.env.example

@@ -5,6 +5,12 @@
 # Example: postgresql://researcher:change_me@localhost:5432/papers
 DATABASE_URL=postgresql://researcher:change_me@localhost:5432/papers
 
+# Optional: privileged connection used by `codex migrate` to apply schema DDL.
+# The app DATABASE_URL is often a least-privilege DML role that cannot CREATE/
+# ALTER owner-held tables; point this at an owner/superuser connection.
+# Falls back to DATABASE_URL when unset.
+# MIGRATION_DATABASE_URL=postgresql://postgres:change_me@localhost:5432/papers
+
 # GROBID service base URL (containerised — see infra/docker-compose.yml)
 GROBID_URL=http://localhost:8070
 

README.md

@@ -19,13 +19,11 @@ $EDITOR .env
 # 3. Install Python dependencies (requires uv)
 uv sync
 
-# 4. Apply the database schema (first run only)
-uv run python -c "
-from codex.db import get_conn, apply_schema
-with get_conn() as conn:
-    apply_schema(conn)
-print('Schema applied.')
-"
+# 4. Apply the database schema (idempotent — safe to re-run after upgrades)
+#    Needs a role that can run DDL. If DATABASE_URL is a least-privilege app
+#    role, point MIGRATION_DATABASE_URL at an owner/superuser connection first:
+#      MIGRATION_DATABASE_URL=postgresql://postgres:...@host:5432/papers
+uv run codex migrate
 ```
 
 ---
@@ -34,7 +32,8 @@ print('Schema applied.')
 
 | Variable | Default | Description |
 |---|---|---|
-| `DATABASE_URL` | `postgresql://researcher:change_me@localhost:5432/papers` | libpq connection string |
+| `DATABASE_URL` | `postgresql://researcher:change_me@localhost:5432/papers` | libpq connection string (app role; DML) |
+| `MIGRATION_DATABASE_URL` | *(falls back to `DATABASE_URL`)* | Privileged connection used by `codex migrate` for schema DDL (owner/superuser) |
 | `GROBID_URL` | `http://localhost:8070` | GROBID HTTP API base URL |
 | `OLLAMA_BASE_URL` | `http://localhost:11434` | Local Ollama endpoint (optional) |
 | `EMBEDDING_MODEL` | `BAAI/bge-m3` | sentence-transformers model name |

codex/cli.py

@@ -29,6 +29,37 @@ app.add_typer(graph_app, name="graph")
 app.add_typer(search_app, name="search")
 
 
+@app.command()
+def migrate() -> None:
+    """Apply infra/schema.sql to bring the database schema up to date (idempotent).
+
+    Must connect as a role that can run DDL (owns / can CREATE + ALTER the tables).
+    The application's DATABASE_URL is usually a least-privilege DML role and will
+    fail with InsufficientPrivilege; set MIGRATION_DATABASE_URL to a privileged
+    (owner/superuser) connection (audit M-1).
+    """
+    import psycopg
+    import psycopg.rows
+
+    from codex.config import get_settings
+    from codex.db import apply_schema
+
+    settings = get_settings()
+    url = (settings.migration_database_url or settings.database_url).get_secret_value()
+    try:
+        with psycopg.connect(url, row_factory=psycopg.rows.dict_row) as conn:
+            apply_schema(conn)
+    except psycopg.errors.InsufficientPrivilege as exc:
+        typer.echo(
+            "ERROR: schema migration needs a role that owns the tables "
+            "(CREATE/ALTER). Set MIGRATION_DATABASE_URL to a privileged connection "
+            f"and retry. ({exc})",
+            err=True,
+        )
+        raise typer.Exit(1) from exc
+    typer.echo("Schema applied — database is up to date.")
+
+
 @app.command()
 def ingest(
     paper_id: str = typer.Argument(..., help="arXiv ID, DOI, or OpenAlex W-ID"),
@@ -71,7 +102,8 @@ def search_paper(
     cite_boost: bool = typer.Option(
         False,
         "--cite-boost",
-        help="Weight results by citation PageRank (F-15). Graceful when corpus < 5 papers.",
+        help="Re-rank the top results by citation PageRank — a within-page "
+        "tie-breaker, not a hard re-ranking (F-15). Graceful when corpus < 5 papers.",
     ),
 ) -> None:
     """Semantic similarity search over paper abstracts."""
@@ -157,6 +189,24 @@ def discover_leads(
         typer.echo(f"{item['pull']:>4}×  {item['cited_id']}")
 
 
+@discover_app.command("recommend")
+def discover_recommend(
+    paper_id: str = typer.Argument(
+        ..., help="Semantic Scholar paper ID (or arXiv:/DOI: prefixed)."
+    ),
+    limit: int = typer.Option(20, "--limit", "-n", help="Number of recommendations."),
+) -> None:
+    """Recommended papers for PAPER_ID via Semantic Scholar."""
+    from codex.sources.semanticscholar import fetch_recommendations
+
+    rec = fetch_recommendations(paper_id, limit=limit)
+    if not rec:
+        typer.echo(f"No recommendations found for {paper_id}.")
+        return
+    for pid in rec:
+        typer.echo(pid)
+
+
 @discover_app.command("citing")
 def discover_citing(paper_id: str = typer.Argument(...)) -> None:
     """List papers that cite PAPER_ID."""
@@ -391,7 +441,15 @@ def synthesis_leads(
         "--lib-path",
         help=(
             "Path to a C++ source tree. Enables improvement leads (@cite-aware) and "
-            "code-vs-corpus gap detection. Without it only connection + topic gaps run."
+            "code-vs-corpus gap detection."
+        ),
+    ),
+    topic: list[str] | None = typer.Option(  # noqa: B008
+        None,
+        "--topic",
+        help=(
+            "Topic to check for coverage gaps (repeatable). Opt-in: without --topic "
+            "no coverage-map gaps run (avoids per-paper false positives, audit R-8)."
         ),
     ),
     output_dir: Optional[str] = typer.Option(  # noqa: UP045
@@ -413,7 +471,7 @@ def synthesis_leads(
     llm = default_llm_client()
 
     connections = find_connections(top_k=settings.synthesis_top_k, llm=llm)
-    gaps = find_gaps(lib_path=lib_path, llm=llm)
+    gaps = find_gaps(lib_path=lib_path, llm=llm, topics=topic or None)
     improvements = (
         find_improvements(lib_path, top_k=settings.synthesis_top_k, llm=llm) if lib_path else []
     )
@@ -543,7 +601,9 @@ def graph_report(
     settings = get_settings()
     with get_conn() as conn:
         graph = build_citation_graph(conn)
-        known_ids = {row["id"] for row in conn.execute("SELECT id FROM papers").fetchall()}
+        paper_rows = conn.execute("SELECT id, title FROM papers").fetchall()
+    known_ids = {row["id"] for row in paper_rows}
+    titles = {row["id"]: row["title"] for row in paper_rows}
 
     if graph.number_of_nodes() == 0:
         typer.echo("Citation graph is empty — ingest some papers first.")
