diff --git a/4-Infrastructure/shim/embed_arxiv.py b/4-Infrastructure/shim/embed_arxiv.py
new file mode 100644
index 00000000..3dc60200
--- /dev/null
+++ b/4-Infrastructure/shim/embed_arxiv.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+"""Embed arxiv abstracts using static-retrieval-mrl-en-v1 (1024-dim)."""
+
+import subprocess
+import time
+
+MODEL_NAME = "sentence-transformers/static-retrieval-mrl-en-v1"
+BATCH_SIZE = 512
+TSV_PATH = "/tmp/embeddings.tsv"
+
+def psql(sql, timeout=60):
+    r = subprocess.run(
+        ['podman', 'exec', 'arxiv-pg', 'psql', '-U', 'postgres', '-d', 'arxiv',
+         '-t', '-A', '-c', sql],
+        capture_output=True, text=True, timeout=timeout
+    )
+    return r.stdout.strip(), r.stderr.strip()
+
+def main():
+    from sentence_transformers import SentenceTransformer
+
+    print(f"Model: {MODEL_NAME}")
+    model = SentenceTransformer(MODEL_NAME)
+    dims = model.get_sentence_embedding_dimension()
+    print(f"Dims: {dims}")
+
+    # Count remaining
+    count, _ = psql("SELECT COUNT(*) FROM arxiv_papers WHERE embedding IS NULL")
+    total = int(count)
+    print(f"Papers to embed: {total}")
+
+    if total == 0:
+        print("All done.")
+        return
+
+    # Fetch all at once
+    print("Fetching papers...")
+    out, _ = psql(
+        "SELECT paper_id || E'\\t' || COALESCE(title,'') || ' ' || COALESCE(abstract,'') "
+        "FROM arxiv_papers WHERE embedding IS NULL ORDER BY paper_id",
+        timeout=600
+    )
+    
+    pids, texts = [], []
+    for line in out.strip().split('\n'):
+        parts = line.split('\t', 1)
+        if len(parts) == 2:
+            pids.append(parts[0])
+            texts.append(parts[1].strip())
+    
+    print(f"Fetched {len(pids)} papers")
+
+    # Embed and write TSV
+    start = time.time()
+    f = open(TSV_PATH, 'w')
+    embedded = 0
+
+    for i in range(0, len(pids), BATCH_SIZE):
+        batch_pids = pids[i:i+BATCH_SIZE]
+        batch_texts = texts[i:i+BATCH_SIZE]
+
+        embeddings = model.encode(batch_texts, show_progress_bar=False, 
+                                  normalize_embeddings=True, batch_size=256)
+
+        for pid, emb in zip(batch_pids, embeddings):
+            emb_str = '[' + ','.join(f'{x:.6f}' for x in emb) + ']'
+            f.write(f"{pid}\t{emb_str}\n")
+
+        embedded += len(batch_pids)
+        elapsed = time.time() - start
+        rate = embedded / elapsed if elapsed > 0 else 0
+        eta = (len(pids) - embedded) / rate if rate > 0 else 0
+        
+        if embedded % (BATCH_SIZE * 10) == 0 or embedded >= len(pids):
+            print(f"  {embedded}/{len(pids)} ({embedded*100/len(pids):.1f}%) | "
+                  f"{rate:.0f}/s | ETA: {eta/60:.1f} min")
+
+    f.close()
+    elapsed = time.time() - start
+    print(f"Embedding done: {embedded} in {elapsed/60:.1f} min ({embedded/elapsed:.0f}/s)")
+
+    # Bulk load
+    print("Loading into database...")
