diff --git a/pyproject.toml b/pyproject.toml
index d96fd965..332d75ba 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -29,6 +29,7 @@ dependencies = [
 
 [project.optional-dependencies]
 dev = [
+    "hypothesis>=6.100,<7",
     "pytest>=8.0.0,<9",
     "ruff>=0.5.0",
 ]
@@ -56,5 +57,6 @@ target-version = "py311"
 
 [dependency-groups]
 dev = [
+    "hypothesis>=6.100,<7",
     "pytest>=8.0.0,<9",
 ]
diff --git a/scripts/build_series_catalog.py b/scripts/build_series_catalog.py
index de6f4380..80186a78 100644
--- a/scripts/build_series_catalog.py
+++ b/scripts/build_series_catalog.py
@@ -1436,61 +1436,81 @@ def _registry_event(
     }
 
 
-def build_catalog(
-    observations_path: pathlib.Path,
-    docket_path: pathlib.Path | None,
-    existing: ExistingCatalog,
-    registry: UuidRegistry,
-) -> tuple[dict, dict]:
-    """Build the catalog and the identity plan.
+def _append_gate_helpers():
+    """Import the append gate's supersede-aware view and content address."""
+    try:
+        from check_thesis_facts_append import (
+            effective_current_rows,
+            expected_assertion_version_id,
+        )
+    except ImportError as exc:  # pragma: no cover - environment guard
+        raise SystemExit(
+            "cannot import the append gate's content address and "
+            "supersede-aware current view from "
+            f"check_thesis_facts_append (receipt package required): {exc}"
+        )
+    return effective_current_rows, expected_assertion_version_id
 