@@ -553,6 +613,13 @@ def graph_report(
     pr = citation_pagerank(graph)
     hubs = sorted(pr.items(), key=lambda x: -x[1])[:top_n]
     dangling = sorted(dangling_citations(graph, known_ids))
+    small_corpus = n_papers < settings.graph_min_corpus_size
+    warning = (
+        f"only {n_papers} ingested papers; recommended >= {settings.graph_min_corpus_size} "
+        "for meaningful ranking"
+        if small_corpus
+        else None
+    )
 
     if output_json:
         typer.echo(
@@ -560,7 +627,11 @@ def graph_report(
                 {
                     "nodes": graph.number_of_nodes(),
                     "edges": graph.number_of_edges(),
-                    "hubs": [{"paper_id": pid, "pagerank": score} for pid, score in hubs],
+                    "small_corpus_warning": warning,  # null unless below threshold (audit U-3)
+                    "hubs": [
+                        {"paper_id": pid, "title": titles.get(pid), "pagerank": score}
+                        for pid, score in hubs
+                    ],
                     "dangling_count": len(dangling),
                     "dangling": dangling,
                 },
@@ -569,18 +640,16 @@ def graph_report(
         )
         return
 
-    if n_papers < settings.graph_min_corpus_size:
-        typer.echo(
-            f"Warning: only {n_papers} ingested papers "
-            f"(recommended ≥ {settings.graph_min_corpus_size} for meaningful ranking).",
-            err=True,
-        )
+    if warning:
+        typer.echo(f"Warning: {warning}.", err=True)
     typer.echo(f"Graph: {graph.number_of_nodes()} nodes, {graph.number_of_edges()} edges")
     typer.echo("")
     typer.echo(f"TOP-{top_n} HUB PAPERS (PageRank)")
     typer.echo("-" * 48)
     for pid, score in hubs:
-        typer.echo(f"  {score:.4f}  {pid}")
+        # in-KB hubs show their title; dangling (OpenAlex-id) hubs are flagged (U-1)
+        label = titles.get(pid) or "(dangling — not ingested)"
+        typer.echo(f"  {score:.4f}  {pid}  {label}")
     typer.echo("")
     typer.echo(f"DANGLING CITATIONS ({len(dangling)} cited but not ingested)")
     typer.echo("-" * 48)
@@ -613,3 +682,23 @@ def graph_related(
     )
     for pid in related:
         typer.echo(f"  {pid}")
+
+
+@graph_app.command("cocited")
+def graph_cocited(
+    paper_id: str = typer.Argument(..., help="Paper ID to find co-cited papers for."),
+) -> None:
+    """List papers frequently co-cited with PAPER_ID (graph co-citation)."""
+    from codex.db import get_conn
+    from codex.graph import build_citation_graph, find_co_cited
+
+    with get_conn() as conn:
+        graph = build_citation_graph(conn)
+
+    results = find_co_cited(paper_id, graph)
+    if not results:
+        typer.echo(f"No papers co-cited with {paper_id}.")
+        return
+    typer.echo(f"Papers co-cited with {paper_id} (count desc):")
+    for pid, count in results:
+        typer.echo(f"  {count:>3}×  {pid}")

codex/config.py

@@ -9,7 +9,7 @@ from __future__ import annotations
 
 from functools import lru_cache
 
-from pydantic import AliasChoices, Field
+from pydantic import AliasChoices, Field, SecretStr
 from pydantic_settings import BaseSettings, SettingsConfigDict
 
 
@@ -26,14 +26,25 @@ class Settings(BaseSettings):
     # ------------------------------------------------------------------
     # Database
     # ------------------------------------------------------------------
-    database_url: str = Field(
-        default="postgresql://researcher:change_me@localhost:5432/papers",
+    database_url: SecretStr = Field(
+        default=SecretStr("postgresql://researcher:change_me@localhost:5432/papers"),
         description=(
             "libpq-compatible connection string consumed by psycopg. "
             "Example: postgresql://user:pass@host:5432/dbname"
         ),
     )
 
+    migration_database_url: SecretStr | None = Field(
+        default=None,
+        description=(
+            "Optional privileged connection string used by `codex migrate` to apply "
+            "schema DDL. The app's database_url is typically a least-privilege DML "
+            "role that cannot CREATE/ALTER owner-held tables (raises "
+            "InsufficientPrivilege); point this at an owner/superuser connection. "
+            "Falls back to database_url when unset."
+        ),
+    )
+
     # ------------------------------------------------------------------
     # External services
     # ------------------------------------------------------------------
@@ -137,7 +148,7 @@ class Settings(BaseSettings):
     # ------------------------------------------------------------------
     # F-09 Rich Parsing
     # ------------------------------------------------------------------
-    mathpix_app_id: str | None = Field(
+    mathpix_app_id: SecretStr | None = Field(
         default=None,
         description=(
             "MathPix App ID for cloud formula extraction. "
@@ -145,7 +156,7 @@ class Settings(BaseSettings):
         ),
     )
 
-    mathpix_app_key: str | None = Field(
+    mathpix_app_key: SecretStr | None = Field(
         default=None,
         description=(
             "MathPix App Key for cloud formula extraction. "
@@ -246,7 +257,7 @@ class Settings(BaseSettings):
         description="Bind port for HTTP transport (ignored for stdio).",
     )
 
-    mcp_auth_token: str | None = Field(
+    mcp_auth_token: SecretStr | None = Field(
         default=None,
         description=(
             "Bearer token required when mcp_transport='http'. "

codex/db.py

@@ -36,7 +36,7 @@ def get_conn() -> Generator[psycopg.Connection[psycopg.rows.DictRow], None, None
     """
     settings = get_settings()
     with psycopg.connect(
-        settings.database_url,
+        settings.database_url.get_secret_value(),
         row_factory=psycopg.rows.dict_row,
     ) as conn:
         yield conn
@@ -45,11 +45,16 @@ def get_conn() -> Generator[psycopg.Connection[psycopg.rows.DictRow], None, None
 def apply_schema(conn: psycopg.Connection[psycopg.rows.DictRow]) -> None:
     """Idempotently apply ``infra/schema.sql`` to the connected database.
 
-    Safe to call on every startup — all DDL statements use
-    ``CREATE … IF NOT EXISTS``.
+    Safe to call repeatedly — every statement is ``CREATE … IF NOT EXISTS`` or
+    ``ADD COLUMN IF NOT EXISTS``, so re-application is a no-op.
+
+    Requires a connection whose role can run DDL (owns / can CREATE + ALTER the
+    tables). The least-privilege application role is typically DML-only and will
+    raise ``InsufficientPrivilege``; use a privileged connection — see
+    ``codex migrate`` and ``MIGRATION_DATABASE_URL`` (audit M-1).
 
     Args:
-        conn: An open psycopg connection (obtained via :func:`get_conn`).
+        conn: An open psycopg connection with DDL privileges.
     """
     schema_path = Path(__file__).parent.parent / "infra" / "schema.sql"
     sql = schema_path.read_text(encoding="utf-8")

codex/embed.py

@@ -1,4 +1,4 @@
-"""Hybrid dense + sparse embeddings via BGE-M3 (ADR-0002).