+    subprocess.run(['podman', 'cp', TSV_PATH, 'arxiv-pg:/tmp/embeddings.tsv'],
+                  capture_output=True, timeout=300)
+
+    psql(f"CREATE TEMP TABLE IF NOT EXISTS tmp_emb (pid text, emb vector({dims})); TRUNCATE tmp_emb;",
+         timeout=30)
+
+    r = subprocess.run(
+        ['podman', 'exec', '-i', 'arxiv-pg', 'psql', '-U', 'postgres', '-d', 'arxiv',
+         '-c', f"\\copy tmp_emb FROM '/tmp/embeddings.tsv' WITH (FORMAT csv, DELIMITER E'\\t')"],
+        capture_output=True, text=True, timeout=600
+    )
+    print(f"COPY: {r.stdout.strip() or r.stderr.strip()}")
+
+    psql("UPDATE arxiv_papers SET embedding = t.emb FROM tmp_emb t WHERE arxiv_papers.paper_id = t.pid;",
+         timeout=600)
+
+    count, _ = psql("SELECT COUNT(*) FROM arxiv_papers WHERE embedding IS NOT NULL")
+    print(f"Total embedded: {count}")
+    print(f"Total time: {(time.time() - start)/60:.1f} min")
+
+if __name__ == "__main__":
+    main()
diff --git a/4-Infrastructure/shim/hybrid_search.sql b/4-Infrastructure/shim/hybrid_search.sql
new file mode 100644
index 00000000..cce18a0a
--- /dev/null
+++ b/4-Infrastructure/shim/hybrid_search.sql
@@ -0,0 +1,67 @@
+-- hybrid_search.sql
+-- Hybrid keyword + semantic search using pg_trgm + pgvector RRF
+-- 
+-- Usage:
+--   SELECT * FROM hybrid_search('braid eigensolid convergence', 
+--     (SELECT embedding FROM arxiv_papers WHERE paper_id = 'some_id'), 10);
+
+CREATE OR REPLACE FUNCTION hybrid_search(
+    query_text TEXT,
+    query_embedding vector(1024),
+    top_k INT DEFAULT 10
+) RETURNS TABLE (
+    paper_id TEXT,
+    title TEXT,
+    trigram_rank BIGINT,
+    vector_rank BIGINT,
+    rrf_score DOUBLE PRECISION
+) AS $$
+WITH trigram_candidates AS (
+    SELECT p.paper_id, p.title,
+           ROW_NUMBER() OVER (ORDER BY similarity(p.title, query_text) DESC) AS trigram_rank
+    FROM arxiv_papers p
+    WHERE p.title % query_text
+    LIMIT 50
+),
+vector_candidates AS (
+    SELECT p.paper_id, p.title,
+           ROW_NUMBER() OVER (ORDER BY p.embedding <=> query_embedding) AS vector_rank
+    FROM arxiv_papers p
+    WHERE p.embedding IS NOT NULL
+    ORDER BY p.embedding <=> query_embedding
+    LIMIT 50
+)
+SELECT 
+    COALESCE(t.paper_id, v.paper_id)::TEXT AS paper_id,
+    COALESCE(t.title, v.title)::TEXT AS title,
+    t.trigram_rank,
+    v.vector_rank,
+    (COALESCE(1.0 / (60 + t.trigram_rank), 0) +
+     COALESCE(1.0 / (60 + v.vector_rank), 0))::DOUBLE PRECISION AS rrf_score
+FROM trigram_candidates t
+FULL OUTER JOIN vector_candidates v ON t.paper_id = v.paper_id
+ORDER BY rrf_score DESC
+LIMIT top_k;
+$$ LANGUAGE sql STABLE;
+
+-- Variant: embed query text inline (for when we don't have a pre-computed embedding)
+-- This uses a placeholder — actual embedding must be computed in Python
+CREATE OR REPLACE FUNCTION hybrid_search_text(
+    query_text TEXT,
+    top_k INT DEFAULT 10
+) RETURNS TABLE (
+    paper_id TEXT,
+    title TEXT,
+    trigram_rank BIGINT,
+    rrf_score DOUBLE PRECISION
+) AS $$
+SELECT 
+    p.paper_id::TEXT,
+    p.title::TEXT,
+    ROW_NUMBER() OVER (ORDER BY similarity(p.title, query_text) DESC) AS trigram_rank,
+    similarity(p.title, query_text)::DOUBLE PRECISION AS rrf_score
+FROM arxiv_papers p
+WHERE p.title % query_text
+ORDER BY similarity(p.title, query_text) DESC
+LIMIT top_k;
+$$ LANGUAGE sql STABLE;
diff --git a/4-Infrastructure/shim/jaccard_hybrid.py b/4-Infrastructure/shim/jaccard_hybrid.py
new file mode 100644
index 00000000..104c0d78
--- /dev/null
+++ b/4-Infrastructure/shim/jaccard_hybrid.py
@@ -0,0 +1,104 @@
+#!/usr/bin/env python3
+"""
+Hybrid Jaccard matcher using pg_trgm + pgvector RRF.