-    The plan records every registry-affecting outcome: ``mints`` (new
-    identity bindings to append), ``supersedes`` (identities whose UUID
-    changes — these require ``--allow-remint``), and ``dropped`` (existing
-    rows whose UUID would vanish from the catalog — also gated).
+
+def effective_assertion_version_id(row: dict, index: int) -> str:
+    """Return the assertion version id the append gate assigns ``row``.
+
+    Mirrors receipt's ``_effective_assertion_id``: a versioned row is
+    addressed by its explicit ``assertionVersion.id``, and a row with no
+    ``assertionVersion`` (every row of the immutable prefix predates
+    versioning) by its recomputed av2 content address. A correction of a
+    prefix row names that address in ``supersedes``. ``index`` only
+    labels refusals.
     """
-    raw = observations_path.read_bytes()
-    observation_lines = raw.decode().split("\n")
-    if observation_lines and observation_lines[-1] == "":
-        observation_lines.pop()
-    rows = [
-        json.loads(
-            line,
-            object_pairs_hook=_reject_duplicate_keys,
-            parse_constant=_reject_json_constants,
+    version = row.get("assertionVersion")
+    if version is None:
+        _, content_address = _append_gate_helpers()
+        try:
+            return content_address(row)
+        except (AttributeError, TypeError, ValueError) as exc:
+            raise SystemExit(
+                f"observation row {index}: cannot compute the content "
+                f"address of a row without assertionVersion: {exc}"
+            ) from None
+    if not isinstance(version, dict) or not isinstance(
+        version.get("id"), str
+    ) or not version["id"]:
+        raise SystemExit(
+            f"observation row {index}: assertionVersion must carry a "
+            "nonempty string id"
         )
-        for line in observation_lines
-        if line.strip()
-    ]
-    # The journal is append-only: a correction appends a row whose
-    # assertionVersion.supersedes names the version it replaces. Series
-    # identity must follow the supersede-aware CURRENT view (the same one
-    # the ledger's aggregate-fact validation uses), or superseded
-    # assertions would keep stale identities alive forever. The imported
-    # helper assumes append-gate-validated input; standalone runs get the
-    # same preconditions enforced here (unique ids, resolvable links, no
-    # cycles).
-    seen_ids: dict[str, int] = {}
+    return version["id"]
+
+
+def check_assertion_versions(rows: list[dict]) -> list[str]:
+    """Enforce the append gate's supersede preconditions; return every id.
+
+    The gate (receipt ``check_rows``) reserves the effective id of EVERY
+    row, versioned or not, and a correction names the effective id of the
+    version it replaces. This check reserves the same ids, so a
+    gate-accepted correction of a prefix row is accepted here too. It
+    refuses the part of the gate's rules the current view relies on: two
+    rows with one effective id (identical unversioned rows, or a row
+    restating an earlier row's exact addressed content), a link to no
+    row's id, a self-link and a cycle. The gate refuses each of these as
+    well. Its other rules (an explicit id equals the content address; a
+    link names the active version of the same record, on an earlier line,
+    so no version is superseded twice) are the gate's alone.
+    """
+    ids: list[str] = []
+    owner: dict[str, int] = {}
     links: dict[str, str] = {}
     for index, row in enumerate(rows):
-        version = row.get("assertionVersion")
-        if version is None:
-            continue
-        if not isinstance(version, dict) or not isinstance(
-            version.get("id"), str
-        ) or not version["id"]:
-            raise SystemExit(
-                f"observation row {index}: assertionVersion must carry a "
-                "nonempty string id"
-            )
-        vid = version["id"]
-        if vid in seen_ids:
+        vid = effective_assertion_version_id(row, index)
+        if vid in owner:
             raise SystemExit(
-                f"observation row {index}: assertionVersion id {vid!r} "
-                f"duplicates row {seen_ids[vid]}"
+                f"observation row {index}: assertion version {vid!r} "
+                f"duplicates row {owner[vid]}"
             )
-        seen_ids[vid] = index
-        supersedes = version.get("supersedes")
+        owner[vid] = index
+        ids.append(vid)
+        version = row.get("assertionVersion")
+        supersedes = version.get("supersedes") if version is not None else None
         if supersedes is not None:
             if not isinstance(supersedes, str) or not supersedes:
                 raise SystemExit(
@@ -1504,7 +1524,7 @@ def build_catalog(
                 )
             links[vid] = supersedes
     for vid, target in links.items():
-        if target not in seen_ids:
+        if target not in owner:
             raise SystemExit(
                 f"assertionVersion {vid!r} supersedes unknown version "
                 f"{target!r}"
@@ -1519,13 +1539,44 @@ def build_catalog(
                 )
             seen_chain.add(cursor)
             cursor = links.get(cursor)
-    try:
-        from check_thesis_facts_append import effective_current_rows
-    except ImportError as exc:  # pragma: no cover - environment guard
-        raise SystemExit(
-            "cannot import the supersede-aware current view from "
-            f"check_thesis_facts_append (receipt package required): {exc}"
+    return ids
+
+
+def build_catalog(
+    observations_path: pathlib.Path,
+    docket_path: pathlib.Path | None,
+    existing: ExistingCatalog,
+    registry: UuidRegistry,
+) -> tuple[dict, dict]:
+    """Build the catalog and the identity plan.
+
+    The plan records every registry-affecting outcome: ``mints`` (new
+    identity bindings to append), ``supersedes`` (identities whose UUID
+    changes — these require ``--allow-remint``), and ``dropped`` (existing
+    rows whose UUID would vanish from the catalog — also gated).
+    """
+    raw = observations_path.read_bytes()
+    observation_lines = raw.decode().split("\n")
+    if observation_lines and observation_lines[-1] == "":
+        observation_lines.pop()
+    rows = [
+        json.loads(
+            line,
+            object_pairs_hook=_reject_duplicate_keys,
+            parse_constant=_reject_json_constants,
         )
+        for line in observation_lines
+        if line.strip()
+    ]
+    # The journal is append-only: a correction appends a row whose
+    # assertionVersion.supersedes names the version it replaces. Series
+    # identity must follow the supersede-aware CURRENT view (the same one
+    # the ledger's aggregate-fact validation uses), or superseded
+    # assertions would keep stale identities alive forever. The imported
+    # helper assumes append-gate-validated input; standalone runs get the
+    # preconditions it relies on from check_assertion_versions.
+    check_assertion_versions(rows)
+    effective_current_rows, _ = _append_gate_helpers()
     current_rows = effective_current_rows(rows)
     identities = build_identities(current_rows)
 