+"""Dense (+ optional sparse) embeddings via BGE-M3 (ADR-0002).
 
 Uses :class:`FlagEmbedding.BGEM3FlagModel` for encoding because the
 ``return_dense`` / ``return_sparse`` kwargs are part of the FlagEmbedding
@@ -7,6 +7,11 @@ vanilla ``SentenceTransformer`` load of ``BAAI/bge-m3`` (same weights,
 same model); sparse output is a list of ``{token_id: weight}`` dicts per
 text.
 
+Status: only the **dense** path is wired into ingest/search today; the search
+"hybrid" is dense + Postgres FTS. :meth:`Embedder.encode_sparse` / :meth:`encode`
+are provided for a future sparse-retrieval layer but are not yet consumed by the
+pipeline (audit C-14).
+
 Notes for callers
 -----------------
 * Empty input is handled explicitly — no model call is issued.

codex/ingest.py

@@ -8,6 +8,7 @@ from dataclasses import dataclass
 from pathlib import Path
 
 import numpy as np
+import psycopg
 
 from codex.config import get_settings
 from codex.db import get_conn
@@ -125,35 +126,64 @@ def ingest_paper(
     # ---------------------------------------------------------------
     # 3. Upsert paper  (INSERT … ON CONFLICT (id) DO UPDATE SET …)
     # ---------------------------------------------------------------
+    upsert_sql = """
+        INSERT INTO papers (id, openalex_id, bibkey, title, authors, year, abstract,
+                            source_path, abstract_emb)
+        VALUES (%(id)s, %(openalex_id)s, %(bibkey)s, %(title)s, %(authors)s, %(year)s,
+                %(abstract)s, %(source_path)s, %(abstract_emb)s)
+        ON CONFLICT (id) DO UPDATE SET
+            openalex_id  = EXCLUDED.openalex_id,
+            bibkey       = COALESCE(papers.bibkey, EXCLUDED.bibkey),
+            title        = EXCLUDED.title,
+            authors      = EXCLUDED.authors,
+            year         = EXCLUDED.year,
+            abstract     = EXCLUDED.abstract,
+            source_path  = COALESCE(EXCLUDED.source_path, papers.source_path),
+            abstract_emb = EXCLUDED.abstract_emb
+    """
     with get_conn() as conn:
-        conn.execute(
-            """
-            INSERT INTO papers (id, openalex_id, bibkey, title, authors, year, abstract,
-                                source_path, abstract_emb)
-            VALUES (%(id)s, %(openalex_id)s, %(bibkey)s, %(title)s, %(authors)s, %(year)s,
-                    %(abstract)s, %(source_path)s, %(abstract_emb)s)
-            ON CONFLICT (id) DO UPDATE SET
-                openalex_id  = EXCLUDED.openalex_id,
-                bibkey       = COALESCE(papers.bibkey, EXCLUDED.bibkey),
-                title        = EXCLUDED.title,
-                authors      = EXCLUDED.authors,
-                year         = EXCLUDED.year,
-                abstract     = EXCLUDED.abstract,
-                source_path  = COALESCE(EXCLUDED.source_path, papers.source_path),
-                abstract_emb = EXCLUDED.abstract_emb
-            """,
-            {
-                "id": paper.id,
-                "openalex_id": paper.openalex_id,
-                "bibkey": paper.bibkey,
-                "title": paper.title,
-                "authors": paper.authors,
-                "year": paper.year,
-                "abstract": paper.abstract,
-                "source_path": source_path,
-                "abstract_emb": abstract_emb,
-            },
-        )
+        # The id-keyed upsert does not catch a papers.bibkey UNIQUE collision (two
+        # same-author/year papers generate the same key). On such a collision retry
+        # with an a/b/c… suffix instead of failing the whole ingest (audit C-15).
+        base_bibkey = paper.bibkey
+        for attempt in range(27):
+            try:
+                conn.execute(
+                    upsert_sql,
+                    {
+                        "id": paper.id,
+                        "openalex_id": paper.openalex_id,
+                        "bibkey": paper.bibkey,
+                        "title": paper.title,
+                        "authors": paper.authors,
+                        "year": paper.year,
+                        "abstract": paper.abstract,
+                        "source_path": source_path,
+                        "abstract_emb": abstract_emb,
+                    },
+                )
+                break
+            except psycopg.errors.UniqueViolation as exc:
+                msg = str(exc).lower()
+                conn.rollback()
+                if "openalex" in msg:
+                    # Two different papers.id claim the same OpenAlex work — a real data
+                    # conflict, not something to auto-rename. Surface it clearly instead
+                    # of the raw psycopg error (companion gap to C-15's bibkey case).
+                    raise ValueError(
+                        f"openalex_id {paper.openalex_id!r} is already attached to a "
+                        f"different paper; ingesting '{paper.id}' would duplicate it — "
+                        "resolve the conflicting paper first."
+                    ) from exc
+                if base_bibkey is None or "bibkey" not in msg or attempt == 26:
+                    raise
+                paper.bibkey = f"{base_bibkey}{chr(ord('a') + attempt)}"
+                logger.warning(
+                    "bibkey %r already exists; ingesting '%s' as %r instead",
+                    base_bibkey,
+                    paper.id,
+                    paper.bibkey,
+                )
 
         # Register openalex_id in paper_identifiers (alias table).
         # Every ingest records the primary openalex_id so the graph JOIN

codex/mcp_server.py

@@ -24,6 +24,7 @@ Transport
 from __future__ import annotations
 
 import logging
+import secrets
 
 from mcp.server.fastmcp import FastMCP
 from mcp.server.transport_security import TransportSecuritySettings
@@ -121,7 +122,6 @@ def wiki_read(concept_slug: str) -> dict[str, object]:
     directory or the requested page does not exist.
     """
     try:
-        import json
         from pathlib import Path
 
         from codex.config import get_settings
@@ -135,16 +135,12 @@ def wiki_read(concept_slug: str) -> dict[str, object]:
 
         markdown = page_path.read_text(encoding="utf-8")
 
-        # Collect cited bibkeys from the compile state
-        state_path = wiki_dir / ".compile-state.json"
-        sources: list[str] = []
-        if state_path.exists():
-            try:
-                state: dict[str, str] = json.loads(state_path.read_text(encoding="utf-8"))
-                if concept_slug in state:
-                    sources = [concept_slug]
-            except (json.JSONDecodeError, OSError):
-                pass
+        # Collect the actual cited bibkeys from the page's inline [BibKey #loc]
+        # citations (audit C-3: this previously returned the concept slug itself,
+        # not the cited sources).
+        from codex.wiki import _parse_claims
+
+        sources = sorted({claim.bibkey for claim in _parse_claims(markdown)})
 
         return {"markdown": markdown, "sources": sources}
     except Exception as exc:  # noqa: BLE001
@@ -298,12 +294,13 @@ def _require_http_token() -> str:
     from codex.config import get_settings
 
     settings = get_settings()
-    if not settings.mcp_auth_token:
+    token = settings.mcp_auth_token.get_secret_value() if settings.mcp_auth_token else ""
+    if not token:
         raise RuntimeError(
             "HTTP transport requires MCP_AUTH_TOKEN to be set. "
             "Set the environment variable or add it to .env."
