diff --git a/README.md b/README.md
index e0775eb..680377e 100644
--- a/README.md
+++ b/README.md
@@ -87,8 +87,10 @@ Answers (through `/v1/fetch` or `/v2/scrape`):
 - `--question "…"` for a **digest** that, on a PDF, cites each fact as `(p. N)`.
 
 A range returns at most 100 pages; grep shows at most 100 matches and takes a pattern of at most
-200 bytes. `pages` and `grep` on anything but a PDF are a `400`. A question over a document too long
-to digest (more than 200 chunks) is refused with
+200 bytes. `pages` and `grep` on anything but a PDF are a `400`. A question on a long document is
+answered first from BM25 (`retrieval: "bm25"`) — lexical, before the document's chunks are
+embedded in the background — and hybrid on later questions, once those embeddings exist. A question
+over a document too long to answer even by retrieval (more than 5000 chunks) is refused with
 `422 document too long for question (N chunks); use grep or pages`.
 
 Scanned PDFs have no text layer and return `no text layer (scanned PDF?)`; point them at an OCR
diff --git a/docs/implementer-log.md b/docs/implementer-log.md
index 45ef4f6..f6fcb3b 100644
--- a/docs/implementer-log.md
+++ b/docs/implementer-log.md
@@ -11,7 +11,10 @@ One row per task session that ends in a commit. Newest last.
 | p5a/05-pdfdoc | 2026-09-25 | done | 1 | gate: ok | none | Implemented the render package with no I/O on a `*pdftext.Doc`. `Marker`/`Full` print each extracted page as `--- page N ---`, text trimmed, joined by a blank line. `Render` dispatches grep → page range → whole. Whole fits in OutCap runes, else a map: title (or `Untitled PDF`)/pages/`~tokens` line with `pages 1-E extracted` only when fewer extracted than `Pages`, a cuttable `## Outline` (two-space indent per level below 1, cut before the header/instruction), the instruction line, and whole leading pages within OutCap/4 (at least page 1, cut to fit). Range parses `a-b`/`a`/`a-`, wraps out-of-range in `ErrBadPages` with `pages out of range (1-E)`, clamps `b`, caps at 100 pages and OutCap runes, and notes the rest as `pages="k-b"`. Grep is RE2 with smart-case `(?i)` prefix, 200-byte cap, per-line matches with previous/next page context in `p. P-`/`p. P:` form, first 100 shown, total counted; RE2 keeps the `(a+)+$` test linear. Every length is in runes. Given test byte-identical; make gate ok. |
 | p5a/06-api-pdf | 2026-09-26 | done | resumed | gate: ok (7 of 10 PDF tests; 3 are task 07's) | none | Served PDFs through `/v1/fetch` (clean) and `/v2/scrape`. Added `RetryAfter int` to `fetch.Error` and a `Retry-After` header line guarded by `> 0`. Added `PDFRunner`/`PDFPool`/`PDFTTL`/`PDFMaxQuestionChunks` Server fields (PDFPool built once via `sync.Once` only when nil, so the test's direct override is respected) and `pdfPoolOnce`. Routed `clean.Kind` in `doFetch`/`cleanFetched` (html/json/text switched, "other"→415, "pdf"→extractPDF); `doFetch`'s switch routes "text" explicitly so a PDF never runs `clean.Text` first. New `internal/api/pdf.go`: `DefaultPDFTTL`/`DefaultPDFMaxQuestionChunks` (task 07), `runner()`/`pool()` defaults, `extractPDF` (pool key `callerClass|SHA256`, two-value assert, `fmt.Errorf("pdf: bad result %T")`), `pdfError` (422 for the five pdftext errors + panic default, 503+RetryAfter 10 for ErrBusy, 429 for ErrCallerBusy), `renderPDF` (`pdfdoc.Render`, whole text or map). `doFetch` returns the 4th `doc *pdftext.Doc`; digest uses `pdfdoc.Full(doc)` (computed once) as content, clean uses `renderPDF.Content`, envelope `pdf` object has pages/title/outline/extracted/first/last/map/grep_hits/note, raw mode→400. Scrape markdown=`renderPDF.Content`, html="", `metadata.numPages`=doc.Pages. 7 of 10 given tests pass under -race -count=3; the 3 failures (`TestPDFPagesAndGrep`, `TestPDFCache`, `TestPDFQuestionTooLong`) are task 07 tests that reference fields not in this task, exactly as the task doc (lines 145, 157-158) predicts; nothing else fails. Given files byte-identical. |
 | p5a/08-digest-cli-docs | 2026-09-26 | done | 1 | gate: ok | none | Added the page-cite sentence to the digest `systemPrompt` ("When the document has `--- page N ---` markers, cite the page of each fact as (p. N).") and set `PromptVersion = "3"`. Added the `sift_pdf_extract_total{outcome}`, `sift_pdf_extract_seconds`, `sift_pdf_pages_total`, `sift_pdf_pool_wait_seconds`, `sift_pdf_cache_hits_total` series to `internal/metrics` (`pdf.go` package) and wired `ObservePDF`/`ObservePDFWait`/`PDFCacheHit` into `internal/api/pdf.go` (`ObservePDF` once per call after `extractPDF`, outcome classified by `pdfOutcome` so raw text never becomes a label; `ObservePDFWait` only when the caller actually waited on `pool().Do`; `PDFCacheHit` on fresh hits and 304s). Refactored `cmd/sift/fetchcmd.go` into a `fetchOpts` struct with `parseFetchOpts` (returns `fetchOpts`, not `string, error`) and a `fetchBody(o fetchOpts) map[string]any` that does the digest/clean default and adds `pages`/`grep` only when set; `--pages`/`--grep` added to `fetchValueFlags`. Updated `skill/SKILL.md` (PDFs section; removed PDF mention from the 415 row). Unit: `nix/module.nix` `MemoryMax = "1G"` (one line). README: added a "PDF documents" section covering detection, limits (100 MB/120 s download, 60 s extraction, 2,000 pages), the child process, the 2-slot/4-wait/20 s pool, the 24 h conditional-GET cache, the answers, the task-06 errors table, and the metrics; noted the `go-pdfkit/extract` v0.3.0 engine chosen by the `docs/P5a.md` §3 bake-off. All tests pass under -race, make gate ok, three given files byte-identical, nix diff is one line. |
+| p5b/01-splitpages-bm25 | 2026-09-26 | done | 1 | gate: ok | none | `splitpages.go`: `SplitPages` is Split's budget/line algorithm plus page awareness — a `--- page N ---` line sets the current page, and a chunk that starts after the first marker but not on a marker line is prefixed `--- page N (cont.) ---\n\n` for the page its first line belongs to (captured at chunk start, so a chunk that crosses a marker is still labelled with its starting page; the marker counts toward the chunk budget). No-marker text yields exactly Split's result, so `TestSplitKeepsPageMarkers` is untouched. `bm25.go`: `BM25` with k1=1.2/b=0.75, term counts via a local `docTerms` (same tokenization as `terms()`, >=2 chars), IDF `ln(1+(N-df+0.5)/(df+0.5))`, avgDL over all docs (guarded to 1 when the corpus is all-empty), one score per doc >= 0 with no query term scoring 0 and empty query/index scoring 0 everywhere. All digest tests pass under -race -count=3, make gate ok, two given files byte-identical. |
+| p5b/02-retrieval | 2026-09-26 | done | 1 | gate: ok | none | Cached chunk embeddings + BM25-first retrieval. `digest.go`: `EmbedSyncMax=48`, `MaxDocChunks=5000`; `Result` gains `Retrieval string` and `Embedded int`; `selectText` now returns `(body, used, total, mode, embedded, err)` and `Run` sets both; `PutDigest` skips storing any `mode=="bm25"` answer (provisional, not cached). `retrieval.go`: `hybridOrBM25` — no cache, `len(chunks)<=48` embeds question+chunks inline and scores hybrid; `>48` scores BM25 and queues; cache present embeds the question and only the uncached chunks inline and scores hybrid on the union; both embed paths return hybrid, both bm25 paths return `bm25`. `background.go`: `bgWorker` with `bgOnce sync.Once` (creates the worker, never starts a goroutine) + `w.started` under `w.mu` (starts the goroutine once), dedup by `contentHash|callerClass`, full-queue drops the doc without marking seen so a later question re-queues, `acquireGate` retries once after 1 s on refusal, `WaitBackground` polls every 20 ms for true idle. `retrieval_test.go` copied byte-identical from the plan. All 12 digest tests pass under `-race -count=3`; `make gate` ok. |