diff --git a/tests/test_build_series_catalog.py b/tests/test_build_series_catalog.py
index 584cb707..fc886040 100644
--- a/tests/test_build_series_catalog.py
+++ b/tests/test_build_series_catalog.py
@@ -10,17 +10,28 @@
 
 from __future__ import annotations
 
+import copy
 import doctest
+import hashlib
 import json
 import pathlib
+import re
 import sys
 
 import pytest
+from hypothesis import given, settings
+from hypothesis import strategies as st
+
+# receipt's effective-id rule (private; effective_current_rows uses it, and
+# check_rows reserves the same id inline after requiring an explicit id to
+# equal the content address): the differential oracle for the generator's.
+from receipt.append_gate import _effective_assertion_id
 
 ROOT = pathlib.Path(__file__).resolve().parents[1]
 sys.path.insert(0, str(ROOT / "scripts"))
 
 import build_series_catalog as bsc  # noqa: E402
+import check_thesis_facts_append as gate  # noqa: E402
 
 PERIOD_SEGMENTS = [
     "fy2026",
@@ -782,6 +793,10 @@ def test_committed_catalog_is_current_and_valid() -> None:
     # Occurrences as of 55bbf3d: both August keys map to
     # dol.eta.continued_claims.sa (joined week_2026-08-15 at d77afe2) and
     # us.dol.initial_claims.sa.
+    # Extended 2026-09-29 to the catalog at 598f394, whose eight-row
+    # first-print append first spelled week_2026-08-29 and week_2026-09-05
+    # (both claims series) and week_2026-09-12 (us.dol.initial_claims.sa
+    # only). Each is the row's own week_ending period, so the strips stand.
     # EVERY stripped spelling is auditable, mapped to the canonical
     # concepts it touched — a statute or edition label colliding with a
     # period spelling can only be caught here.
@@ -794,7 +809,8 @@ def test_committed_catalog_is_current_and_valid() -> None:
         "week_2026-06-20", "week_2026-06-27", "week_2026-07-04",
         "week_2026-07-11", "week_2026-07-13", "week_2026-07-18",
         "week_2026-07-25", "week_2026-08-01", "week_2026-08-08",
-        "week_2026-08-15", "week_2026-08-22", "week_2026_06_13",
+        "week_2026-08-15", "week_2026-08-22", "week_2026-08-29",
+        "week_2026-09-05", "week_2026-09-12", "week_2026_06_13",
         "week_ending_2026_06_06",
     ]
     assert committed["stripped_segments"]["after_mpc_june_2026"] == [
@@ -2188,6 +2204,409 @@ def test_assertion_version_preconditions(tmp_path: pathlib.Path) -> None:
         _build(tmp_path, [f])
 