         )
-    return settings.mcp_auth_token
+    return token
 
 
 # ---------------------------------------------------------------------------
@@ -337,7 +334,9 @@ def main() -> None:
                 self, request: Request, call_next: RequestResponseEndpoint
             ) -> Response:
                 auth = request.headers.get("Authorization", "")
-                if auth != f"Bearer {token}":
+                # Constant-time comparison to avoid a token-length/equality timing
+                # side-channel (audit S-2).
+                if not secrets.compare_digest(auth, f"Bearer {token}"):
                     return Response("Unauthorized", status_code=401)
                 return await call_next(request)
 

codex/parsing/mathpix.py

@@ -302,8 +302,10 @@ def extract_formulas(
     """
     settings = get_settings()
 
-    app_id = mathpix_app_id or settings.mathpix_app_id or ""
-    app_key = mathpix_app_key or settings.mathpix_app_key or ""
+    settings_id = settings.mathpix_app_id.get_secret_value() if settings.mathpix_app_id else ""
+    settings_key = settings.mathpix_app_key.get_secret_value() if settings.mathpix_app_key else ""
+    app_id = mathpix_app_id or settings_id
+    app_key = mathpix_app_key or settings_key
 
     if app_id and app_key:
         logger.info("Using MathPix backend for %s", pdf_path)

codex/sources/arxiv.py

@@ -38,10 +38,7 @@ def fetch_source(arxiv_id: str) -> str | None:
         file is present (signals Nougat fallback).
     """
     url = f"{_BASE}/src/{arxiv_id}"
-    try:
-        response = httpx.get(url, timeout=60, follow_redirects=True)
-    except httpx.RequestError:
-        raise
+    response = httpx.get(url, timeout=60, follow_redirects=True)
     if response.status_code == 404:
         logger.debug("arXiv 404 for source id=%s", arxiv_id)
         return None

codex/sources/semanticscholar.py

@@ -14,6 +14,7 @@ import logging
 import threading
 import time
 from typing import Any
+from urllib.parse import quote
 
 import httpx
 from tenacity import retry, retry_if_exception, stop_after_attempt, wait_exponential
@@ -77,7 +78,9 @@ def fetch_references(paper_id: str) -> list[Citation]:
     list[Citation]
         One Citation per reference, with optional context snippet.
     """
-    url = f"{_BASE_GRAPH}/paper/{paper_id}/references"
+    # quote the id so a legacy-arXiv "/" (e.g. arXiv:math/0603097) doesn't break
+    # the URL path; keep ":" for the arXiv:/DOI: scheme prefix (audit R-5).
+    url = f"{_BASE_GRAPH}/paper/{quote(paper_id, safe=':')}/references"
     params: dict[str, Any] = {"fields": "externalIds,contexts"}
     try:
         response = _get(url, params=params)
@@ -118,7 +121,7 @@ def fetch_recommendations(paper_id: str, limit: int = 20) -> list[str]:
     list[str]
         List of recommended paper IDs.
     """
-    url = f"{_BASE_RECS}/papers/forpaper/{paper_id}"
+    url = f"{_BASE_RECS}/papers/forpaper/{quote(paper_id, safe=':')}"
     params: dict[str, Any] = {"limit": limit}
     try:
         response = _get(url, params=params)

codex/synthesis.py

@@ -416,11 +416,12 @@ def find_gaps(
 
     Two complementary signals are used:
 
-    * **Topic coverage map** — for each topic in ``topics`` (or, if
-      ``None``, the union of paper titles), retrieve chunks and check
-      bibkey coverage. A topic covered by < ``synthesis_gap_min_coverage``
-      bibkeys is reported as a gap candidate and the LLM is asked to
-      articulate it.
+    * **Topic coverage map** — for each **explicitly-requested** topic in
+      ``topics``, retrieve chunks and check bibkey coverage. A topic covered by
+      < ``synthesis_gap_min_coverage`` bibkeys is a gap candidate and the LLM is
+      asked to articulate it. Defaulting to paper titles flagged almost every
+      paper as a gap (a title retrieves mostly its own single bibkey), so the
+      coverage map is opt-in now; pass ``topics`` / CLI ``--topic`` (audit R-8).
     * **Code-vs-corpus gap** — when ``lib_path`` is given, any @cite
       bibkey scanned from code that is NOT present in the corpus is
       flagged. This catches the "cited in code, never ingested" case.
@@ -429,9 +430,9 @@ def find_gaps(
     seq = 1
     leads: list[Lead] = []
 
+    # Coverage-map probes are the explicit topics only — no default-to-titles,
+    # which turned every paper into a spurious gap (audit R-8).
     probe_topics: list[str] = list(topics or [])
-    if not probe_topics:
-        probe_topics = [title for _, title in _list_paper_titles(db_conn)]
 
     known_bibkeys = {bk for bk, _ in _list_paper_titles(db_conn)}
 

codex/wiki.py

@@ -186,8 +186,15 @@ def _retrieve_chunks(
         ).fetchall()
 
     # Filter reference-list chunks: skip chunks whose content looks like a bibliography
-    # (heuristic: > 60 % of lines match "^\[\d+\]" or "^[A-Z][a-z]+,?\s+[A-Z]\.").
-    ref_pattern = re.compile(r"^\s*(\[\d+\]|[A-Z][a-z]+,?\s+[A-Z]\.)", re.MULTILINE)
+    # (heuristic: > 60 % of lines look like "[12]" refs or "Surname, I." authors).
+    # The author alternative excludes common math-structure words ("Theorem A.",
+    # "Lemma B.") so theorem-dense chunks aren't mistaken for a reference list (R-2).
+    ref_pattern = re.compile(
+        r"^\s*(\[\d+\]|(?!(?:Theorem|Lemma|Proposition|Corollary|Definition|Proof|"
+        r"Section|Figure|Fig|Table|Equation|Eq|Remark|Example|Chapter)\b)"
+        r"[A-Z][a-z]+,?\s+[A-Z]\.)",
+        re.MULTILINE,
+    )
     filtered: list[dict[str, Any]] = []
     for row in rows:
         content: str = row["content"]
@@ -273,7 +280,13 @@ _STOPWORDS: frozenset[str] = frozenset(
     }
 )
 
-_SENTENCE_SPLIT_RE = re.compile(r"[.!?]")
+# Split on sentence-ending punctuation only when followed by whitespace/end, so a
+# decimal like "1.5" does not create a spurious sentence boundary (audit R-1).
+_SENTENCE_SPLIT_RE = re.compile(r"[.!?]+(?=\s|$)")
+
+# Punctuation stripped from token edges before grounding comparison — sentence/
+# clause marks and quotes, NOT math delimiters like ()=+ (audit R-1).