 | p5a/07-api-cache-pages | 2026-09-26 | done | 1 | gate: ok | none | Implemented the PDF document cache with revalidation in `doFetch`: `pdfFromCache` (miss / fresh within `PDFTTL` / stale → `FetchIf` with 304→`TouchPDF`+answer-fresh / 200→return response with ok=false and no second GET) and `storePDF` after `extractPDF` (`ContentHash=res.SHA256`, ETag/Last-Modified from headers, FetchedAt=now, Meta=JSON of `doc.Meta`, Pages=`doc.Text`). `pages`/`grep` passed into `pdfdoc.Options` in `renderPDF`; `ErrBadPages`/`ErrBadGrep`→400 with the error's own text, non-PDF→400 "pages and grep apply to PDFs only" before the doc block. Question limit in digest mode: `n=len(digest.Split(pdfdoc.Full(doc), ChunkTokens))`, `n>PDFMaxQuestionChunks`→422 "document too long for question (n chunks); use grep or pages" before any digest call. Envelope `cached` set true for cache answers via the synthetic cache res's empty body (`len(res.Body)==0`); the one `doFetch` change beyond the rule-1 call was reusing that 200 response instead of a second `Fetch`. Added `fmt` import to api.go. Given file byte-identical; make gate ok. |
+| p5b/03-api | 2026-09-26 | done | 1 | gate: ok | none | The digest now answers long documents itself (task 02), so the API's refusal limit is only a safety cap: `DefaultPDFMaxQuestionChunks` 200→5000 in `internal/api/pdf.go` (the 422 message text unchanged, still "document too long for question (N chunks); use grep or pages"). In `v1fetch` (`internal/api/api.go`) the digest-meta map gains `"retrieval": dr.Retrieval` and `"embedded": dr.Embedded` next to `chunks_used`/`chunks_total`, only when the digest ran without a fallback. Copied the two given tests byte-identical from the plan — the replacement `pdf_test.go` is now the protected one and asserts `DefaultPDFMaxQuestionChunks == 5000`; `pdf_retrieval_test.go` asserts the first long-doc question returns `retrieval=bm25`, `embedded=0`. README PDF section: a long-doc question is answered first from BM25 (`retrieval: "bm25"`) while its chunks embed in the background and hybrid on later questions, plus the 5000-chunk cap. One sentence added to `skill/SKILL.md`. All api tests pass under `-race -count=3`; make gate ok; given files byte-identical. |
 
 ## P5a review (owner, 2026-09-26)
 
diff --git a/internal/api/api.go b/internal/api/api.go
index 715a057..a9cfe46 100644
--- a/internal/api/api.go
+++ b/internal/api/api.go
@@ -569,6 +569,8 @@ func (s *Server) v1fetch(w http.ResponseWriter, r *http.Request) {
 					"model":        dr.Model,
 					"chunks_used":  dr.ChunksUsed,
 					"chunks_total": dr.ChunksTotal,
+					"retrieval":    dr.Retrieval,
+					"embedded":     dr.Embedded,
 					"fallback":     false,
 					"cached":       dr.Cached,
 				}
diff --git a/internal/api/pdf.go b/internal/api/pdf.go
index 7c7179f..d13e313 100644
--- a/internal/api/pdf.go
+++ b/internal/api/pdf.go
@@ -20,9 +20,11 @@ import (
 const (
 	// DefaultPDFTTL is how long a cached PDF is served before it is revalidated.
 	DefaultPDFTTL = 24 * time.Hour
-	// DefaultPDFMaxQuestionChunks is the longest document (in digest chunks) a question is
-	// answered over; a longer one is refused in favour of grep or pages.
-	DefaultPDFMaxQuestionChunks = 200
+	// DefaultPDFMaxQuestionChunks is the safety cap on how long a document a question is
+	// answered over; beyond it the question is refused in favour of grep or pages. Longer
+	// documents are handled by retrieval (BM25 first, embedding their chunks in the
+	// background), so this only bounds the un-answerable.
+	DefaultPDFMaxQuestionChunks = 5000
 )
 
 // runner returns the configured extraction child, or a zero Runner that runs
diff --git a/internal/api/pdf_retrieval_test.go b/internal/api/pdf_retrieval_test.go
new file mode 100644
index 0000000..2793160
--- /dev/null
+++ b/internal/api/pdf_retrieval_test.go
@@ -0,0 +1,75 @@
+package api
+
+// P5b task 03: a question on a long PDF is answered (by BM25 first) instead of refused, and the
+// envelope says how the digest was built.
+
+import (
+	"encoding/json"
+	"net/http"
+	"net/http/httptest"
+	"strings"
+	"testing"
+	"time"
+
+	"git.wntrmute.dev/kyle/sift/internal/digest"
+	"git.wntrmute.dev/kyle/sift/internal/pdftest"
+)
+
+// fakeModel answers /embed with a fixed vector and /chat with a one-word SSE reply.
+func fakeModel(t *testing.T) *httptest.Server {
+	mux := http.NewServeMux()
+	mux.HandleFunc("/embed", func(w http.ResponseWriter, r *http.Request) {
+		var body struct {
+			Input []string `json:"input"`
+		}
+		_ = json.NewDecoder(r.Body).Decode(&body)
+		var data []map[string]any
+		for i := range body.Input {
+			data = append(data, map[string]any{"index": i, "embedding": []float64{1, float64(i % 7)}})
+		}
+		_ = json.NewEncoder(w).Encode(map[string]any{"data": data})
+	})
+	mux.HandleFunc("/chat", func(w http.ResponseWriter, r *http.Request) {
+		w.Header().Set("Content-Type", "text/event-stream")
+		_, _ = w.Write([]byte(`data: {"choices":[{"delta":{"content":"answer (p. 3)"}}]}` + "\n\ndata: [DONE]\n\n"))
+	})
+	srv := httptest.NewServer(mux)
+	t.Cleanup(srv.Close)
+	return srv
+}
+
+func TestPDFLongQuestionIsAnswered(t *testing.T) {
+	r := newPDFRig(t)
+	m := fakeModel(t)
+	db := r.s.Digest.Cache
+	r.s.Digest = &digest.Engine{ChatURL: m.URL + "/chat", EmbedURL: m.URL + "/embed", Cache: db, Gate: digest.NewGate(2, 8, 5*time.Second), Client: m.Client()}
+	var pages []string
+	for p := 1; p <= 260; p++ { // ~260 pages × 40 lines: well over EmbedSyncMax chunks
+		pages = append(pages, pdftest.Lorem(p, 40))
+	}
+	o := newOrigin(t, "application/pdf", pdftest.Build(pdftest.Doc{Title: "Long", Pages: pages}))
+	code, out, _ := r.fetch(t, r.fleet, map[string]any{"url": o.srv.URL, "question": "what is on page three?", "context": false})
+	if code != 200 {
+		t.Fatalf("long question: %d %v, want 200 (P5a refused this)", code, out)
+	}
+	dg, _ := out["digest"].(map[string]any)
+	if dg == nil || dg["retrieval"] != "bm25" || dg["embedded"] != 0.0 {
+		t.Errorf("digest meta = %v, want retrieval bm25 and embedded 0 on the first question", dg)
+	}
+	if c, _ := out["content"].(string); !strings.Contains(c, "answer") {
+		t.Errorf("content %q", c)
+	}
+}
+
+func TestPDFSmallQuestionReportsRetrieval(t *testing.T) {
+	r := newPDFRig(t)
+	m := fakeModel(t)
+	db := r.s.Digest.Cache
+	r.s.Digest = &digest.Engine{ChatURL: m.URL + "/chat", EmbedURL: m.URL + "/embed", Cache: db, Gate: digest.NewGate(2, 8, 5*time.Second), Client: m.Client()}
+	o := newOrigin(t, "application/pdf", threePDF())
+	code, out, _ := r.fetch(t, r.fleet, map[string]any{"url": o.srv.URL, "question": "what is on page two?", "context": false})
+	dg, _ := out["digest"].(map[string]any)
+	if code != 200 || dg == nil || dg["retrieval"] != "whole" {
+		t.Errorf("small document: %d digest %v, want retrieval whole", code, dg)
+	}
+}
diff --git a/internal/api/pdf_test.go b/internal/api/pdf_test.go
index 041978a..2874eea 100644
--- a/internal/api/pdf_test.go
+++ b/internal/api/pdf_test.go
@@ -396,7 +396,8 @@ func TestPDFQuestionTooLong(t *testing.T) {
 	if msg, _ := out["error"].(string); code != 422 || !strings.Contains(msg, "too long") || !strings.Contains(msg, "grep") {
 		t.Errorf("long question: %d %v; want 422 … too long … grep", code, out)
 	}
-	if DefaultPDFMaxQuestionChunks != 200 {
-		t.Errorf("DefaultPDFMaxQuestionChunks = %d, want 200", DefaultPDFMaxQuestionChunks)
+	// P5b: long documents are answered by retrieval now; the limit is only a safety cap.