 
+# The append gate (receipt check_rows) gives EVERY journal row one effective
+# assertion version id: its explicit assertionVersion.id, or, for a row
+# without one (the whole immutable prefix), its recomputed av2 content
+# address. It reserves every such id and a correction names one of them.
+# The generator's preconditions must accept whatever the gate accepts; on
+# journals whose explicit ids are their content addresses (the gate's first
+# row rule), refuse a duplicate id, a self-link, an unresolvable link and a
+# cycle exactly when the gate refuses for that reason; and with any defects
+# at all, refuse only what the gate refuses. 2026-09-29 repro: six
+# corrections of the June 2026 Table A-19 prefix rows passed the gate and
+# were refused here as superseding an "unknown version", which would have
+# failed every later resolver append.
+
+PREFIX_LINE_COUNT = json.loads(
+    (ROOT / "ledger" / "immutable_prefix.json").read_text(encoding="utf-8")
+)["prefixLineCount"]
+
+
+def _address(row: dict) -> str:
+    return _effective_assertion_id(row, gate.APPEND_GATE_SPEC)
+
+
+def _journal_row(
+    record: str,
+    value: float,
+    supersedes: str | None = None,
+    *,
+    versioned: bool = True,
+) -> dict:
+    """A row check_rows accepts; ``versioned=False`` is a prefix-style row."""
+    row = _row("agency.rate", rid=record)
+    row["value"] = value
+    row.update(
+        retrievedAt="2026-06-01T00:00:00Z",
+        sourceVintage="first_print",
+        ledgerRepoSha="0" * 40,
+        responseArchive={"sha256": "0" * 64},
+    )
+    if versioned:
+        # The content address excludes the link, so relinking keeps the id.
+        row["assertionVersion"] = {
+            "id": gate.expected_assertion_version_id(row),
+            "supersedes": supersedes,
+        }
+    return row
+
+
+def _gate_refusal(rows: list[dict], prefix_count: int) -> str | None:
+    try:
+        gate.check_rows([json.dumps(row) for row in rows], prefix_count)
+    except gate.AppendError as exc:
+        return str(exc)
+    return None
+
+
+GENERATOR_REASONS = {
+    "duplicates row": "duplicate",
+    "supersedes itself": "self",
+    "supersedes unknown version": "unknown",
+    "supersede cycle": "cycle",
+}
+
+
+def _generator_refusal(rows: list[dict]) -> str | None:
+    """The generator's refusal reason, or its raw message if unclassified."""
+    try:
+        bsc.check_assertion_versions(rows)
+    except SystemExit as exc:
+        message = str(exc)
+        return next(
+            (reason for text, reason in GENERATOR_REASONS.items()
+             if text in message),
+            message,
+        )
+    return None
+
+
+GATE_LINK_REFUSAL = re.compile(r"line (\d+) supersedes (\S+) but ")
+
+
+def _gate_reason(rows: list[dict], refusal: str | None) -> str | None:
+    """Classify the gate's refusal by the generator's reasons.
+
+    The gate names only the first line it refuses. A restated id is a
+    duplicate. A refused link is classified by where its target lies among
+    the gate's own effective ids: this row (self), no row (unknown), or a
+    row whose chain leads back here (cycle). Every other refusal (a link to
+    a non-active, other-record or later version outside a cycle, a missing
+    link) is a rule the gate alone enforces, which the generator must
+    accept: None. So is an explicit id that is not the content address,
+    but the generator trusts explicit ids, so such a journal can still be
+    refused there for a duplicate or orphaned link; journals with one are
+    held only to containment.
+    """
+    if refusal is None:
+        return None
+    if " restates assertion version " in refusal:
+        return "duplicate"
+    match = GATE_LINK_REFUSAL.match(refusal)
+    if match is None:
+        return None
+    ids = [_address(row) for row in rows]
+    own, target = ids[int(match[1]) - 1], match[2]
+    if target == own:
+        return "self"
+    if target not in ids:
+        return "unknown"
+    links = {
+        ids[index]: (row.get("assertionVersion") or {}).get("supersedes")
+        for index, row in enumerate(rows)
+    }
+    cursor, seen = target, set()
+    while cursor is not None and cursor not in seen:
+        if cursor == own:
+            return "cycle"