+_EDGE_PUNCT = ".,;:!?\"'"
 
 
 def _last_sentence(text: str) -> str:
@@ -292,8 +305,16 @@ def _last_sentence(text: str) -> str:
 
 
 def _content_words(text: str) -> list[str]:
-    """Return lowercased tokens with stopwords removed."""
-    return [w for w in text.lower().split() if w not in _STOPWORDS]
+    """Return lowercased content tokens, edge-punctuation-stripped, stopwords removed.
+
+    Stripping leading/trailing sentence punctuation makes grounding robust to
+    surface variation ("volume," vs "volume") so a faithful paraphrase is not
+    marked ungrounded over a comma (audit R-1). Math delimiters (``()=+``) are
+    preserved. Claim and chunk tokens are normalised identically, so matching
+    stays consistent.
+    """
+    tokens = (w.strip(_EDGE_PUNCT) for w in text.lower().split())
+    return [w for w in tokens if w and w not in _STOPWORDS]
 
 
 def _run_grounding_guard(
@@ -322,8 +343,9 @@ def _run_grounding_guard(
     for chunk in chunks:
         bk = str(chunk.get("bibkey") or "")
         if bk:
-            # Content words of the chunk (stopwords removed, lowercased)
-            cw = " ".join(_content_words(chunk["content"]))
+            # Content words of the chunk, space-padded so a 5-gram match is bounded
+            # by whole tokens, not a substring bleeding across words (audit C-6).
+            cw = " " + " ".join(_content_words(chunk["content"])) + " "
             bib_index.setdefault(bk, []).append(cw)
 
     for claim in claims:
@@ -345,7 +367,7 @@ def _run_grounding_guard(
 
         found = False
         for i in range(len(content) - 4):  # content-5-grams
-            gram = " ".join(content[i : i + 5])
+            gram = " " + " ".join(content[i : i + 5]) + " "  # padded: token-boundary match
             if any(gram in src for src in sources):
                 found = True
                 break
@@ -402,6 +424,13 @@ def _detect_conflicts(
 
 _INLINE_CODE_RE = re.compile(r"`[^`]+`")
 
+# LaTeX math spans — protected from cross-ref injection so a concept name inside
+# a formula is not rewritten to a [[slug]] link, corrupting the LaTeX (audit R-9).
+_MATH_SPAN_RE = re.compile(
+    r"\$\$.*?\$\$|\$[^$\n]*?\$|\\\(.*?\\\)|\\\[.*?\\\]",
+    re.DOTALL,
+)
+
 
 def _inject_cross_refs(
     markdown: str,
@@ -411,11 +440,12 @@ def _inject_cross_refs(
     """Replace occurrences of other concept titles/aliases with ``[[slug]]`` links.
 
     Only exact case-insensitive whole-word matches outside of existing
-    ``[[…]]`` blocks or inline code spans are replaced.
-    Inline-code spans (`` `…` ``) are temporarily protected by null-byte
-    placeholders and restored after injection.
+    ``[[…]]`` blocks, inline code spans, or LaTeX math spans are replaced.
+    Inline-code (`` `…` ``) and math (``$…$``, ``$$…$$``, ``\\(…\\)``,
+    ``\\[…\\]``) spans are temporarily protected by null-byte placeholders and
+    restored after injection.
     """
-    # Step 1: protect inline-code spans from replacement
+    # Step 1: protect inline-code and math spans from replacement
     placeholders: dict[str, str] = {}
 
     def _protect(m: re.Match[str]) -> str:
@@ -424,6 +454,7 @@ def _inject_cross_refs(
         return key
 
     markdown = _INLINE_CODE_RE.sub(_protect, markdown)
+    markdown = _MATH_SPAN_RE.sub(_protect, markdown)  # don't rewrite names inside LaTeX (R-9)
 
     # Step 2: inject cross-refs on unprotected text
     for concept in all_concepts:
@@ -602,14 +633,14 @@ def compile_concept(
     claims = _parse_claims(raw_output)
     claims = _run_grounding_guard(claims, chunks)
 
-    _all_concepts = all_concepts or []
-    raw_output = _inject_cross_refs(raw_output, _all_concepts, concept.slug)
-
-    # Graceful: try to embed formula chunks (F-09) — skip if table missing
+    # Graceful: formula-embedding hook (F-09) — currently a no-op (audit C-12).
     _try_embed_formulas(concept, chunks)
 
     compiled_at = datetime.now(UTC)
+    # Mark ungrounded claims on the raw body FIRST, then inject cross-refs: a
+    # concept name inside a claim must not stop the ⚠ regex from matching (C-13).
     markdown = _render_page_markdown(concept, raw_output, claims, compiled_at)
+    markdown = _inject_cross_refs(markdown, all_concepts or [], concept.slug)
 
     return ConceptPage(
         concept=concept,
@@ -621,20 +652,13 @@ def compile_concept(
 
 
 def _try_embed_formulas(concept: Concept, chunks: list[dict[str, Any]]) -> None:
-    """Attempt to look up formula chunks for the concept — graceful no-op if F-09 absent."""
-    try:
-        from codex.db import get_conn
+    """Reserved hook for embedding F-09 formula chunks into a page.
 
-        with get_conn() as conn:
-            # Check if formulas table exists
-            row = conn.execute(
-                "SELECT 1 FROM information_schema.tables WHERE table_name = 'formulas'"
-            ).fetchone()
-            if row is None:
-                return  # F-09 not present
-            # (Future: embed relevant raw_latex into the page)
-    except Exception:  # noqa: BLE001
-        return  # DB not reachable or other error — degrade gracefully
+    Currently a no-op — formula embedding is not implemented yet. Kept as a stable
+    seam for compile_concept's call site. The previous body issued a per-concept
+    DB round-trip (information_schema lookup) that did nothing (audit C-12).
+    """
+    return
 
 
 # ---------------------------------------------------------------------------

docs/adr/ADR-F15-literature-graph.md

@@ -177,13 +177,28 @@ was measured on a graph the current code no longer produces:
   diverge (audit C-1). Ingest stores the caller's canonical id as `papers.id`
   instead of OpenAlex's URL-form doi (audit C-7). Inter-KB citations are
   therefore represented as edges — the "Known Limitation" above is obsolete.
-- **Spike numbers are stale.** The 478 dangling nodes, the rank-7
-  Bobenko/Springborn result, and the 5.7 % score spread were measured *before*
-  the resolution + canonicalisation. They must be **re-measured after the corpus
-  is re-ingested** onto canonical ids (the chosen C-7 migration); until then the
-  GO rests on a superseded topology.
+- **Spike re-measured after migration (2026-06-15).** The corpus was re-ingested
+  onto canonical bare ids (29 papers, all bare — verified `url_form_ids = 0`), and
+  the graph re-run on the post-migration corpus:
 
-**Action (pending):** after re-ingesting via `ingest_all.sh`, re-run
-`codex graph report`, refresh the Spike Result table, and confirm the
-foundational hubs (Pinkall/Polthier, Yamabe, Schoen, Bobenko/Springborn) still
-surface.
