feat(brain): hybrid BM25 + pgvector retrieval (opt-in)

Wires nomic-embed-text (iguana ollama) + pgvector on the shared
postgres18 into brain_query / brain_answer via Reciprocal Rank Fusion.
Pure BM25 stays the default; setting BRAIN_PG_DSN and BRAIN_EMBED_URL
together opts in. Setting one without the other is misconfiguration →
exit 1.

New packages:

- internal/embed
  Client.Embed(ctx, text) → []float32 via POST {URL}/api/embed.
  Defaults to nomic-embed-text:latest (768 dim). nil-on-empty-URL so
  callers gate on a single nil check.

- internal/vectorstore
  PGStore wraps a pgxpool against postgres18. Init creates
  brain_embeddings(path PK, vector(768), updated_at) + HNSW cosine
  index idempotently. Upsert / Delete / Search / KnownPaths.
  Sync(brainDir, store, embedder) diffs brain/wiki/ against the store
  and upserts new files / deletes removed ones; StartSync runs it on
  a ticker (default 300s). Integration tests gated by BRAIN_PG_TEST_DSN.

- scripts/brain-embeddings-init.sql
  One-time DBA setup: brain DB, brain_app role, vector extension,
  GRANTs. Idempotent.

Search layer:

- search.QueryOptions gains Vector + Embedder fields.
- QueryContext is the cancellable variant; Query stays for callers.
- When both are set, BM25 (top-N) and pgvector (top-4N) candidates
  merge via Reciprocal Rank Fusion (k=60, Cormack et al. 2009 — no
  tuning knob, robust to scale differences between rankers).
- Vector-only hits are hydrated from disk so callers see uniform
  Result records (path, title, excerpt, wing, hall, score).
- Wing/hall filters still apply to vector candidates via path-prefix.
- On embedder/vector errors the search falls back to BM25 — embedding
  outage degrades quality but doesn't take the brain offline.

MCP wiring:

- mcp.Server.WithHybridRetrieval(v, e) opt-in setter, same shape as
  WithReranker.
- brainQuery and brainAnswer pass the wired vector/embedder through
  to search.QueryContext.

REST:

- POST /backfill-embeddings drives Sync synchronously. Returns
  {added, deleted, errors[]}. 503 when feature is unconfigured.

cmd/server/main.go:

- BRAIN_PG_DSN + BRAIN_EMBED_URL together enable hybrid; one alone
  → exit 1.
- vectorAdapter bridges *PGStore (returns []Hit) to
  search.VectorSearcher (which takes []VectorHit) without either
  package importing the other.
- BRAIN_EMBED_SYNC_INTERVAL (default 300s) controls the background
  Sync ticker.

Backend pivot from Qdrant to pgvector recorded in DECISIONS.md
2026-05-18 (supersedes 2026-04-08): postgres18 already runs in
databases/ ns, Qdrant was never deployed, one engine beats two.

Dependency: github.com/jackc/pgx/v5 — modern, native pgvector via
parametric vector literals.

Tests:
- embed.Client: empty-URL nil, request shape, dimension, upstream
  error propagation, empty-text rejection.
- vectorstore.PGStore: dimension validation (unit); upsert/search/
  KnownPaths (integration, BRAIN_PG_TEST_DSN-gated).
- vectorstore.Sync: adds new files, skips known, deletes
  disappeared, skips _index.md, no-op when nil, collects embedder
  errors.
- search.Query: hybrid promotes vector-only hits via RRF; falls
  back to BM25 on embedder error.

Closes hyperguild#8.