+        seen.add(cursor)
+        cursor = links.get(cursor)
+    return None
+
+
+def _relink(row: dict, target: str | None) -> None:
+    row["assertionVersion"]["supersedes"] = target
+
+
+def test_live_ledger_reserves_the_gates_ids() -> None:
+    # Regression on the live ledger: the gate accepts it, and every row,
+    # the prefix rows without assertionVersion included, gets the gate's
+    # effective id. test_committed_catalog_is_current_and_valid pins the
+    # catalog bytes, which this change leaves identical.
+    lines = bsc.OBSERVATIONS.read_text(encoding="utf-8").splitlines()
+    rows = [json.loads(line) for line in lines]
+    assert all(
+        "assertionVersion" not in row for row in rows[:PREFIX_LINE_COUNT]
+    )
+    gate.check_rows(lines, PREFIX_LINE_COUNT)
+    assert bsc.check_assertion_versions(rows) == [_address(r) for r in rows]
+
+
+def test_correction_of_a_prefix_row_is_accepted_like_the_gate(
+    tmp_path: pathlib.Path,
+) -> None:
+    # The 2026-09-29 repro on the live ledger. SYNTHETIC corrections: the
+    # restatement in millions is the repro's, not a chosen remedy (that is
+    # decision d397), and each archive digest is synthetic so no real
+    # correction can share its content address. Each supersedes the active
+    # version of its June record, which is the prefix row's av2 address
+    # until a real correction lands.
+    lines = bsc.OBSERVATIONS.read_text(encoding="utf-8").splitlines()
+    rows = [json.loads(line) for line in lines]
+    june = [
+        row for row in rows[:PREFIX_LINE_COUNT]
+        if row["source_record_id"].startswith(
+            "bls.cps.employed_people_by_occupation."
+        )
+        and row["source_record_id"].endswith(".june_2026.first_print")
+    ]
+    assert len(june) == 6
+    assert all("assertionVersion" not in row for row in june)
+    corrections = []
+    for original in june:
+        record = original["source_record_id"]
+        active = [r for r in rows if r["source_record_id"] == record][-1]
+        correction = copy.deepcopy(original)
+        correction["value"] = round(original["value"] / 1000, 3)
+        correction["measure"]["unit"] = "millions"
+        correction["responseArchive"]["sha256"] = hashlib.sha256(
+            f"synthetic correction of {record}".encode()
+        ).hexdigest()
+        correction["assertionVersion"] = {
+            "id": gate.expected_assertion_version_id(correction),
+            "supersedes": _address(active),
+        }
+        corrections.append(correction)
+    journal = rows + corrections
+
+    assert _gate_refusal(journal, PREFIX_LINE_COUNT) is None
+    ids = bsc.check_assertion_versions(journal)
+    assert ids == [_address(row) for row in journal]
+
+    observations = tmp_path / "obs.jsonl"
+    observations.write_text(
+        "".join(json.dumps(row) + "\n" for row in journal), encoding="utf-8"
+    )
+    catalog, plan = bsc.build_catalog(
+        observations,
+        bsc.DOCKET_SEED,
+        bsc.ExistingCatalog(bsc.CATALOG),
+        bsc.UuidRegistry.load(bsc.UUID_REGISTRY),
+    )
+    assert not plan["mints"] and not plan["supersedes"] and not plan["dropped"]
+    occupations = [
+        series for series in catalog["series"]
+        if series["concept"].startswith(
+            "bls.cps.employed_people_by_occupation."
+        )
+    ]
+    assert len(occupations) == 6
+    assert all(series["unit"] == "millions" for series in occupations)
+    assert catalog["observation_rows"] == len(journal)
+    # Each correction replaces its target, so the current count is the
+    # live ledger's.
+    assert catalog["current_assertion_rows"] == len(
+        gate.effective_current_rows(rows)
+    )
+
+
+def test_every_rows_effective_id_is_reserved() -> None:
+    # A row without assertionVersion reserves its content address exactly
+    # as the gate does, so two identical such rows, a versioned re-append
+    # of one, and an A -> B -> A restore of one all collide. So does an
+    # A -> B -> A restore among versioned rows.
+    legacy = _journal_row("rec.a", 1.0, versioned=False)
+    reissued = copy.deepcopy(legacy)
+    reissued["assertionVersion"] = {"id": _address(legacy), "supersedes": None}
+    b = _journal_row("rec.a", 2.0, _address(legacy))