+  | Metric | Original spike (pre-fix) | Post-migration (re-measured) |
+  |--------|--------------------------|------------------------------|
+  | Ingested papers | 29 | 29 |
+  | Graph nodes | 495 | 489 |
+  | Graph edges | 590 | 590 |
+  | Dangling nodes | 478 | 472 |
+  | Top-10 PR spread | 5.7 % | 5.4 % |
+  | Rank-1 hub | W1974956622 (dangling) | **Pinkall/Polthier 1993 — in-KB (resolved)** |
+  | Bobenko/Springborn 2007 | rank 7 | rank 7 |
+
+  The resolution fix's signature is visible: Pinkall/Polthier 1993 now resolves to
+  its canonical DOI and rises to **rank 1 as an in-KB hub** (previously a dangling
+  OpenAlex node). Bobenko/Springborn 2007 holds rank 7, and the foundational works
+  (Pinkall/Polthier, Yamabe, Schoen, Bobenko/Springborn) still surface. **GO
+  re-affirmed** on the shipping topology.
+
+  Migration footnotes: two papers initially survived in URL form because the
+  id-keyed upsert did not catch a `papers.openalex_id` collision, and `2305.10988`
+  failed on a `papers.bibkey` collision with `2310.17529` (both →
+  `BobenkoLutz2023`). Same upsert gap — resolved by the bibkey-retry (audit C-15)
+  plus a delete + re-ingest of the two stragglers; corpus is now 29/29 canonical.

infra/reingest_canonical_ids.sh

@@ -76,11 +76,13 @@ PYEOF
 )"
 if [[ "$SECTION_OK" != "yes" ]]; then
   echo "ABORT — schema not ready: chunks.section is missing (audit M-1)."
-  echo "The app user cannot add it (chunks is owned by 'postgres'). Apply it as"
-  echo "the table owner, then re-run this script:"
+  echo "The app user cannot add it (core tables are owned by 'postgres'). Sync the"
+  echo "schema with a privileged role, then re-run this script. Either:"
   echo ""
-  echo "    ssh alfred@192.168.178.103 \\"
-  echo "      \"sudo -u postgres psql -d papers -c \\\\\"ALTER TABLE chunks ADD COLUMN IF NOT EXISTS section TEXT;\\\\\"\""
+  echo "  (a) MIGRATION_DATABASE_URL=postgresql://postgres:PASS@HOST:PORT/papers \\"
+  echo "        \"$CODEX_DIR/.venv/bin/codex\" migrate     # applies schema.sql idempotently"
+  echo "  (b) sudo -u postgres psql -d papers \\"
+  echo "        -c \"ALTER TABLE chunks ADD COLUMN IF NOT EXISTS section TEXT;\""
   echo ""
   echo "Nothing was changed — no TRUNCATE was issued."
   exit 1

infra/schema.sql

@@ -13,7 +13,7 @@ CREATE EXTENSION IF NOT EXISTS vector;
 -- ---------------------------------------------------------------------
 -- Layer 1: Papers + full-text chunks
 -- ---------------------------------------------------------------------
-CREATE TABLE papers (
+CREATE TABLE IF NOT EXISTS papers (
     id            TEXT PRIMARY KEY,        -- canonical ID: arXiv ID or DOI
     openalex_id   TEXT UNIQUE,             -- e.g. W2741809807
     bibkey        TEXT UNIQUE,             -- BibTeX key -> .bib + Doxygen @cite
@@ -27,10 +27,10 @@ CREATE TABLE papers (
 );
 
 -- HNSW index for fast approximate nearest-neighbour search on abstracts.
-CREATE INDEX papers_abstract_emb_idx
+CREATE INDEX IF NOT EXISTS papers_abstract_emb_idx
     ON papers USING hnsw (abstract_emb vector_cosine_ops);
 
-CREATE TABLE chunks (
+CREATE TABLE IF NOT EXISTS chunks (
     id        BIGSERIAL PRIMARY KEY,
     paper_id  TEXT REFERENCES papers(id) ON DELETE CASCADE,
     ord       INT NOT NULL,               -- position within the paper
@@ -38,13 +38,13 @@ CREATE TABLE chunks (
     embedding vector(1024)
 );
 
-CREATE INDEX chunks_emb_idx
+CREATE INDEX IF NOT EXISTS chunks_emb_idx
     ON chunks USING hnsw (embedding vector_cosine_ops);
-CREATE INDEX chunks_paper_idx ON chunks (paper_id);
+CREATE INDEX IF NOT EXISTS chunks_paper_idx ON chunks (paper_id);
 
 -- Sparse / keyword hits for exact mathematical terminology (hybrid search).
 -- Dense (above) + full-text (below) combined = robust against math terms.
-CREATE INDEX chunks_fts_idx
+CREATE INDEX IF NOT EXISTS chunks_fts_idx
     ON chunks USING gin (to_tsvector('english', content));
 
 -- ---------------------------------------------------------------------
@@ -53,19 +53,19 @@ CREATE INDEX chunks_fts_idx
 --   edges to not-yet-ingested papers are intentionally preserved —
 --   those are your discovery leads.
 -- ---------------------------------------------------------------------
-CREATE TABLE citations (
+CREATE TABLE IF NOT EXISTS citations (
     citing_id TEXT REFERENCES papers(id) ON DELETE CASCADE,
     cited_id  TEXT NOT NULL,               -- arXiv/DOI/OpenAlex ID of the target
     context   TEXT,                        -- optional: citation context (S2)
     PRIMARY KEY (citing_id, cited_id)
 );
 
-CREATE INDEX citations_cited_idx ON citations (cited_id);
+CREATE INDEX IF NOT EXISTS citations_cited_idx ON citations (cited_id);
 
 -- ---------------------------------------------------------------------
 -- Layer 3: Provenance  (the "cleanly couple" goal)
 -- ---------------------------------------------------------------------
-CREATE TABLE code_links (
+CREATE TABLE IF NOT EXISTS code_links (
     id        BIGSERIAL PRIMARY KEY,
     symbol    TEXT NOT NULL,               -- e.g. 'dec::hodge_star' or 'file.cpp:120'
     paper_id  TEXT REFERENCES papers(id) ON DELETE SET NULL,
@@ -74,8 +74,8 @@ CREATE TABLE code_links (
     added_at  TIMESTAMPTZ DEFAULT now()
 );
 
-CREATE INDEX code_links_symbol_idx ON code_links (symbol);
-CREATE INDEX code_links_paper_idx  ON code_links (paper_id);
+CREATE INDEX IF NOT EXISTS code_links_symbol_idx ON code_links (symbol);
+CREATE INDEX IF NOT EXISTS code_links_paper_idx  ON code_links (paper_id);
 
 -- ---------------------------------------------------------------------
 -- Example query: discovery leads

tests/graph/test_cli.py

@@ -28,9 +28,11 @@ def _make_conn_cm(conn: MagicMock):
 
 
 def _make_conn_with_paper_ids(*paper_ids: str) -> MagicMock:
-    """Mock conn that returns paper rows for SELECT id FROM papers."""