+Computes concept embeddings, then queries hybrid_search().
+
+Usage:
+  nix-shell /tmp/embed_env.nix --run "python3 /tmp/jaccard_hybrid.py"
+"""
+
+import json
+import subprocess
+import re
+from pathlib import Path
+
+CONCEPTS_PATH = "/tmp/cornfield_concepts.json"
+MODEL_NAME = "sentence-transformers/static-retrieval-mrl-en-v1"
+
+def psql(sql, timeout=60):
+    r = subprocess.run(
+        ['podman', 'exec', 'arxiv-pg', 'psql', '-U', 'postgres', '-d', 'arxiv',
+         '-t', '-A', '-c', sql],
+        capture_output=True, text=True, timeout=timeout
+    )
+    return r.stdout.strip(), r.stderr.strip()
+
+def extract_query(concept):
+    parts = [concept.get("name", "")]
+    parts.extend(concept.get("tags", []))
+    desc = concept.get("description", "")
+    if desc:
+        parts.append(desc[:200])
+    novelty = concept.get("novelty_statement", "")
+    if novelty:
+        parts.append(novelty[:200])
+    return " ".join(filter(None, parts))
+
+def main():
+    from sentence_transformers import SentenceTransformer
+
+    print(f"Loading model: {MODEL_NAME}")
+    model = SentenceTransformer(MODEL_NAME)
+    print("Model loaded")
+
+    # hybrid_search function already installed in DB
+    print("Using existing hybrid_search function...")
+
+    # Load concepts
+    data = json.loads(Path(CONCEPTS_PATH).read_text())
+    concepts = [c for c in data["concepts"] if c.get("id", "").startswith("cf_")]
+    print(f"Processing {len(concepts)} cornfield concepts")
+
+    results = []
+    for i, concept in enumerate(concepts):
+        cid = concept["id"]
+        query_text = extract_query(concept)
+        query_text_escaped = query_text.replace("'", "''")
+
+        # Embed the concept query
+        embedding = model.encode(query_text, normalize_embeddings=True)
+        emb_str = '[' + ','.join(f'{x:.6f}' for x in embedding) + ']'
+
+        # Hybrid search
+        sql = f"""
+        SELECT paper_id, title, trigram_rank, vector_rank, rrf_score
+        FROM hybrid_search('{query_text_escaped}', '{emb_str}'::vector(1024), 10)
+        """
+        out, err = psql(sql, timeout=30)
+
+        if err and "ERROR" in err:
+            print(f"  [{i+1}/{len(concepts)}] {cid}: ERROR - {err[:80]}")
+            continue
+
+        matches = []
+        for line in out.split("\n"):
+            if not line.strip():
+                continue
+            parts = line.split("|")
+            if len(parts) >= 5:
+                matches.append({
+                    "paper_id": parts[0],
+                    "title": parts[1][:200],
+                    "trigram_rank": parts[2],
+                    "vector_rank": parts[3],
+                    "rrf_score": float(parts[4])
+                })
+
+        if matches:
+            print(f"  [{i+1}/{len(concepts)}] {cid}: {len(matches)} matches (best={matches[0]['rrf_score']:.6f})")
+            results.append({
+                "concept_id": cid,
+                "query": query_text[:100],
+                "top_matches": matches[:5]
+            })
+        else:
+            print(f"  [{i+1}/{len(concepts)}] {cid}: no matches")
+
+    # Save
+    out_path = Path("/tmp/hybrid_matches.json")
+    out_path.write_text(json.dumps(results, indent=2))
+    total = sum(len(r["top_matches"]) for r in results)
+    print(f"\nDone: {len(results)} concepts, {total} citations → {out_path}")
+
+if __name__ == "__main__":
+    main()