+    restore = copy.deepcopy(legacy)
+    restore["assertionVersion"] = {
+        "id": _address(legacy), "supersedes": _address(b)
+    }
+    a2 = _journal_row("rec.b", 1.0)
+    b2 = _journal_row("rec.b", 2.0, _address(a2))
+    back = _journal_row("rec.b", 1.0, _address(b2))
+    for journal, prefix, match in (
+        ([legacy, copy.deepcopy(legacy)], 2, "row 1: .* duplicates row 0"),
+        ([legacy, reissued], 1, "row 1: .* duplicates row 0"),
+        ([legacy, b, restore], 1, "row 2: .* duplicates row 0"),
+        ([a2, b2, back], 0, "row 2: .* duplicates row 0"),
+    ):
+        assert _gate_reason(journal, _gate_refusal(journal, prefix)) == (
+            "duplicate"
+        )
+        with pytest.raises(SystemExit, match=match):
+            bsc.check_assertion_versions(journal)
+
+
+def test_link_refusals_fire_where_the_gate_refuses() -> None:
+    legacy = _journal_row("rec.a", 1.0, versioned=False)
+    unknown = _journal_row("rec.a", 2.0, "av2:" + "f" * 64)
+    # A near miss: the address the prefix row would have at another value.
+    near = _journal_row("rec.a", 2.0, _address(dict(legacy, value=3.0)))
+    itself = _journal_row("rec.a", 2.0)
+    _relink(itself, _address(itself))
+    x, y = (_journal_row(f"rec.{n}", 1.0) for n in "xy")
+    _relink(x, _address(y))
+    _relink(y, _address(x))
+    two_cycle = [legacy, x, y]
+    p, q, r = (_journal_row(f"rec.{n}", 1.0) for n in "pqr")
+    _relink(p, _address(q))
+    _relink(q, _address(r))
+    _relink(r, _address(p))
+    three_cycle = [legacy, p, q, r]
+    for journal, match, reason in (
+        ([legacy, unknown], "supersedes unknown version", "unknown"),
+        ([legacy, near], "supersedes unknown version", "unknown"),
+        ([legacy, itself], "supersedes itself", "self"),
+        (two_cycle, "supersede cycle", "cycle"),
+        (three_cycle, "supersede cycle", "cycle"),
+    ):
+        assert _gate_reason(journal, _gate_refusal(journal, 1)) == reason
+        with pytest.raises(SystemExit, match=match):
+            bsc.check_assertion_versions(journal)
+
+
+@st.composite
+def _gate_valid_journals(draw) -> tuple[list[dict], int]:
+    """A journal check_rows accepts: prefix-style rows without
+    assertionVersion, then versioned appends, each a new record or a
+    correction of a record's active version (a prefix row's by its
+    content address)."""
+    prefix = draw(st.integers(0, 4))
+    steps = draw(st.lists(st.one_of(st.none(), st.integers(0, 7)), max_size=8))
+    rows: list[dict] = []
+    active: dict[str, str] = {}
+    for _ in range(prefix):
+        row = _journal_row(f"rec.{len(active)}", float(len(rows)),
+                           versioned=False)
+        rows.append(row)
+        active[row["source_record_id"]] = _address(row)
+    for step in steps:
+        if step is None or not active:
+            record, supersedes = f"rec.{len(active)}", None
+        else:
+            record = sorted(active)[step % len(active)]
+            supersedes = active[record]
+        row = _journal_row(record, float(len(rows)), supersedes)
+        rows.append(row)
+        active[record] = _address(row)
+    return rows, prefix
+
+
+MUTATIONS = (
+    "unknown", "self", "cycle", "relink", "unlink", "duplicate", "restore"
+)
+# An explicit id that is not the row's content address: the gate refuses
+# it outright, and only containment is claimed for it.
+ANY_MUTATION = (*MUTATIONS, "reid")
+
+
+def _mutate(draw, kind: str, rows: list[dict], prefix: int):
+    """Apply one defect. Only ``supersedes`` changes, which leaves every id
+    alone, or a row is added: a copy of any row, or an A -> B -> A
+    restore. The exception is "reid", which rewrites one explicit id to
+    another row's id or to an address no row has."""
+    ids = [_address(row) for row in rows]
+    versioned = [i for i, row in enumerate(rows) if "assertionVersion" in row]
+    if kind == "unknown" and versioned:
+        target = "av2:" + hashlib.sha256(
+            draw(st.binary(min_size=1, max_size=8))
+        ).hexdigest()
+        _relink(rows[draw(st.sampled_from(versioned))], target)
+    elif kind == "self" and versioned:
+        i = draw(st.sampled_from(versioned))
+        _relink(rows[i], ids[i])
+    elif kind == "cycle" and len(versioned) >= 2:
