diff --git a/engineering/pid/drawlines.py b/engineering/pid/drawlines.py
index 149922d..cbbecb8 100644
--- a/engineering/pid/drawlines.py
+++ b/engineering/pid/drawlines.py
@@ -13,6 +13,7 @@ from .lines import (
     PID_LINE_LAYERS,
     aim_points,
     count_crossings,
+    flatten_bulges,
     format_line_number,
     label_placement,
     marker_positions,
@@ -106,13 +107,57 @@ def _vertices(info) -> list[tuple[float, float]]:
     return [(float(p[0]), float(p[1])) for p in info.properties.get("points") or []]
 
 
+def _bulges(info, count: int) -> list[float]:
+    """Per-vertex bulges as the engine reports them (both engines put a
+    ``bulges`` list next to ``points``); straight when it reports none."""
+    raw = info.properties.get("bulges") or []
+    out = []
+    for value in raw[:count]:
+        try:
+            out.append(float(value or 0.0))
+        except (TypeError, ValueError):
+            out.append(0.0)
+    return out + [0.0] * (count - len(out))
+
+
+def payload_port_refs(payload) -> list[tuple[str, str]]:
+    """``(handle, port)`` for each well-formed ``from``/``to`` in a line payload.
+
+    A foreign or hand-edited payload can carry anything under those keys
+    (``"garbage"``, ``None``, a number); reading it used to raise
+    ``TypeError`` out of ``draw_line``. Reader results never raise: a
+    malformed end is simply not a reference.
+    """
+    refs = []
+    if not isinstance(payload, dict):
+        return refs
+    for key in ("from", "to"):
+        ref = payload.get(key)
+        if not isinstance(ref, dict):
+            continue
+        handle, port = ref.get("handle"), ref.get("port")
+        if isinstance(handle, str) and isinstance(port, str):
+            refs.append((handle, port))
+    return refs
+
+
+def payload_seq(payload) -> int | None:
+    """The payload's sequence number when it is a genuine int (``True`` is not)."""
+    if not isinstance(payload, dict):
+        return None
+    seq = payload.get("seq")
+    return seq if type(seq) is int else None
+
+
 async def existing_pid_lines(backend: AutoCADBackend) -> list[dict]:
     """Every LINE/polyline on a P&ID line layer, with its payload when it has one.
 
     Listed without a type filter: the two engines name a lightweight polyline
     differently (``_POLY_TYPES``), and a filter spelled for one of them is blind
     on the other — every auto-built number would restart at 1 and no crossing
-    or port reuse would ever be reported there.
+    or port reuse would ever be reported there. ``vertices`` are the raw
+    vertices; ``bulges`` (one per vertex, DXF convention) let the crossing test
+    follow an arc instead of its chord.
     """
     out = []
     offset = 0
@@ -124,7 +169,15 @@ async def existing_pid_lines(backend: AutoCADBackend) -> list[dict]:
             if info.layer.upper() not in PID_LINE_LAYERS:
                 continue
             payload = await read_payload(backend, info.handle) if info.type in _POLY_TYPES else None
-            out.append({"handle": info.handle, "vertices": _vertices(info), "payload": payload})
+            vertices = _vertices(info)
+            out.append(
+                {
+                    "handle": info.handle,
+                    "vertices": vertices,
+                    "bulges": _bulges(info, len(vertices)),
+                    "payload": payload,
+                }
+            )
         if len(page) < _PAGE:
             break
         offset += _PAGE
@@ -184,17 +237,16 @@ async def draw_line(
     path = route(s_point, s_dir, e_point, e_dir, stub=stub, mode=route_mode)
 
     existing = await existing_pid_lines(backend)
-    crossings = count_crossings(path, [ln["vertices"] for ln in existing])
+    crossings = count_crossings(
+        path, [flatten_bulges(ln["vertices"], ln["bulges"]) for ln in existing]
+    )
     used: set[tuple[str, str]] = set()
     max_seq = 0
     for ln in existing:
-        payload = ln["payload"] or {}
-        for key in ("from", "to"):
-            ref = payload.get(key)
-            if ref:
-                used.add((ref["handle"], ref["port"]))
-        if isinstance(payload.get("seq"), int):
-            max_seq = max(max_seq, payload["seq"])
+        used.update(payload_port_refs(ln["payload"]))
+        seq = payload_seq(ln["payload"])
+        if seq is not None:
+            max_seq = max(max_seq, seq)
     port_reuse = [
         {"handle": ep["handle"], "port": ep["port"]}
         for ep in (start, end)
diff --git a/engineering/pid/lines.py b/engineering/pid/lines.py
index fed14f3..4f9afda 100644
--- a/engineering/pid/lines.py
+++ b/engineering/pid/lines.py
@@ -238,6 +238,53 @@ def marker_positions(vertices, min_len: float = 15.0) -> list[tuple[float, float
     return out
 