+	if DefaultPDFMaxQuestionChunks != 5000 {
+		t.Errorf("DefaultPDFMaxQuestionChunks = %d, want 5000", DefaultPDFMaxQuestionChunks)
 	}
 }
diff --git a/internal/digest/background.go b/internal/digest/background.go
new file mode 100644
index 0000000..1cc4819
--- /dev/null
+++ b/internal/digest/background.go
@@ -0,0 +1,172 @@
+package digest
+
+import (
+	"context"
+	"sync"
+	"time"
+
+	"git.wntrmute.dev/kyle/sift/internal/dcache"
+)
+
+// maxBgQueue is the number of documents the background worker may hold at once.
+const maxBgQueue = 4
+
+// bgWorker is the single background goroutine that embeds the chunks of a long document after a
+// bm25 answer queued it. It owns a bounded, deduplicated queue and yields the Dixie gate to
+// interactive digests one batch at a time.
+type bgWorker struct {
+	engine *Engine
+
+	mu      sync.Mutex
+	cond    *sync.Cond
+	queue   []embedJob
+	seen    map[string]struct{}
+	inProg  bool
+	started bool
+}
+
+type embedJob struct {
+	chunks      []string
+	contentHash string
+	callerClass string
+}
+
+// worker returns the engine's background worker, creating it once. It does not start the goroutine.
+func (e *Engine) worker() *bgWorker {
+	e.bgOnce.Do(func() {
+		w := &bgWorker{engine: e}
+		w.cond = sync.NewCond(&w.mu)
+		w.seen = map[string]struct{}{}
+		e.bg = w
+	})
+	return e.bg
+}
+
+// queueForEmbed asks the background worker to embed a document's chunks. The document is
+// deduplicated by contentHash+"|"+callerClass; a full queue drops it (and logs) so a later
+// question re-queues it.
+func (e *Engine) queueForEmbed(chunks []string, contentHash, callerClass string) {
+	if e == nil {
+		return
+	}
+	w := e.worker()
+	w.mu.Lock()
+	defer w.mu.Unlock()
+	if !w.started {
+		w.started = true
+		go w.run()
+	}
+	key := contentHash + "|" + callerClass
+	if _, ok := w.seen[key]; ok {
+		return
+	}
+	if len(w.queue) >= maxBgQueue {
+		// Leave it un-seen: a later question re-queues it.
+		if e.Log != nil {
+			e.Log.Warn("background embed queue full")
+		}
+		return
+	}
+	w.seen[key] = struct{}{}
+	w.queue = append(w.queue, embedJob{chunks: chunks, contentHash: contentHash, callerClass: callerClass})
+	w.cond.Signal()
+}
+
+func (w *bgWorker) run() {
+	for {
+		w.mu.Lock()
+		for len(w.queue) == 0 {
+			w.cond.Wait()
+		}
+		job := w.queue[0]
+		w.queue = w.queue[1:]
+		w.inProg = true
+		w.mu.Unlock()
+
+		w.process(job)
+
+		// Forget the document whether it finished or not: dedupe covers only queued and
+		// in-progress work, so a later question re-queues a document whose embedding failed.
+		w.mu.Lock()
+		delete(w.seen, job.contentHash+"|"+job.callerClass)
+		w.inProg = false
+		w.mu.Unlock()
+	}
+}
+
+// process embeds the first MaxDocChunks chunks that lack a vector, EmbedBatch at a time, yielding
+// the gate between batches and storing each vector. On any embedding error it drops the rest of
+// the document.
+func (w *bgWorker) process(job embedJob) {
+	e := w.engine
+	key := func(i int) string {
+		return dcache.EmbedKey(job.contentHash+"/sp1200", i, e.embedModel(), job.callerClass)
+	}
+	var idx []int
+	for i := range job.chunks {
+		if i >= MaxDocChunks {
+			break
+		}
+		if _, ok := e.Cache.GetEmbed(key(i)); ok {
+			continue
+		}
+		idx = append(idx, i)
+		if len(idx) >= MaxDocChunks {
+			break
+		}
+	}
+	for b := 0; b < len(idx); b += EmbedBatch {
+		j := b + EmbedBatch
+		if j > len(idx) {
+			j = len(idx)
+		}
+		batch := make([]string, j-b)
+		for k := range batch {
+			batch[k] = job.chunks[idx[b+k]]
+		}
+		w.acquireGate()
+		ectx, cancel := context.WithTimeout(context.Background(), e.timeout())
+		vecs, err := e.embed(ectx, batch)
+		cancel()
+		e.Gate.Release()
+		if err != nil {
+			if e.Log != nil {
+				e.Log.Warn("background embed", "err", truncateErr(err, 512))
+			}
+			return
+		}
+		for k := range batch {
+			if k < len(vecs) && len(vecs[k]) > 0 {
+				e.Cache.PutEmbed(key(idx[b+k]), vecs[k])
+			}
+		}
+	}
+}
+
+// acquireGate takes the Dixie gate, sleeping a second after each refusal (queue full or wait
+// expired) so interactive digests get their turns. Background work has no deadline: it waits.
+func (w *bgWorker) acquireGate() {
+	for {
+		if ok, _ := w.engine.Gate.Acquire(context.Background()); ok {
+			return
+		}
+		time.Sleep(time.Second)
+	}
+}
+
+// WaitBackground returns when the background worker is idle: the queue empty and nothing embedding.
+func (e *Engine) WaitBackground(ctx context.Context) error {
+	w := e.worker()
+	for {
+		w.mu.Lock()
+		idle := len(w.queue) == 0 && !w.inProg
+		w.mu.Unlock()
+		if idle {
+			return nil
+		}
+		if err := ctx.Err(); err != nil {
+			return err
+		}
+		time.Sleep(20 * time.Millisecond)
+	}
+}
diff --git a/internal/digest/bm25.go b/internal/digest/bm25.go
new file mode 100644
index 0000000..5f82e53
--- /dev/null
+++ b/internal/digest/bm25.go
@@ -0,0 +1,109 @@
+package digest
+
+import (
+	"math"
+	"strings"
+	"unicode"
+)
+
+const (
+	bm25K1  = 1.2
+	bm25B   = 0.75
+	bm25Min = 2
+)
+
+// BM25 is a lexical ranker over a fixed set of documents. Terms are the same tokens as
+// terms() — lower-case runs of letters and digits, at least bm25Min characters — counted
+// with frequency rather than kept as a set.
+type BM25 struct {
+	nDocs int
+	avgDL float64
+	df    map[string]int
+	toks  []map[string]int
+	len   []int
+}
+
+// NewBM25 indexes docs with the default BM25 parameters (k1 = 1.2, b = 0.75).
+func NewBM25(docs []string) *BM25 {
+	b := &BM25{
+		nDocs: len(docs),
+		df:    map[string]int{},
+		toks:  make([]map[string]int, len(docs)),
+		len:   make([]int, len(docs)),
+	}
+	var total int
+	for i, doc := range docs {
+		counts := docTerms(doc)
+		n := 0
+		for _, c := range counts {
+			n += c
+		}
+		b.toks[i] = counts
+		b.len[i] = n
+		total += n
+		for t := range counts {
+			b.df[t]++
+		}
+	}
+	if len(docs) > 0 {
+		b.avgDL = float64(total) / float64(len(docs))
+	}
+	return b
+}
+
+// Scores returns one score per document, in order, each >= 0 and never NaN or Inf. An empty
+// query, an empty index or a document without any query term scores 0.