+        ring = sorted(draw(st.lists(st.sampled_from(versioned), min_size=2,
+                                    max_size=3, unique=True)))
+        for a, b in zip(ring, ring[1:] + ring[:1]):
+            _relink(rows[a], ids[b])
+    elif kind == "relink" and versioned and len(rows) >= 2:
+        # Any other row, earlier or later: the valid target, a stale or
+        # other-record version, or a forward link that may close a cycle.
+        i = draw(st.sampled_from(versioned))
+        j = draw(st.sampled_from([k for k in range(len(rows)) if k != i]))
+        _relink(rows[i], ids[j])
+    elif kind == "unlink" and versioned:
+        _relink(rows[draw(st.sampled_from(versioned))], None)
+    elif kind == "duplicate" and rows:
+        j = draw(st.integers(0, len(rows) - 1))
+        at = draw(st.integers(j + 1, len(rows)))
+        rows.insert(at, copy.deepcopy(rows[j]))
+        prefix += at < prefix
+    elif kind == "restore":
+        versions: dict[str, list[int]] = {}
+        for i, row in enumerate(rows):
+            versions.setdefault(row["source_record_id"], []).append(i)
+        chains = [v for _, v in sorted(versions.items()) if len(v) >= 2]
+        if chains:
+            chain = draw(st.sampled_from(chains))
+            first = copy.deepcopy(rows[chain[0]])
+            first["assertionVersion"] = {
+                "id": ids[chain[0]], "supersedes": ids[chain[-1]]
+            }
+            rows.append(first)
+    elif kind == "reid" and versioned:
+        i = draw(st.sampled_from(versioned))
+        stray = "av2:" + hashlib.sha256(
+            draw(st.binary(min_size=1, max_size=8))
+        ).hexdigest()
+        rows[i]["assertionVersion"]["id"] = draw(st.sampled_from([*ids, stray]))
+    return rows, prefix
+
+
+@st.composite
+def _mutated_journals(draw, max_mutations: int, kinds=MUTATIONS):
+    rows, prefix = draw(_gate_valid_journals())
+    rows = copy.deepcopy(rows)
+    kinds = draw(st.lists(st.sampled_from(kinds), max_size=max_mutations))
+    for kind in kinds:
+        rows, prefix = _mutate(draw, kind, rows, prefix)
+    return rows, prefix
+
+
+PROPERTY_SETTINGS = settings(
+    max_examples=400, deadline=None, derandomize=True, database=None
+)
+
+
+@PROPERTY_SETTINGS
+@given(_gate_valid_journals())
+def test_gate_accepted_journals_pass_the_preconditions(journal) -> None:
+    # Invariant: the gate accepts => the generator accepts, and both assign
+    # every row the same effective id.
+    rows, prefix = journal
+    assert _gate_refusal(rows, prefix) is None
+    assert bsc.check_assertion_versions(rows) == [_address(r) for r in rows]
+
+
+@PROPERTY_SETTINGS
+@given(_mutated_journals(max_mutations=1))
+def test_generator_refuses_iff_the_gate_does_for_that_reason(journal) -> None:
+    # Invariant, on journals with at most one defect: the generator refuses
+    # for reason R exactly when the gate's refusal classifies as R, and
+    # accepts every journal the gate accepts or refuses for its own rules.
+    rows, prefix = journal
+    refusal = _gate_refusal(rows, prefix)
+    assert _generator_refusal(rows) == _gate_reason(rows, refusal), refusal
+
+
+@PROPERTY_SETTINGS
+@given(_mutated_journals(max_mutations=3, kinds=ANY_MUTATION))
+def test_generator_refusals_are_gate_refusals(journal) -> None:
+    # Invariant, with several defects, ids rewritten away from their content
+    # addresses included: every generator refusal is a gate refusal, and a
+    # gate refusal for a generator reason is refused here.
+    rows, prefix = journal
+    refusal = _gate_refusal(rows, prefix)
+    generator = _generator_refusal(rows)
+    if generator is not None:
+        assert refusal is not None
+    if _gate_reason(rows, refusal) is not None:
+        assert generator is not None
+
+
 def test_cross_dimension_ambiguous_alias_never_steals(
     tmp_path: pathlib.Path,
 ) -> None:
diff --git a/uv.lock b/uv.lock
index 3a5807ed..1d609318 100644
--- a/uv.lock
+++ b/uv.lock
@@ -635,6 +635,94 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/48/30/47d0bf6072f7252e6521f3447ccfa40b421b6824517f82854703d0f5a98b/hyperframe-6.1.0-py3-none-any.whl", hash = "sha256:b03380493a519fce58ea5af42e4a42317bf9bd425596f7a0835ffce80f1a42e5", size = 13007, upload-time = "2025-01-22T21:41:47.295Z" },
 ]
 