ingestion/internal/vectorstore/pg.go

@@ -0,0 +1,155 @@
+// Package vectorstore stores brain note embeddings in pgvector on the
+// shared postgres18 instance. One row per markdown path, cosine-distance
+// indexed via HNSW for sub-millisecond top-k retrieval.
+package vectorstore
+
+import (
+	"context"
+	"errors"
+	"fmt"
+	"strings"
+
+	"github.com/jackc/pgx/v5"
+	"github.com/jackc/pgx/v5/pgxpool"
+)
+
+// Hit is a single result from a cosine-distance search.
+type Hit struct {
+	Path     string
+	Distance float64 // 0 = identical, 2 = opposite
+}
+
+// PGStore is a pgvector-backed embeddings store. Construct with New and
+// call Init once to create the table + HNSW index. Use Close to release
+// the underlying pool.
+type PGStore struct {
+	pool *pgxpool.Pool
+}
+
+// New opens a connection pool against dsn (a libpq-style URL). Caller
+// owns the resulting *PGStore and must invoke Close.
+func New(ctx context.Context, dsn string) (*PGStore, error) {
+	pool, err := pgxpool.New(ctx, dsn)
+	if err != nil {
+		return nil, fmt.Errorf("pgxpool: %w", err)
+	}
+	if err := pool.Ping(ctx); err != nil {
+		pool.Close()
+		return nil, fmt.Errorf("ping: %w", err)
+	}
+	return &PGStore{pool: pool}, nil
+}
+
+// Close releases the underlying connection pool.
+func (s *PGStore) Close() {
+	if s.pool != nil {
+		s.pool.Close()
+	}
+}
+
+// Init creates the brain_embeddings table and its HNSW index if they
+// don't already exist. Safe to call on every startup. Assumes the
+// `vector` extension is already installed (one-time DBA setup; see
+// scripts/brain-embeddings-init.sql).
+func (s *PGStore) Init(ctx context.Context) error {
+	const ddl = `
+CREATE TABLE IF NOT EXISTS brain_embeddings (
+    path       TEXT PRIMARY KEY,
+    embedding  vector(768) NOT NULL,
+    updated_at TIMESTAMPTZ NOT NULL DEFAULT now()
+);
+CREATE INDEX IF NOT EXISTS brain_embeddings_embedding_idx
+    ON brain_embeddings USING hnsw (embedding vector_cosine_ops);
+`
+	_, err := s.pool.Exec(ctx, ddl)
+	return err
+}
+
+// Upsert inserts or replaces the embedding for path. Embedding must be
+// 768-dim (nomic-embed-text). Caller is responsible for normalising
+// paths to forward-slash form.
+func (s *PGStore) Upsert(ctx context.Context, path string, embedding []float32) error {
+	if len(embedding) != 768 {
+		return fmt.Errorf("expected 768-dim embedding, got %d", len(embedding))
+	}
+	_, err := s.pool.Exec(ctx, `
+        INSERT INTO brain_embeddings (path, embedding, updated_at)
+        VALUES ($1, $2, now())
+        ON CONFLICT (path) DO UPDATE
+        SET embedding = EXCLUDED.embedding, updated_at = now()
+    `, path, vectorLiteral(embedding))
+	return err
+}
+
+// Delete removes the row at path. No-op when the row doesn't exist.
+func (s *PGStore) Delete(ctx context.Context, path string) error {
+	_, err := s.pool.Exec(ctx, `DELETE FROM brain_embeddings WHERE path = $1`, path)
+	return err
+}
+
+// Search returns the top-limit nearest paths by cosine distance.
+func (s *PGStore) Search(ctx context.Context, query []float32, limit int) ([]Hit, error) {
+	if len(query) != 768 {
+		return nil, fmt.Errorf("expected 768-dim query, got %d", len(query))
+	}
+	if limit <= 0 {
+		limit = 10
+	}
+	rows, err := s.pool.Query(ctx, `
+        SELECT path, embedding <=> $1 AS distance
+        FROM brain_embeddings
+        ORDER BY embedding <=> $1
+        LIMIT $2
+    `, vectorLiteral(query), limit)
+	if err != nil {
+		return nil, fmt.Errorf("query: %w", err)
+	}
+	defer rows.Close()
+
+	var hits []Hit
+	for rows.Next() {
+		var h Hit
+		if err := rows.Scan(&h.Path, &h.Distance); err != nil {
+			return nil, fmt.Errorf("scan: %w", err)
+		}
+		hits = append(hits, h)
+	}
+	if err := rows.Err(); err != nil && !errors.Is(err, pgx.ErrNoRows) {
+		return nil, err
+	}
+	return hits, nil
+}
+
+// KnownPaths returns the path set already present in the store. Used by
+// the watcher to diff against the wiki/ tree and decide what to upsert.
+func (s *PGStore) KnownPaths(ctx context.Context) (map[string]struct{}, error) {
+	rows, err := s.pool.Query(ctx, `SELECT path FROM brain_embeddings`)
+	if err != nil {
+		return nil, fmt.Errorf("query paths: %w", err)
+	}
+	defer rows.Close()
+	out := make(map[string]struct{})
+	for rows.Next() {
+		var p string
+		if err := rows.Scan(&p); err != nil {
+			return nil, err
+		}
+		out[p] = struct{}{}
+	}
+	return out, rows.Err()
+}
+
+// vectorLiteral renders a Go float32 slice as the literal representation
+// pgvector accepts as a parametric input: `[v1,v2,...,vN]`.
+func vectorLiteral(v []float32) string {
+	var b strings.Builder
+	b.WriteByte('[')
+	for i, x := range v {
+		if i > 0 {
+			b.WriteByte(',')
+		}
+		fmt.Fprintf(&b, "%g", x)
+	}
+	b.WriteByte(']')
+	return b.String()
+}