+func (b *BM25) Scores(query string) []float64 {
+	if b == nil {
+		return nil
+	}
+	if b.nDocs == 0 {
+		return make([]float64, len(b.toks))
+	}
+	out := make([]float64, len(b.toks))
+	qterms := docTerms(query)
+	if len(qterms) == 0 {
+		return out
+	}
+	avgDL := b.avgDL
+	if avgDL == 0 {
+		avgDL = 1
+	}
+	for i, toks := range b.toks {
+		var score float64
+		for term := range qterms {
+			tf, ok := toks[term]
+			if !ok {
+				continue
+			}
+			idf := math.Log(1 + (float64(b.nDocs)-float64(b.df[term])+0.5)/(float64(b.df[term])+0.5))
+			denom := float64(tf) + bm25K1*(1-bm25B+bm25B*float64(b.len[i])/avgDL)
+			score += idf * (float64(tf) * (bm25K1 + 1)) / denom
+		}
+		out[i] = score
+	}
+	return out
+}
+
+// docTerms counts occurrences of each BM25 term in s, using the same tokenization as terms().
+func docTerms(s string) map[string]int {
+	out := map[string]int{}
+	var b strings.Builder
+	flush := func() {
+		t := b.String()
+		b.Reset()
+		if len(t) < bm25Min {
+			return
+		}
+		out[t]++
+	}
+	for _, r := range strings.ToLower(s) {
+		if unicode.IsLetter(r) || unicode.IsDigit(r) {
+			b.WriteRune(r)
+		} else {
+			flush()
+		}
+	}
+	flush()
+	return out
+}
diff --git a/internal/digest/bm25_test.go b/internal/digest/bm25_test.go
new file mode 100644
index 0000000..ca9f084
--- /dev/null
+++ b/internal/digest/bm25_test.go
@@ -0,0 +1,89 @@
+package digest
+
+// P5b task 01: BM25, the lexical ranking used while a long document's embeddings are still
+// being built (and inside the hybrid score after).
+
+import (
+	"math"
+	"strings"
+	"testing"
+)
+
+func TestBM25RanksTheRareTerm(t *testing.T) {
+	docs := []string{
+		"the ship sailed from helsinki to tallinn in the morning",
+		"the ship stayed in port all day",
+		"a zanzibarite sample was found near the harbour",
+		"the harbour master logged the ship",
+	}
+	s := NewBM25(docs).Scores("where was the zanzibarite found")
+	if len(s) != len(docs) {
+		t.Fatalf("%d scores for %d docs", len(s), len(docs))
+	}
+	best := 0
+	for i := range s {
+		if s[i] > s[best] {
+			best = i
+		}
+	}
+	if best != 2 {
+		t.Errorf("best = doc %d (%v), want doc 2, the only one with the rare term", best, s)
+	}
+}
+
+func TestBM25Properties(t *testing.T) {
+	filler := strings.Repeat("word ", 50)
+	docs := []string{
+		"alpha " + filler,                     // 0: tf 1
+		strings.Repeat("alpha ", 10) + filler, // 1: tf 10, same filler
+		"alpha common",                        // 2: tf 1, short
+		"common " + filler,                    // 3: no alpha
+	}
+	idx := NewBM25(docs)
+	s := idx.Scores("alpha")
+	if !(s[1] > s[0]) {
+		t.Errorf("more occurrences must score higher: tf10 %v vs tf1 %v", s[1], s[0])
+	}
+	if !(s[1] < 10*s[0]) {
+		t.Errorf("term frequency must saturate: tf10 %v, 10 × tf1 %v", s[1], 10*s[0])
+	}
+	if !(s[2] > s[0]) {
+		t.Errorf("the same term in a shorter document must score higher: short %v, long %v", s[2], s[0])
+	}
+	if s[3] != 0 {
+		t.Errorf("a document without the term scores %v, want 0", s[3])
+	}
+	// IDF: a term in every document is worth less than a rare one.
+	all := NewBM25([]string{"xx yy", "xx zz", "xx ww"}).Scores("xx")
+	rare := NewBM25([]string{"xx yy", "qq zz", "qq ww"}).Scores("xx")
+	if !(rare[0] > all[0]) {
+		t.Errorf("idf: a term in 1 of 3 docs must outscore one in 3 of 3: %v vs %v", rare[0], all[0])
+	}
+}
+
+func TestBM25Degenerate(t *testing.T) {
+	for _, docs := range [][]string{nil, {}, {""}, {"", "a b"}} {
+		s := NewBM25(docs).Scores("a")
+		if len(s) != len(docs) {
+			t.Errorf("%q: %d scores", docs, len(s))
+		}
+		for _, v := range s {
+			if math.IsNaN(v) || math.IsInf(v, 0) || v < 0 {
+				t.Errorf("%q: score %v", docs, v)
+			}
+		}
+	}
+	for _, v := range NewBM25([]string{"a b", "c d"}).Scores("") {
+		if v != 0 {
+			t.Errorf("empty query scored %v", v)
+		}
+	}
+	// Deterministic.
+	a := NewBM25([]string{"alpha beta", "beta gamma", "gamma alpha"}).Scores("alpha gamma")
+	b := NewBM25([]string{"alpha beta", "beta gamma", "gamma alpha"}).Scores("alpha gamma")
+	for i := range a {
+		if a[i] != b[i] {
+			t.Fatal("scores differ between identical runs")
+		}
+	}
+}
diff --git a/internal/digest/digest.go b/internal/digest/digest.go
index 1c0ca10..5df263d 100644
--- a/internal/digest/digest.go
+++ b/internal/digest/digest.go
@@ -33,6 +33,8 @@ const (
 	ChunkTokens    = 1200
 	EmbedBatch     = 16
 	EmbedMaxRunes  = 3000
+	EmbedSyncMax   = 48
+	MaxDocChunks   = 5000
 	DefaultPermit  = 2
 	DefaultQDepth  = 8
 	DefaultQWait   = 20 * time.Second
@@ -191,6 +193,9 @@ type Engine struct {
 	Log        *slog.Logger
 	Cache      *dcache.DB
 
+	bgOnce sync.Once
+	bg     *bgWorker
+
 	mu       sync.Mutex
 	Calls    uint64
 	Fallback map[string]uint64
@@ -205,6 +210,8 @@ type Result struct {
 	DigestMS    int64
 	ReturnedTok int
 	Cached      bool
+	Retrieval   string // "whole", "head", "hybrid", "bm25" or "cached"
+	Embedded    int    // chunks that had an embedding when the answer was built
 }
 
 func (e *Engine) timeout() time.Duration {
@@ -305,6 +312,7 @@ func (e *Engine) Run(ctx context.Context, cleaned, question, finalURL, callerCla
 			r.ChunksUsed = h.ChunksUsed
 			r.ReturnedTok = EstTokens(h.Text)
 			r.Cached = true
+			r.Retrieval = "cached"
 			r.DigestMS = time.Since(start).Milliseconds()
 			return r
 		}
@@ -327,8 +335,10 @@ func (e *Engine) Run(ctx context.Context, cleaned, question, finalURL, callerCla
 	dctx, cancel := context.WithTimeout(ctx, e.timeout())
 	defer cancel()
 
-	body, nUsed, nTotal, err := e.selectText(dctx, cleaned, question)
+	body, nUsed, nTotal, mode, embedded, err := e.selectText(dctx, cleaned, question, contentHash, callerClass)
 	r.ChunksUsed, r.ChunksTotal = nUsed, nTotal
+	r.Retrieval = mode
+	r.Embedded = embedded
 	if err != nil {
 		e.logFallback("embed", err)
 		r.Fallback = "embed"
@@ -359,72 +369,26 @@ func (e *Engine) Run(ctx context.Context, cleaned, question, finalURL, callerCla
 	}
 	r.Text = text
 	r.ReturnedTok = EstTokens(text)
-	if e != nil && e.Cache != nil {
+	// A bm25 answer is provisional: once the embeddings exist the same question
+	// must get a hybrid answer, so it does not go in the digest cache.
