation fire-and-forget; 400 empty selection (empty intersection with live nodes — the vanished-nodes edge) / bad params; 503 model/key refusal. `GET /api/practice/sets` · `GET/DELETE /api/practice/sets/[id]` (delete aborts live runs first) · `POST /api/practice/sets/[id]/answers` (202; 409 when not ready). Surfaces: `/practice` (the list — status/counts rows, delete confirm, the new-set dialog with the three dials and the cluster picker — the ONLY creation entry for now; the graph-view cluster entry comes later with the free-form selection UI) and `/practice/[id]` (the exam page — numbered problems, markdown statements with math healing at the display seam, a textarea + focus-gated dictation bar per problem, one Submit per set, the post-grade reveal). Entry: the sidebar's Practice nav row.
+**API + UI.** Creation is GRAPH-DOMAIN, not chat-domain (owner ruling 2026-09-29: "problem sets always take in nodes — graph objects"): `POST /api/practice/sets` takes `{nodeIds, params, title?}` ONLY — no chatId, no clusterId; the UI resolves a picked cluster to its member node ids and passes the cluster's label as the title. `GET /api/graph/clusters` serves the picker: the birth-session partition itself (`birthSessionPartition`, same ordering — size desc, ties by id) — EVERY group regardless of size (owner ruling, same evening: MIN_CLUSTER_SIZE is a hull-drawing rule; practice availability must not inherit a visual threshold), each as `{key, kind: "chat"|"notes", label, nodeIds, nodeCount}`; a cluster whose naming record is gone keeps `label: null` — honest, never guessed. 202 `{id}` with generation fire-and-forget; 400 empty selection (empty intersection with live nodes — the vanished-nodes edge) / bad params; 503 model/key refusal. `GET /api/practice/sets` · `GET/DELETE /api/practice/sets/[id]` (delete aborts live runs first) · `POST /api/practice/sets/[id]/answers` (202; 409 when not ready). Surfaces: `/practice` (the list — status/counts rows, delete confirm, the new-set dialog with the three dials and the cluster picker — the ONLY creation entry for now; the graph-view cluster entry comes later with the free-form selection UI) and `/practice/[id]` (the exam page — numbered problems, markdown statements with math healing at the display seam, a textarea + focus-gated dictation bar per problem, one Submit per set, the post-grade reveal). Entry: the sidebar's Practice nav row.
 
 **Model wiring.** Three roles — `partitioner`, `problemGenerator`, `grader` — all pinned to the **strong** slot (quality-critical, one settings edit from cheap) and in `BACKGROUND_MODEL_ROLES` (per-role overrides). The stage agents are single-submit loops on the shared `runSubmitAgent` seam (`submit-agent.ts`, extracted from extraction for exactly this): a `validate` hook turns a bad submit into a tool-input error the model retries against, within `maxTurns 4`; exhaustion fails the stage honestly (the set says so, the chains re-run cleanly on a new set).