+[[package]]
+name = "hypothesis"
+version = "6.168.3"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "sortedcontainers" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/09/b7/13118bbc45d6d8b9d04e2de779e2a4ff23145ea39efa692b994fb874ca72/hypothesis-6.168.3.tar.gz", hash = "sha256:a43388f9067678fef6e13bdff325b6cfa6961a590498bb37f7ff31589c83bc75", size = 511022, upload-time = "2026-09-28T05:20:58.499Z" }
+wheels = [
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+
 [[package]]
 name = "idna"
 version = "3.11"
@@ -1661,6 +1749,7 @@ dependencies = [
 
 [package.optional-dependencies]
 dev = [
+    { name = "hypothesis" },
     { name = "pytest" },
     { name = "ruff" },
 ]
@@ -1670,6 +1759,7 @@ policyengine = [
 
 [package.dev-dependencies]
 dev = [
+    { name = "hypothesis" },
     { name = "pytest" },
 ]
 
@@ -1677,6 +1767,7 @@ dev = [
 requires-dist = [
     { name = "cryptography", specifier = ">=46.0.3" },
     { name = "httpx", specifier = ">=0.27.0" },
+    { name = "hypothesis", marker = "extra == 'dev'", specifier = ">=6.100,<7" },
     { name = "microplex", specifier = ">=0.1.0" },
     { name = "numpy", specifier = ">=1.24.0" },
     { name = "odfpy", specifier = ">=1.4.1" },
@@ -1697,7 +1788,10 @@ requires-dist = [
 provides-extras = ["dev", "policyengine"]
 
 [package.metadata.requires-dev]
-dev = [{ name = "pytest", specifier = ">=8.0.0,<9" }]
+dev = [
+    { name = "hypothesis", specifier = ">=6.100,<7" },
+    { name = "pytest", specifier = ">=8.0.0,<9" },
+]
 
 [[package]]
 name = "policyengine-core"