+    """Mock conn that returns paper rows for SELECT id, title FROM papers."""
     conn = MagicMock()
-    conn.execute.return_value.fetchall.return_value = [{"id": pid} for pid in paper_ids]
+    conn.execute.return_value.fetchall.return_value = [
+        {"id": pid, "title": f"Title of {pid}"} for pid in paper_ids
+    ]
     return conn
 
 

tests/ingest/test_ingest.py

@@ -11,6 +11,7 @@ from typing import Any
 from unittest.mock import MagicMock, patch
 
 import numpy as np
+import psycopg
 import pytest
 
 from codex.ingest import IngestResult, _make_bibkey, ingest_paper
@@ -525,6 +526,69 @@ def test_ingest_sets_bibkey_when_none(tmp_path: Any) -> None:
     assert upsert_params["bibkey"] == "AliceBob2023"
 
 
+def test_ingest_disambiguates_bibkey_on_unique_violation() -> None:
+    """A papers.bibkey UNIQUE collision is retried with an a/b/c suffix (audit C-15)."""
+    paper = _make_paper()  # bibkey auto-generates to "AliceBob2023"
+    mock_conn = MagicMock()
+    state = {"first": True}
+
+    def execute_side_effect(sql: str, params: Any = None) -> MagicMock:
+        # The first papers INSERT collides on the bibkey; the retry must succeed.
+        if "INSERT INTO papers" in sql and state["first"]:
+            state["first"] = False
+            raise psycopg.errors.UniqueViolation(
+                'duplicate key value violates unique constraint "papers_bibkey_key"'
+            )
+        return MagicMock()
+
+    mock_conn.execute.side_effect = execute_side_effect
+
+    with (
+        patch("codex.ingest.openalex.fetch_paper", return_value=paper),
+        patch("codex.ingest.openalex.fetch_citations", return_value=[]),
+        patch("codex.ingest.get_embedder", return_value=_fake_embedder()),
+        patch("codex.ingest.get_conn", side_effect=_make_conn_cm(mock_conn)),
+    ):
+        ingest_paper(paper.id)
+
+    papers_inserts = [
+        c for c in mock_conn.execute.call_args_list if "INSERT INTO papers" in c[0][0]
+    ]
+    assert len(papers_inserts) == 2, "expected one retry after the bibkey collision"
+    assert papers_inserts[0][0][1]["bibkey"] == "AliceBob2023"
+    assert papers_inserts[1][0][1]["bibkey"] == "AliceBob2023a"
+    mock_conn.rollback.assert_called_once()
+
+
+def test_ingest_openalex_collision_raises_clear_error() -> None:
+    """An openalex_id UNIQUE collision raises a clear, actionable error (audit C-15).
+
+    Unlike a bibkey clash (auto-suffixed), a shared openalex_id means two papers
+    claim the same OpenAlex work — a real data conflict that must surface, not the
+    raw psycopg error.
+    """
+    paper = _make_paper()
+    mock_conn = MagicMock()
+
+    def execute_side_effect(sql: str, params: Any = None) -> MagicMock:
+        if "INSERT INTO papers" in sql:
+            raise psycopg.errors.UniqueViolation(
+                'duplicate key value violates unique constraint "papers_openalex_id_key"'
+            )
+        return MagicMock()
+
+    mock_conn.execute.side_effect = execute_side_effect
+
+    with (
+        patch("codex.ingest.openalex.fetch_paper", return_value=paper),
+        patch("codex.ingest.openalex.fetch_citations", return_value=[]),
+        patch("codex.ingest.get_embedder", return_value=_fake_embedder()),
+        patch("codex.ingest.get_conn", side_effect=_make_conn_cm(mock_conn)),
+        pytest.raises(ValueError, match="openalex_id"),
+    ):
+        ingest_paper(paper.id)
+
+
 # ---------------------------------------------------------------------------
 
 

tests/mcp/test_http_auth.py

@@ -12,6 +12,7 @@ from __future__ import annotations
 from unittest.mock import MagicMock, patch
 
 import pytest
+from pydantic import SecretStr
 
 # ---------------------------------------------------------------------------
 # _require_http_token
@@ -37,7 +38,7 @@ def test_require_http_token_returns_token_when_set() -> None:
     from codex.mcp_server import _require_http_token
 
     mock_settings = MagicMock()
-    mock_settings.mcp_auth_token = "super-secret-token"
+    mock_settings.mcp_auth_token = SecretStr("super-secret-token")
 
     with patch("codex.config.get_settings", return_value=mock_settings):
         result = _require_http_token()
@@ -97,7 +98,7 @@ def test_main_http_with_token_calls_uvicorn() -> None:
 
     mock_settings = MagicMock()
     mock_settings.mcp_transport = "http"
-    mock_settings.mcp_auth_token = "test-token"
+    mock_settings.mcp_auth_token = SecretStr("test-token")
     mock_settings.mcp_host = "127.0.0.1"
     mock_settings.mcp_port = 8765
 

tests/parsing/test_mathpix.py

@@ -10,6 +10,7 @@ from typing import Any
 from unittest.mock import MagicMock, patch
 
 import pytest
+from pydantic import SecretStr
 
 from codex.models import FormulaChunk
 
@@ -295,8 +296,8 @@ class TestRouteSelection:
     def test_mathpix_selected_when_creds_present(self) -> None:
         """extract_formulas calls MathPix backend when both creds are set."""
         mock_settings = MagicMock()
-        mock_settings.mathpix_app_id = "my_id"
-        mock_settings.mathpix_app_key = "my_key"
+        mock_settings.mathpix_app_id = SecretStr("my_id")
+        mock_settings.mathpix_app_key = SecretStr("my_key")
         mock_settings.pix2tex_fallback = True
 
         with (

tests/scaffold/test_config.py

@@ -8,7 +8,10 @@ from codex.config import Settings, get_settings
 def test_settings_defaults() -> None:
     """Settings() is constructable without env vars; expected defaults are set."""
     s = Settings()
-    assert s.database_url == "postgresql://researcher:change_me@localhost:5432/papers"
+    assert (
+        s.database_url.get_secret_value()
+        == "postgresql://researcher:change_me@localhost:5432/papers"
+    )
     assert s.embedding_model == "BAAI/bge-m3"
     assert s.embedding_dim == 1024
 
@@ -20,7 +23,7 @@ def test_settings_env_override(monkeypatch: object) -> None:
     mp: pytest.MonkeyPatch = monkeypatch  # type: ignore[assignment]
     mp.setenv("DATABASE_URL", "postgresql://x:y@h:5432/db")
     s = Settings()
-    assert s.database_url == "postgresql://x:y@h:5432/db"
+    assert s.database_url.get_secret_value() == "postgresql://x:y@h:5432/db"
 
 
 def test_get_settings_is_singleton() -> None:

tests/scaffold/test_db.py

@@ -33,3 +33,40 @@ def test_apply_schema_executes_sql() -> None:
 
     mock_conn.execute.assert_called_once()
     mock_conn.commit.assert_called_once()
+
+
+def test_schema_sql_is_idempotent() -> None:
+    """Every CREATE TABLE/INDEX in infra/schema.sql uses IF NOT EXISTS (audit M-1, T-2).