+	if e != nil && e.Cache != nil && mode != "bm25" {
 		e.Cache.PutDigest(dkey, text, r.ChunksUsed)
 	}
 	return r
 }
 
-func (e *Engine) selectText(ctx context.Context, cleaned, question string) (string, int, int, error) {
+func (e *Engine) selectText(ctx context.Context, cleaned, question, contentHash, callerClass string) (string, int, int, string, int, error) {
 	if EstTokens(cleaned) <= SmallDoc {
-		return cleaned, 1, 1, nil
+		return cleaned, 1, 1, "whole", 0, nil
 	}
-	chunks := Split(cleaned, ChunkTokens)
+	chunks := SplitPages(cleaned, ChunkTokens)
 	if len(chunks) == 0 {
-		return cleaned, 1, 1, nil
+		return cleaned, 1, 1, "whole", 0, nil
 	}
 	if question == "" {
-		return joinBudget(chunks, SmallDoc), min(len(chunks), countBudget(chunks, SmallDoc)), len(chunks), nil
+		return joinBudget(chunks, SmallDoc), min(len(chunks), countBudget(chunks, SmallDoc)), len(chunks), "head", 0, nil
 	}
-	vecs, err := e.embed(ctx, append([]string{question}, capEmbed(chunks)...))
-	if err != nil || len(vecs) < 2 {
-		return joinBudget(chunks, SmallDoc), min(len(chunks), countBudget(chunks, SmallDoc)), len(chunks), err
-	}
-	q := vecs[0]
-	type scored struct {
-		i int
-		s float64
-	}
-	var ss []scored
-	for i, c := range chunks {
-		if i+1 >= len(vecs) {
-			break
-		}
-		ss = append(ss, scored{i: i, s: 0.7*cosine(q, vecs[i+1]) + 0.3*lexicalOverlap(question, c)})
-	}
-	picked := map[int]struct{}{}
-	used := 0
-	if len(chunks) > 0 {
-		picked[0] = struct{}{}
-		used = EstTokens(chunks[0])
-	}
-	for len(picked) < len(ss) {
-		best, bi := -1.0, -1
-		for _, x := range ss {
-			if _, ok := picked[x.i]; ok {
-				continue
-			}
-			if x.s > best {
-				best, bi = x.s, x.i
-			}
-		}
-		if bi < 0 {
-			break
-		}
-		need := EstTokens(chunks[bi])
-		if used+need > SmallDoc && used > 0 {
-			break
-		}
-		picked[bi] = struct{}{}
-		used += need
-	}
-	var ordered []string
-	for i := range chunks {
-		if _, ok := picked[i]; ok {
-			ordered = append(ordered, chunks[i])
-		}
-	}
-	return strings.Join(ordered, "\n\n"), len(ordered), len(chunks), nil
+	return e.hybridOrBM25(ctx, chunks, question, contentHash, callerClass)
 }
 
 func capEmbed(chunks []string) []string {
diff --git a/internal/digest/digest_test.go b/internal/digest/digest_test.go
index cbbcdfe..a0373ad 100644
--- a/internal/digest/digest_test.go
+++ b/internal/digest/digest_test.go
@@ -374,7 +374,7 @@ func TestPinChunk0Infobox(t *testing.T) {
 	if EstTokens(cleaned) <= SmallDoc {
 		t.Fatalf("fixture too small: %d", EstTokens(cleaned))
 	}
-	body, nUsed, nTotal, err := e.selectText(context.Background(), cleaned, "when was the initial release?")
+	body, nUsed, nTotal, _, _, err := e.selectText(context.Background(), cleaned, "when was the initial release?", "", dcache.ClassFleet)
 	if err != nil {
 		t.Fatal(err)
 	}
diff --git a/internal/digest/retrieval.go b/internal/digest/retrieval.go
new file mode 100644
index 0000000..01d0558
--- /dev/null
+++ b/internal/digest/retrieval.go
@@ -0,0 +1,149 @@
+package digest
+
+import (
+	"context"
+	"strings"
+
+	"git.wntrmute.dev/kyle/sift/internal/dcache"
+)
+
+// hybridOrBM25 scores a chunked document either hybrid (cosine + lexical overlap) or, when there
+// are too many uncached chunks to embed inline, lexical-only BM25. mode is "hybrid" or "bm25".
+func (e *Engine) hybridOrBM25(ctx context.Context, chunks []string, question, contentHash, callerClass string) (string, int, int, string, int, error) {
+	key := func(i int) string {
+		return dcache.EmbedKey(contentHash+"/sp1200", i, e.embedModel(), callerClass)
+	}
+
+	if e.Cache == nil {
+		if len(chunks) <= EmbedSyncMax {
+			vecs, err := e.embed(ctx, append([]string{question}, capEmbed(chunks)...))
+			if err != nil {
+				return joinBudget(chunks, SmallDoc), min(len(chunks), countBudget(chunks, SmallDoc)), len(chunks), "hybrid", 0, err
+			}
+			chunkVecs := make([][]float64, len(chunks))
+			for i := range chunks {
+				chunkVecs[i] = vecs[i+1]
+			}
+			body, used := greedyBudget(chunks, hybridScores(chunks, question, vecs[0], chunkVecs), SmallDoc)
+			return body, used, len(chunks), "hybrid", len(chunks), nil
+		}
+		body, used := greedyBudget(chunks, bm25Scores(chunks, question), SmallDoc)
+		return body, used, len(chunks), "bm25", 0, nil
+	}
+
+	// Cache present: look up every chunk's vector.
+	var cached []int
+	var cachedVecs [][]float64
+	var uncached []int
+	for i := range chunks {
+		if v, ok := e.Cache.GetEmbed(key(i)); ok {
+			cached = append(cached, i)
+			cachedVecs = append(cachedVecs, v)
+			continue
+		}
+		uncached = append(uncached, i)
+	}
+
+	if len(uncached) <= EmbedSyncMax {
+		in := append([]string{question}, capEmbed(uncachedChunks(chunks, uncached))...)
+		vecs, err := e.embed(ctx, in)
+		if err != nil {
+			return joinBudget(chunks, SmallDoc), min(len(chunks), countBudget(chunks, SmallDoc)), len(chunks), "hybrid", len(cached), err
+		}
+		for j, i := range uncached {
+			if len(vecs[j+1]) > 0 { // a vector the server left out is not cached as empty
+				e.Cache.PutEmbed(key(i), vecs[j+1])
+			}
+		}
+		chunkVecs := make([][]float64, len(chunks))
+		for k, i := range cached {
+			chunkVecs[i] = cachedVecs[k]
+		}
+		for j, i := range uncached {
+			chunkVecs[i] = vecs[j+1]
+		}
+		body, used := greedyBudget(chunks, hybridScores(chunks, question, vecs[0], chunkVecs), SmallDoc)
+		return body, used, len(chunks), "hybrid", len(chunks), nil
+	}
+
+	body, used := greedyBudget(chunks, bm25Scores(chunks, question), SmallDoc)
+	e.queueForEmbed(chunks, contentHash, callerClass)
+	return body, used, len(chunks), "bm25", len(cached), nil
+}
+
+func uncachedChunks(chunks []string, uncached []int) []string {
+	out := make([]string, len(uncached))
+	for j, i := range uncached {
+		out[j] = chunks[i]
+	}
+	return out
+}
+
+// hybridScores builds the hybrid scorer 0.7*cosine(q, v_i) + 0.3*lexicalOverlap(question, chunk),
+// where chunkVecs[i] is chunk i's vector.
+func hybridScores(chunks []string, question string, q []float64, chunkVecs [][]float64) func(int) float64 {
+	return func(i int) float64 {
+		return 0.7*cosine(q, chunkVecs[i]) + 0.3*lexicalOverlap(question, chunks[i])
+	}
+}
+
+// bm25Scores builds the BM25 scorer, normalised by its maximum so scores land in [0, 1].
+func bm25Scores(chunks []string, question string) func(int) float64 {
+	scores := NewBM25(chunks).Scores(question)
+	var max float64
+	for _, s := range scores {
+		if s > max {
+			max = s
+		}
+	}
+	if max == 0 {
+		return func(int) float64 { return 0 }
+	}
+	return func(i int) float64 { return scores[i] / max }
+}
+
+// greedyBudget picks chunk 0 first, then the highest-scoring remaining chunks while the total
+// stays within budget tokens, and returns them in document order with the count used.
