diff --git a/ledger/src/m2_ledger/__pycache__/models.cpython-312.pyc b/ledger/src/m2_ledger/__pycache__/models.cpython-312.pyc
index 48525db..78ebe84 100644
Binary files a/ledger/src/m2_ledger/__pycache__/models.cpython-312.pyc and b/ledger/src/m2_ledger/__pycache__/models.cpython-312.pyc differ
diff --git a/ledger/src/m2_ledger/models.py b/ledger/src/m2_ledger/models.py
index 383d59b..d6b1079 100644
--- a/ledger/src/m2_ledger/models.py
+++ b/ledger/src/m2_ledger/models.py
@@ -121,8 +121,17 @@ def record_install(
         cut = int(amount * platform_pct)
         seller_amount = amount - cut
 
-        net_tx_id = _insert_tx(conn, ts, buyer, seller, seller_amount, "install", ref)
-        cut_tx_id = _insert_tx(conn, ts, buyer, "platform", cut, "install", ref)
+        # The tx table CHECKs amount > 0: a pct that rounds either side to zero
+        # (0.0 -> cut == 0, 1.0 -> seller_amount == 0) must skip that row, not
+        # violate the constraint. amount >= 1 guarantees at least one row.
+        tx_ids: list[int] = []
+        net_tx_id = None
+        if seller_amount > 0:
+            net_tx_id = _insert_tx(conn, ts, buyer, seller, seller_amount, "install", ref)
+            tx_ids.append(net_tx_id)
+        if cut > 0:
+            tx_ids.append(_insert_tx(conn, ts, buyer, "platform", cut, "install", ref))
+        paying_tx_id = net_tx_id if net_tx_id is not None else tx_ids[0]
 
         grant_id = f"gr_{uuid.uuid4().hex}"
         conn.execute(
@@ -131,14 +140,14 @@ def record_install(
                                  solution_version_major, tx_id, ts)
             VALUES (?, ?, ?, ?, ?, ?)
             """,
-            (grant_id, buyer, ref, 1, net_tx_id, ts),
+            (grant_id, buyer, ref, 1, paying_tx_id, ts),
         )
 
         grant_row = conn.execute(
             "SELECT * FROM grant_ WHERE grant_id = ?", (grant_id,)
         ).fetchone()
 
-    return {"tx_ids": [net_tx_id, cut_tx_id], "grant": dict(grant_row)}
+    return {"tx_ids": tx_ids, "grant": dict(grant_row)}
 
 
 def record_refund(conn: sqlite3.Connection, ref: str) -> dict:
diff --git a/ledger/tests/__pycache__/conftest.cpython-312-pytest-9.1.1.pyc b/ledger/tests/__pycache__/conftest.cpython-312-pytest-9.1.1.pyc
new file mode 100644
index 0000000..60d4cfe
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diff --git a/ledger/tests/__pycache__/test_properties.cpython-312-pytest-9.1.1.pyc b/ledger/tests/__pycache__/test_properties.cpython-312-pytest-9.1.1.pyc
new file mode 100644
index 0000000..8bc7dee
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diff --git a/ledger/tests/test_properties.py b/ledger/tests/test_properties.py
index 9f67b0e..d33ab40 100644
--- a/ledger/tests/test_properties.py
+++ b/ledger/tests/test_properties.py
@@ -246,3 +246,26 @@ def test_api_install_402_leaves_tx_log_unchanged(client, service_headers, admin_
 
     after = client.get("/tx", headers=service_headers).json()["transactions"]
     assert after == before
+
+
+def test_edge_platform_pct_zero_and_one(tmp_path):
+    """Regression: pct that rounds a row to zero must skip it, not 500.
+
+    (T013 worker finding: CHECK amount > 0 was violated by cut == 0 or
+    seller_amount == 0; fixed in models.record_install.)
+    """
+    from m2_ledger import models as M
+
+    conn = M.init_db(str(tmp_path / "edge.db"))
+    M.record_grant(conn, "buyer", 100)
+
+    r0 = M.record_install(conn, "buyer", "seller", 10, 0.0, "ref:pct0")
+    assert M.balance(conn, "seller") == 10
+    assert M.balance(conn, "platform") == 0
+    assert len(r0["tx_ids"]) == 1
+
+    r1 = M.record_install(conn, "buyer", "seller", 10, 1.0, "ref:pct1")
+    assert M.balance(conn, "platform") == 10
+    assert len(r1["tx_ids"]) == 1
+    assert r1["grant"]["tx_id"] == r1["tx_ids"][0]
+    assert M.balance(conn, "buyer") == 80
diff --git a/specs/001-market-first-wedge/tasks.md b/specs/001-market-first-wedge/tasks.md
index 88b32e5..e88022e 100644
--- a/specs/001-market-first-wedge/tasks.md
+++ b/specs/001-market-first-wedge/tasks.md
@@ -51,7 +51,7 @@ published listing
 - [x] T010 [P] [US1] Implement tx + grant models and derived-balance queries in `ledger/src/m2_ledger/models.py` (SQLite WAL, append-only invariants, data-model.md Transaction/LicenseGrant)
 - [x] T011 [P] [US1] Implement X-API-Key auth (service/admin key classes) in `ledger/src/m2_ledger/auth.py`
 - [x] T012 [US1] Implement API routes `/health`, `/balance/{op}`, `/tx/install`, `/tx/refund`, `/tx`, `/license/{op}/{listing}` in `ledger/src/m2_ledger/api.py` (402/409 semantics, all-or-nothing install tx, idempotent by ref)
-- [ ] T013 [US1] Ledger unit + property tests in `ledger/tests/test_properties.py`: balance==fold(log) under generated sequences; no grant without tx; install atomicity; duplicate-ref 409
+- [x] T013 [US1] Ledger unit + property tests in `ledger/tests/test_properties.py`: balance==fold(log) under generated sequences; no grant without tx; install atomicity; duplicate-ref 409
 - [ ] T014 [US1] Dockerfile + Coolify deployment for m2-ledger on the `coolify` network in `ledger/Dockerfile` + `ledger/README.md` deploy notes; verify `GET /health` from the network
 - [x] T015 [US1] Create `market:catalog` partition and implement indexer `indexer/src/m2_market_indexer/reindex.py` + `watch.py` per contracts/catalog-index.md (registry → memory-api upsert, tenant_visibility payload, delist removal)