+
+    Re-applying schema.sql must be a safe no-op so the migration can run
+    repeatedly against an existing database.
+    """
+    import re
+    from pathlib import Path
+
+    schema = (Path(__file__).resolve().parents[2] / "infra" / "schema.sql").read_text()
+    # Drop line comments so commented-out example queries don't count.
+    code = "\n".join(line.split("--", 1)[0] for line in schema.splitlines())
+    non_idempotent = re.findall(
+        r"CREATE\s+(?:UNIQUE\s+)?(?:TABLE|INDEX)\s+(?!IF\s+NOT\s+EXISTS)(\w+)",
+        code,
+        re.IGNORECASE,
+    )
+    assert not non_idempotent, f"schema.sql has non-idempotent CREATE statements: {non_idempotent}"
+
+
+def test_migrate_command_reports_privilege_error() -> None:
+    """`codex migrate` surfaces InsufficientPrivilege with guidance and exits 1 (M-1)."""
+    import psycopg
+    from typer.testing import CliRunner
+
+    from codex.cli import app
+
+    def boom(*args: object, **kwargs: object) -> object:
+        raise psycopg.errors.InsufficientPrivilege("must be owner of table chunks")
+
+    with patch("psycopg.connect", boom):
+        result = CliRunner().invoke(app, ["migrate"])
+
+    assert result.exit_code == 1
+    assert "MIGRATION_DATABASE_URL" in result.output

tests/synthesis/test_gaps.py

@@ -112,10 +112,35 @@ def test_find_gaps_coverage_map_low_coverage_triggers_llm(
         "For an ideal tetrahedron with dihedral angles the hyperbolic volume is "
         "V = L(gamma1) + L(gamma2) + L(gamma3). [Springborn2008 #chunk 16]\n"
     )
-    leads = find_gaps(llm=StubLLM(grounded_body))
+    # Coverage gaps are opt-in (audit R-8): pass the topic explicitly.
+    leads = find_gaps(llm=StubLLM(grounded_body), topics=["hyperbolic volume formula"])
     assert any(lead.kind == "gap" for lead in leads)
 
 
+def test_find_gaps_no_coverage_gaps_without_explicit_topics(
+    monkeypatch: pytest.MonkeyPatch,
+    mock_paper_titles: None,
+    mock_settings: Path,
+) -> None:
+    """Without explicit topics, paper titles do NOT auto-generate coverage gaps (R-8)."""
+    sparse_chunks: list[dict[str, Any]] = [
+        {
+            "id": 10,
+            "paper_id": "springborn-2008",
+            "ord": 16,
+            "content": "the hyperbolic volume is V = L(gamma1) + L(gamma2) + L(gamma3)",
+            "bibkey": "Springborn2008",
+        },
+    ]
+    monkeypatch.setattr(
+        "codex.synthesis._retrieve_chunks",
+        lambda queries, top_k: [dict(c) for c in sparse_chunks],
+    )
+    # No lib_path, no topics → the coverage map must not run despite sparse coverage.
+    leads = find_gaps(llm=StubLLM("a gap. [Springborn2008 #chunk 16]"))
+    assert leads == []
+
+
 def test_find_gaps_explicit_topics_override_default(
     monkeypatch: pytest.MonkeyPatch,
     mock_paper_titles: None,

tests/synthesis/test_grounded.py

@@ -148,7 +148,8 @@ def test_find_gaps_topic_with_no_chunks(
 ) -> None:
     """When retrieval returns no chunks, a gap lead is emitted directly."""
     monkeypatch.setattr("codex.synthesis._retrieve_chunks", lambda queries, top_k: [])
-    leads = find_gaps(llm=StubLLM(""))
+    # Coverage gaps are opt-in now (audit R-8): pass an explicit topic.
+    leads = find_gaps(llm=StubLLM(""), topics=["nonexistent topic"])
     assert len(leads) >= 1
     assert all(lead.kind == "gap" for lead in leads)
     # Direct gap leads carry a validation hint (re-ingest)

tests/wiki/test_compile.py

@@ -213,6 +213,47 @@ def test_grounding_guard_last_sentence_grounded_earlier_hallucination_ignored()
     )
 
 
+def test_grounding_guard_robust_to_trailing_comma() -> None:
+    """A faithful 5-word claim grounds despite a trailing comma (audit R-1).
+
+    The chunk says "... the volume function V0 is strictly concave on the angle
+    domain." Before edge-punctuation stripping, the claim token "concave," != the
+    chunk token "concave", so the only content-5-gram failed to match and the
+    claim was wrongly marked ungrounded.
+    """
+    claim = Claim(
+        text="the volume function V0 is strictly concave,",
+        bibkey="Springborn2008",
+        locator="chunk 16",
+    )
+    result = _run_grounding_guard([claim], FIXTURE_CHUNKS)
+    assert result[0].grounded is True
+
+
+def test_grounding_guard_no_substring_bleed_across_tokens() -> None:
+    """A 5-gram must match whole tokens, not bleed into a longer chunk word (audit C-6).
+
+    The chunk contains 'subset'; a claim whose first token is 'set' must NOT ground
+    by substring-matching the suffix of 'subset'.
+    """
+    chunks = [
+        {
+            "id": 99,
+            "paper_id": "p",
+            "ord": 0,
+            "bibkey": "TestBib",
+            "content": "the subset conformal map energy functional is minimized here",
+        }
+    ]
+    claim = Claim(
+        text="the set conformal map energy functional",
+        bibkey="TestBib",
+        locator="chunk 0",
+    )
+    result = _run_grounding_guard([claim], chunks)
+    assert result[0].grounded is False
+
+
 # ---------------------------------------------------------------------------
 # _inject_cross_refs
 # ---------------------------------------------------------------------------
@@ -274,6 +315,19 @@ def test_inject_cross_refs_skips_inline_code() -> None:
     assert "[[circle-packing]]" in result  # bare occurrence replaced
 
 
+def test_inject_cross_refs_skips_math_spans() -> None:
+    """Concept names inside LaTeX math are NOT rewritten to [[slug]] links (audit R-9)."""
+    concepts = [
+        Concept(slug="energy", title="Energy", aliases=[]),
+        FIXTURE_CONCEPT,
+    ]
+    text = "Prose Energy here. Math $x = Energy^2$ and inline \\(Energy\\) stay literal."
+    result = _inject_cross_refs(text, concepts, current_slug="lobachevsky-function")
+    assert "$x = Energy^2$" in result  # display/inline $...$ math untouched
+    assert "\\(Energy\\)" in result  # \(...\) math untouched
+    assert "Prose [[energy]] here." in result  # prose occurrence still linked
+
+
 def test_inject_cross_refs_full_list_even_when_single_concept() -> None:
     """Cross-ref injection uses the full concept list, not just the compiled concept."""
     concepts = [