+func greedyBudget(chunks []string, score func(int) float64, budget int) (string, int) {
+	type scored struct {
+		i int
+		s float64
+	}
+	var ss []scored
+	for i := range chunks {
+		ss = append(ss, scored{i: i, s: score(i)})
+	}
+	picked := map[int]struct{}{}
+	used := 0
+	if len(chunks) > 0 {
+		picked[0] = struct{}{}
+		used = EstTokens(chunks[0])
+	}
+	for len(picked) < len(ss) {
+		best, bi := -1.0, -1
+		for _, x := range ss {
+			if _, ok := picked[x.i]; ok {
+				continue
+			}
+			if x.s > best {
+				best, bi = x.s, x.i
+			}
+		}
+		if bi < 0 {
+			break
+		}
+		need := EstTokens(chunks[bi])
+		if used+need > budget && used > 0 {
+			break
+		}
+		picked[bi] = struct{}{}
+		used += need
+	}
+	var ordered []string
+	for i := range chunks {
+		if _, ok := picked[i]; ok {
+			ordered = append(ordered, chunks[i])
+		}
+	}
+	return strings.Join(ordered, "\n\n"), len(ordered)
+}
diff --git a/internal/digest/retrieval_test.go b/internal/digest/retrieval_test.go
new file mode 100644
index 0000000..c7193c0
--- /dev/null
+++ b/internal/digest/retrieval_test.go
@@ -0,0 +1,247 @@
+package digest
+
+// P5b task 02: retrieval for long documents. Embeddings are cached per chunk; a document with
+// more uncached chunks than EmbedSyncMax is answered at once from BM25 while its chunks are
+// embedded in the background, and later questions use the hybrid score.
+
+import (
+	"context"
+	"encoding/json"
+	"fmt"
+	"hash/fnv"
+	"net/http"
+	"net/http/httptest"
+	"path/filepath"
+	"strings"
+	"sync"
+	"sync/atomic"
+	"testing"
+	"time"
+
+	"git.wntrmute.dev/kyle/sift/internal/dcache"
+)
+
+// fakeDixie serves /embed (a bag-of-words hash into 64 dims, so cosine similarity means
+// something) and /chat (the SSE stub). It counts embedded inputs and can hold /embed shut.
+type fakeDixie struct {
+	srv      *httptest.Server
+	embedded atomic.Int64 // inputs embedded, questions included
+	hold     chan struct{}
+	holdOnce sync.Once
+	lastChat atomic.Pointer[chatReq]
+}
+
+func newFakeDixie(t *testing.T, hold bool) *fakeDixie {
+	f := &fakeDixie{}
+	if hold {
+		f.hold = make(chan struct{})
+	}
+	var disc atomic.Bool
+	mux := http.NewServeMux()
+	mux.HandleFunc("/embed", func(w http.ResponseWriter, r *http.Request) {
+		if f.hold != nil {
+			select {
+			case <-f.hold:
+			case <-r.Context().Done():
+				return
+			}
+		}
+		var body struct {
+			Input []string `json:"input"`
+		}
+		_ = json.NewDecoder(r.Body).Decode(&body)
+		var data []map[string]any
+		for i, s := range body.Input {
+			data = append(data, map[string]any{"index": i, "embedding": bow(s)})
+		}
+		f.embedded.Add(int64(len(body.Input)))
+		_ = json.NewEncoder(w).Encode(map[string]any{"data": data})
+	})
+	mux.Handle("/chat", sseHandler(t, "ok", &f.lastChat, &disc))
+	f.srv = httptest.NewServer(mux)
+	t.Cleanup(func() { f.release(); f.srv.Close() })
+	return f
+}
+
+func (f *fakeDixie) release() {
+	if f.hold != nil {
+		f.holdOnce.Do(func() { close(f.hold) })
+	}
+}
+
+func bow(s string) []float64 {
+	v := make([]float64, 64)
+	for t := range terms(s) {
+		h := fnv.New32a()
+		_, _ = h.Write([]byte(t))
+		v[h.Sum32()%64]++
+	}
+	return v
+}
+
+func (f *fakeDixie) engine(t *testing.T, gate *Gate, withCache bool) *Engine {
+	e := &Engine{ChatURL: f.srv.URL + "/chat", EmbedURL: f.srv.URL + "/embed", Gate: gate, Client: f.srv.Client()}
+	if withCache {
+		db, err := dcache.Open(filepath.Join(t.TempDir(), "c.db"), 0, nil)
+		if err != nil {
+			t.Fatal(err)
+		}
+		t.Cleanup(func() { _ = db.Close() })
+		e.Cache = db
+	}
+	return e
+}
+
+// longDoc is n pages of distinct filler; the page named rare carries a rare term.
+func longDoc(n, rare int) string {
+	var b strings.Builder
+	words := []string{"harbour", "vessel", "cargo", "anchor", "pilot", "tug", "berth", "quay", "hull", "keel", "mast", "deck"}
+	for p := 1; p <= n; p++ {
+		if p > 1 {
+			b.WriteString("\n\n")
+		}
+		fmt.Fprintf(&b, "--- page %d ---\n\n", p)
+		for l := 0; l < 40; l++ {
+			fmt.Fprintf(&b, "page %d line %d %s %s %s %s\n", p, l, words[(p+l)%12], words[(p*3+l)%12], words[(p*5+l)%12], words[(p*7+l)%12])
+		}
+		if p == rare {
+			b.WriteString("the zanzibarite cargo manifest was signed by the second officer\n")
+		}
+	}
+	return b.String()
+}
+
+func chatDoc(f *fakeDixie) string {
+	req := f.lastChat.Load()
+	if req == nil {
+		return ""
+	}
+	var s strings.Builder
+	for _, m := range req.Messages {
+		s.WriteString(m.Content)
+	}
+	return s.String()
+}
+
+func TestEmbeddingsAreCachedAcrossQuestions(t *testing.T) {
+	f := newFakeDixie(t, false)
+	e := f.engine(t, NewGate(2, 8, 5*time.Second), true)
+	doc := longDoc(30, 0) // ~11.5k tokens: over SmallDoc (so not "whole"), ~10 chunks: under EmbedSyncMax
+	if EstTokens(doc) <= SmallDoc {
+		t.Fatalf("test document is %d tokens; it must exceed SmallDoc (%d) to reach retrieval", EstTokens(doc), SmallDoc)
+	}
+	r := e.Run(context.Background(), doc, "which berth did the tug use?", "https://ex.test/a.pdf", dcache.ClassFleet)
+	if r.Fallback != "" || r.Retrieval != "hybrid" {
+		t.Fatalf("first question: fallback %q retrieval %q", r.Fallback, r.Retrieval)
+	}
+	n := len(SplitPages(doc, ChunkTokens))
+	if got := f.embedded.Load(); got != int64(n+1) {
+		t.Fatalf("first question embedded %d inputs, want %d chunks + the question", got, n)
+	}
+	r = e.Run(context.Background(), doc, "where was the pilot?", "https://ex.test/a.pdf", dcache.ClassFleet)
+	if r.Fallback != "" || r.Retrieval != "hybrid" || r.Embedded != n {
+		t.Fatalf("second question: %+v", r)
+	}
+	if got := f.embedded.Load(); got != int64(n+2) {
+		t.Errorf("second question embedded %d inputs in total, want %d: only its own question is new", got, n+2)
+	}
+}
+
+// A long document is answered from BM25 without waiting for a single embedding, and becomes
+// hybrid once the background has embedded every chunk.
+func TestLongDocumentBM25ThenHybrid(t *testing.T) {
+	f := newFakeDixie(t, true) // /embed held shut until release
+	e := f.engine(t, NewGate(2, 8, 5*time.Second), true)
+	doc := longDoc(300, 250)
+	n := len(SplitPages(doc, ChunkTokens))
+	if n <= EmbedSyncMax {
+		t.Fatalf("test document has %d chunks; it must exceed EmbedSyncMax (%d)", n, EmbedSyncMax)
+	}
+	start := time.Now()
+	r := e.Run(context.Background(), doc, "who signed the zanzibarite manifest?", "https://ex.test/big.pdf", dcache.ClassFleet)
+	if d := time.Since(start); d > 10*time.Second {
+		t.Fatalf("first answer took %v: it waited on embeddings", d)
+	}
+	if r.Fallback != "" || r.Retrieval != "bm25" || r.Embedded != 0 {
+		t.Fatalf("first answer: %+v, want retrieval bm25 with 0 embedded", r)
+	}
+	if doc := chatDoc(f); !strings.Contains(doc, "zanzibarite") || !strings.Contains(doc, "page 250") {
+		t.Errorf("BM25 did not bring page 250 (the only one with the term) into the prompt")
+	}
+
+	f.release()
+	ctx, cancel := context.WithTimeout(context.Background(), 60*time.Second)
+	defer cancel()
+	if err := e.WaitBackground(ctx); err != nil {
+		t.Fatalf("background embedding did not finish: %v", err)
+	}
+	r = e.Run(context.Background(), doc, "who signed the zanzibarite manifest?", "https://ex.test/big.pdf", dcache.ClassFleet)
+	if r.Fallback != "" || r.Retrieval != "hybrid" || r.Embedded != n {
+		t.Fatalf("after background: %+v, want hybrid with all %d embedded", r, n)
+	}
+	if doc := chatDoc(f); !strings.Contains(doc, "zanzibarite") {
+		t.Errorf("hybrid lost the page with the term")
+	}
+}
+
+// Two questions on the same long document queue it once: every chunk is embedded once.
+func TestBackgroundDedupes(t *testing.T) {
+	f := newFakeDixie(t, true)
+	e := f.engine(t, NewGate(2, 8, 5*time.Second), true)
+	doc := longDoc(200, 0)
+	n := len(SplitPages(doc, ChunkTokens))
+	e.Run(context.Background(), doc, "first question about the quay", "https://ex.test/b.pdf", dcache.ClassFleet)
+	e.Run(context.Background(), doc, "second question about the keel", "https://ex.test/b.pdf", dcache.ClassFleet)
+	f.release()
+	ctx, cancel := context.WithTimeout(context.Background(), 60*time.Second)
+	defer cancel()
+	if err := e.WaitBackground(ctx); err != nil {
+		t.Fatal(err)
+	}
+	if got := f.embedded.Load(); got > int64(n) {
+		t.Errorf("embedded %d inputs for a %d-chunk document: queued twice", got, n)
+	}
+}
+
+// Background work takes the gate one batch at a time, so an interactive digest is not starved.
+func TestBackgroundYieldsTheGate(t *testing.T) {
+	f := newFakeDixie(t, false)
+	e := f.engine(t, NewGate(1, 8, 10*time.Second), true)
+	e.Run(context.Background(), longDoc(400, 0), "start the background", "https://ex.test/c.pdf", dcache.ClassFleet)
+	start := time.Now()
+	r := e.Run(context.Background(), "a short page about a tug and a quay", "what is here?", "https://ex.test/small", dcache.ClassFleet)
+	if r.Fallback != "" {
+		t.Fatalf("interactive digest fell back (%q) while background embedding ran", r.Fallback)
+	}
+	if d := time.Since(start); d > 5*time.Second {
+		t.Errorf("interactive digest waited %v behind background embedding", d)
+	}
+	ctx, cancel := context.WithTimeout(context.Background(), 60*time.Second)
+	defer cancel()
+	_ = e.WaitBackground(ctx)
+}
+
+// Without a cache there is nowhere to keep background work: a long document is BM25 and
+// nothing is embedded.
+func TestNoCacheLongDocumentIsBM25Only(t *testing.T) {
+	f := newFakeDixie(t, false)
+	e := f.engine(t, NewGate(2, 8, 5*time.Second), false)
+	r := e.Run(context.Background(), longDoc(300, 250), "who signed the zanzibarite manifest?", "https://ex.test/d.pdf", dcache.ClassFleet)
+	if r.Fallback != "" || r.Retrieval != "bm25" {
+		t.Fatalf("%+v, want bm25", r)
+	}
+	time.Sleep(200 * time.Millisecond)
+	if got := f.embedded.Load(); got != 0 {
+		t.Errorf("embedded %d inputs with no cache to keep them in", got)
+	}
+}
+
+// A document that fits the digest budget whole is sent whole, as today.
+func TestSmallDocumentIsWhole(t *testing.T) {
+	f := newFakeDixie(t, false)
+	e := f.engine(t, NewGate(2, 8, 5*time.Second), true)
+	r := e.Run(context.Background(), "--- page 1 ---\n\nOne short page.", "what is it?", "https://ex.test/e.pdf", dcache.ClassFleet)
+	if r.Fallback != "" || r.Retrieval != "whole" {
+		t.Fatalf("%+v, want whole", r)
+	}
+}
diff --git a/internal/digest/review_test.go b/internal/digest/review_test.go
new file mode 100644
index 0000000..ca9a918
--- /dev/null
+++ b/internal/digest/review_test.go
@@ -0,0 +1,96 @@
+package digest
+
+// P5b owner review: regression tests for the background embedder.
+
+import (
+	"context"
+	"encoding/json"
+	"net/http"
+	"net/http/httptest"
+	"sync/atomic"
+	"testing"
+	"time"
+)
+
+// flakyDixie is fakeDixie whose /embed answers 500 to its first failN requests.
+func flakyDixie(t *testing.T, failN int64) (*fakeDixie, *atomic.Int64) {
+	f := &fakeDixie{}
+	var calls atomic.Int64
+	var disc atomic.Bool
+	mux := http.NewServeMux()
+	mux.HandleFunc("/embed", func(w http.ResponseWriter, r *http.Request) {
+		if calls.Add(1) <= failN {
+			http.Error(w, "boom", http.StatusInternalServerError)
+			return
+		}
+		var body struct {
+			Input []string `json:"input"`
+		}
+		_ = json.NewDecoder(r.Body).Decode(&body)
+		var data []map[string]any
+		for i, s := range body.Input {
+			data = append(data, map[string]any{"index": i, "embedding": bow(s)})
+		}
+		f.embedded.Add(int64(len(body.Input)))
+		_ = json.NewEncoder(w).Encode(map[string]any{"data": data})
+	})
+	mux.Handle("/chat", sseHandler(t, "ok", &f.lastChat, &disc))
+	f.srv = httptest.NewServer(mux)
+	t.Cleanup(f.srv.Close)
+	return f, &calls
+}
+
+// A document whose background embedding failed is queued again by a later question; it must
+// not stay "seen" (and so BM25-only) for the life of the process.
+func TestBackgroundRequeuesAfterFailure(t *testing.T) {
+	f, _ := flakyDixie(t, 1)
+	e := f.engine(t, NewGate(2, 8, 5*time.Second), true)
+	doc := longDoc(300, 250)
+	n := len(SplitPages(doc, ChunkTokens))
+	wait := func() {
+		t.Helper()
+		ctx, cancel := context.WithTimeout(context.Background(), 30*time.Second)
+		defer cancel()
+		if err := e.WaitBackground(ctx); err != nil {
+			t.Fatal(err)
+		}
+	}
+	q := "who signed the zanzibarite manifest?"
+	if r := e.Run(context.Background(), doc, q, "https://ex.test/f.pdf", "fleet"); r.Retrieval != "bm25" {
+		t.Fatalf("first: %+v", r)
+	}
+	wait() // the first batch failed: the document was dropped
+	if r := e.Run(context.Background(), doc, q, "https://ex.test/f.pdf", "fleet"); r.Retrieval != "bm25" {
+		t.Fatalf("second: %+v, want bm25 (nothing embedded yet)", r)
+	}
+	wait() // re-queued by the second question, and embedded this time
+	r := e.Run(context.Background(), doc, q, "https://ex.test/f.pdf", "fleet")
+	if r.Retrieval != "hybrid" || r.Embedded != n {
+		t.Fatalf("third: %+v, want hybrid with all %d embedded", r, n)
+	}
+}
+
+// The background worker waits for a busy gate; it does not give up on the document.
+func TestBackgroundWaitsForBusyGate(t *testing.T) {
+	f := newFakeDixie(t, false)
+	gate := NewGate(1, 0, 50*time.Millisecond) // no queue: a busy gate refuses at once
+	e := f.engine(t, gate, true)
+	doc := longDoc(100, 0)
+	n := len(SplitPages(doc, ChunkTokens))
+	if ok, _ := gate.Acquire(context.Background()); !ok {
+		t.Fatal("could not take the gate")
+	}
+	// Run takes the gate before it chooses a retrieval mode, so queue the document directly.
+	chunks := SplitPages(doc, ChunkTokens)
+	e.queueForEmbed(chunks, "hash-g", "fleet")
+	time.Sleep(2500 * time.Millisecond) // longer than the old single retry
+	gate.Release()
+	ctx, cancel := context.WithTimeout(context.Background(), 30*time.Second)
+	defer cancel()
+	if err := e.WaitBackground(ctx); err != nil {
+		t.Fatal(err)
+	}
+	if got := f.embedded.Load(); got != int64(n) {
+		t.Fatalf("embedded %d of %d chunks: the worker gave up on a busy gate", got, n)
+	}
+}
diff --git a/internal/digest/splitpages.go b/internal/digest/splitpages.go
new file mode 100644
index 0000000..f4406d9
--- /dev/null
+++ b/internal/digest/splitpages.go
@@ -0,0 +1,74 @@
+package digest
+
+import (
+	"fmt"
+	"regexp"
+	"strconv"
+	"strings"
+)
+
+// pageMarker matches a page header line like "--- page 7 ---"; the number is group 1.
+var pageMarker = regexp.MustCompile(`^--- page (\d+) ---$`)
+
+// SplitPages splits text into chunks of at most maxTok tokens (EstTokens) on line
+// boundaries, like Split, but page-aware. The text is expected to carry "--- page N ---"
+// markers (as pdfdoc.Full produces). A marker line sets the current page; a chunk that
+// starts after the first marker but not on a marker line is prefixed with
+// "--- page N (cont.) ---\n\n" for the page its first line belongs to, so every chunk
+// names the page it cites. Text with no marker lines yields exactly Split's result.
+func SplitPages(text string, maxTok int) []string {
+	if maxTok <= 0 {
+		maxTok = ChunkTokens
+	}
+	lines := strings.Split(text, "\n")
+	var chunks []string
+	var buf strings.Builder
+	var firstLine string
+	var chunkPage int
+	hasLines, startedAfterMarker, markerSeen := false, false, false
+	currentPage := 0
+
+	flush := func() {
+		s := strings.TrimSpace(buf.String())
+		if s == "" {
+			buf.Reset()
+			hasLines = false
+			return
+		}
+		if pageMarker.MatchString(firstLine) || !startedAfterMarker {
+			chunks = append(chunks, s)
+		} else {
+			chunks = append(chunks, fmt.Sprintf("--- page %d (cont.) ---\n\n", chunkPage)+s)
+		}
+		buf.Reset()
+		hasLines = false
+	}
+
+	for _, line := range lines {
+		if m := pageMarker.FindStringSubmatch(line); m != nil {
+			if n, err := strconv.Atoi(m[1]); err == nil {
+				currentPage = n
+				markerSeen = true
+			}
+		}
+		next := line + "\n"
+		if hasLines {
+			est := EstTokens(buf.String() + next)
+			if startedAfterMarker {
+				est += EstTokens(fmt.Sprintf("--- page %d (cont.) ---\n\n", chunkPage))
+			}
+			if est > maxTok {
+				flush()
+			}
+		}
+		if !hasLines {
+			firstLine = line
+			chunkPage = currentPage
+			startedAfterMarker = markerSeen
+			hasLines = true
+		}
+		buf.WriteString(next)
+	}
+	flush()
+	return chunks
+}
diff --git a/internal/digest/splitpages_test.go b/internal/digest/splitpages_test.go
new file mode 100644
index 0000000..785698b
--- /dev/null
+++ b/internal/digest/splitpages_test.go
@@ -0,0 +1,90 @@
+package digest
+
+// P5b task 01: SplitPages keeps every chunk of a PDF's text attached to its page, so a digest
+// built from a chunk that starts mid-page can still cite the page.
+
+import (
+	"fmt"
+	"regexp"
+	"strings"
+	"testing"
+)
+
+// pagesText builds n pages of about perPage tokens each, every line naming its page.
+func pagesText(n, perPage int) string {
+	var b strings.Builder
+	for p := 1; p <= n; p++ {
+		if p > 1 {
+			b.WriteString("\n\n")
+		}
+		fmt.Fprintf(&b, "--- page %d ---\n\n", p)
+		for l := 0; l*12 < perPage; l++ {
+			fmt.Fprintf(&b, "page %d line %d alpha bravo charlie delta echo foxtrot golf hotel\n", p, l)
+		}
+	}
+	return b.String()
+}
+
+var markerRE = regexp.MustCompile(`^--- page (\d+)( \(cont\.\))? ---`)
+
+func TestSplitPagesEveryChunkNamesItsPage(t *testing.T) {
+	text := pagesText(4, 3000) // each page ~3000 tokens: several chunks per page at 1200
+	chunks := SplitPages(text, ChunkTokens)
+	if len(chunks) < 8 {
+		t.Fatalf("%d chunks, want at least 8 for 4 × 3000 tokens at %d", len(chunks), ChunkTokens)
+	}
+	cont := 0
+	for i, c := range chunks {
+		m := markerRE.FindStringSubmatch(c)
+		if m == nil {
+			t.Fatalf("chunk %d does not start with a page marker: %.80q", i, c)
+		}
+		if m[2] != "" {
+			cont++
+			// A continuation marker names the page the chunk's first line belongs to.
+			first := strings.SplitN(strings.TrimPrefix(c, m[0]), "\n", 3)
+			line := strings.TrimSpace(strings.Join(first, " "))
+			if !strings.Contains(line, "page "+m[1]+" line ") {
+				t.Errorf("chunk %d marked page %s but starts with %.60q", i, m[1], line)
+			}
+		}
+		if EstTokens(c) > ChunkTokens+20 {
+			t.Errorf("chunk %d is %d tokens, over the %d budget (plus a marker line)", i, EstTokens(c), ChunkTokens)
+		}
+	}
+	if cont == 0 {
+		t.Error("no continuation markers: pages longer than a chunk must produce some")
+	}
+}
+
+// Nothing is lost or duplicated: removing the continuation markers gives back the original lines.
+func TestSplitPagesPreservesContent(t *testing.T) {
+	text := pagesText(3, 2500)
+	var got []string
+	for _, c := range SplitPages(text, ChunkTokens) {
+		for _, line := range strings.Split(c, "\n") {
+			if strings.HasSuffix(line, " (cont.) ---") || strings.TrimSpace(line) == "" {
+				continue
+			}
+			got = append(got, line)
+		}
+	}
+	var want []string
+	for _, line := range strings.Split(text, "\n") {
+		if strings.TrimSpace(line) != "" {
+			want = append(want, line)
+		}
+	}
+	if strings.Join(got, "\n") != strings.Join(want, "\n") {
+		t.Errorf("content changed: %d lines back, %d in", len(got), len(want))
+	}
+}
+
+// Text with no markers splits exactly as Split does.
+func TestSplitPagesWithoutMarkersIsSplit(t *testing.T) {
+	text := strings.Repeat("plain words without any page markers at all\n", 2000)
+	a, b := SplitPages(text, ChunkTokens), Split(text, ChunkTokens)
+	if strings.Join(a, "\x00") != strings.Join(b, "\x00") {
+		t.Errorf("SplitPages differs from Split on unmarked text: %d vs %d chunks", len(a), len(b))
+	}
+}
diff --git a/skill/SKILL.md b/skill/SKILL.md
index 4a0fe97..7ea19c4 100644
--- a/skill/SKILL.md
+++ b/skill/SKILL.md
@@ -61,7 +61,8 @@ PDFs work: `sift fetch` extracts them and returns the text. A short one comes ba
 long one comes back as a map — an outline with page numbers, then the first pages. Then:
 
 - `sift fetch URL --pages 41-60` for a page range, `--grep 'pattern'` for matching lines, or
-  `--question "…"` for a digest that cites each fact as `(p. N)`.
+  `--question "…"` for a digest that cites each fact as `(p. N)`; `--question` works on long
+  PDFs, and the first answer may be `bm25` (lexical) — ask again later for a sharper one.
 - Scanned PDFs have no text layer: sift reports `no text layer (scanned PDF?)` — point it at an
   OCR source rather than trying to fix it here.
 - A range returns at most 100 pages and grep at most 100 matches. On a very long document