 
+#: Max chord deviation (mm) when a bulged polyline edge is flattened for the
+#: crossing test — a tenth of the thinnest ISO 128 lineweight.
+FLATTEN_SAGITTA = 0.05
+
+
+def flatten_bulges(points, bulges, sagitta: float = FLATTEN_SAGITTA) -> list[Point]:
+    """The polyline as straight segments, every bulged edge replaced by chords
+    that deviate from the arc by at most ``sagitta``.
+
+    Same arc arithmetic as ``engineering/measure.py`` (sweep ``4·atan(bulge)``,
+    radius ``chord / 2·sin(|sweep|/2)``) and ``graph._point_segment_distance``
+    (centre on the chord's left normal, ``radius - sagitta`` carrying it across
+    the chord past a semicircle). Checked against ``ezdxf.math.bulge_to_arc``
+    + ``ConstructionArc.flattening`` in ``tests/test_pid_lines.py``: identical
+    vertex count and positions to 1e-12 for bulges 0.2 … 2.0 of either sign.
+    A straight edge (bulge 0) is passed through; ``bulges`` shorter than the
+    edge count is padded with zeros.
+    """
+    pts = [(float(x), float(y)) for x, y in points]
+    if len(pts) < 2:
+        return pts
+    out: list[Point] = []
+    for i, (a, b) in enumerate(zip(pts, pts[1:], strict=False)):
+        out.append(a)
+        bulge = float(bulges[i]) if i < len(bulges) and bulges[i] else 0.0
+        chord = _dist(a, b)
+        if abs(bulge) < 1e-12 or chord < 1e-12:
+            continue
+        theta = 4.0 * math.atan(bulge)  # signed sweep, radians
+        radius = chord / (2.0 * math.sin(abs(theta) / 2.0))
+        sag = abs(bulge) * chord / 2.0
+        nx, ny = -(b[1] - a[1]) / chord, (b[0] - a[0]) / chord  # left of a→b
+        offset = (radius - sag) * (1.0 if bulge > 0 else -1.0)
+        cx = (a[0] + b[0]) / 2.0 + offset * nx
+        cy = (a[1] + b[1]) / 2.0 + offset * ny
+        start = math.atan2(a[1] - cy, a[0] - cx)
+        if sagitta >= radius:
+            segments = 1
+        else:
+            segments = max(1, math.ceil(abs(theta) / (2.0 * math.acos(1.0 - sagitta / radius))))
+        for k in range(1, segments):
+            angle = start + theta * k / segments
+            out.append((cx + radius * math.cos(angle), cy + radius * math.sin(angle)))
+    out.append(pts[-1])
+    return out
+
+
 def _orient(a: Point, b: Point, c: Point) -> float:
     return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0])
 
diff --git a/tests/test_pid_line_draw.py b/tests/test_pid_line_draw.py
index 6ad95d3..de34e1b 100644
--- a/tests/test_pid_line_draw.py
+++ b/tests/test_pid_line_draw.py
@@ -424,3 +424,72 @@ async def test_dry_run_plans_the_same_bubble_exit_as_the_real_run(backend):
     drawn = await run_spec(backend, spec)
     edge = drawn["graph"]["edges"][0]
     assert edge["line_number"] is None, "signal lines from a spec are unnumbered too"
+
+
+# ── Track A hardening (track E wave 0, Task 7) ───────────────────────────────
+
+
+async def test_foreign_line_payloads_are_tolerated_not_raised(backend):
+    """A hand-edited payload with a non-dict ``from``, a ``None`` ``to`` and a
+    bool ``seq`` used to escape as ``TypeError: string indices must be
+    integers``; reader results never raise."""
+    poly = await backend.entity_create_polyline([[0, 0], [10, 0]], layer="PROCESS-PIPING-MAIN")
+    await write_payload(
+        backend,
+        poly.handle,
+        {"v": 1, "kind": "line", "seq": True, "from": "garbage", "to": None, "number": 7},
+    )
+    other = await backend.entity_create_polyline([[0, 5], [10, 5]], layer="PROCESS-PIPING-MAIN")
+    await write_payload(
+        backend,
+        other.handle,
+        {"v": 1, "kind": "line", "seq": "9", "from": {"handle": 3, "port": "x"}, "to": 4},
+    )
+    result = await draw_line(
+        backend, {"x": 0, "y": 50}, {"x": 50, "y": 50}, size="100", service="P"
+    )
+    assert result["line_number"] == "100-P-1", "neither True nor '9' counts as a sequence number"
+    assert result["port_reuse"] == []
+
+
+def test_payload_helpers_accept_only_well_formed_values():
+    from engineering.pid.drawlines import payload_port_refs, payload_seq
+
+    good = {"from": {"handle": "2A", "port": "discharge"}, "to": {"handle": "2B", "port": None}}
+    assert payload_port_refs(good) == [("2A", "discharge")]
+    assert payload_port_refs("garbage") == [] and payload_port_refs(None) == []
+    assert payload_port_refs({"from": "x", "to": 5}) == []
+    assert payload_seq({"seq": 7}) == 7
+    assert payload_seq({"seq": True}) is None and payload_seq({"seq": "9"}) is None
+    assert payload_seq({"seq": 7.0}) is None and payload_seq(None) is None
+
+
+async def test_crossings_follow_a_bulged_line_not_its_chord(backend):
+    """A foreign P&ID line with a semicircular jump (bulge -1 from (0,0) to
+    (100,0) bows to +Y, apex (50,50)): a vertical utility line at x=30 from
+    y=20 to y=60 crosses the arc once at y≈45.8 and its chord never."""
+    msp = backend._msp()
+    msp.add_lwpolyline(
+        [(0, 0, 0, 0, -1.0), (100, 0, 0, 0, 0)],
+        format="xyseb",
+        dxfattribs={"layer": "PROCESS-PIPING-MAIN"},
+    )
+    backend._mark_dirty()
+    lines = await existing_pid_lines(backend)
+    assert lines[0]["vertices"] == [(0.0, 0.0), (100.0, 0.0)]
+    assert lines[0]["bulges"] == [-1.0, 0.0]
+    result = await draw_line(backend, {"x": 30, "y": 20}, {"x": 30, "y": 60}, line_class="utility")
+    assert result["crossings"] == 1
+    below = await draw_line(backend, {"x": 70, "y": -20}, {"x": 70, "y": -60}, line_class="utility")
+    assert below["crossings"] == 0, "the chord side of the arc is empty"
+
+
+async def test_com_existing_lines_carry_bulges(monkeypatch):
+    payload = line_payload("process_major", "100-P-7", "100", "P", None, None, 7, None, None)
+    poly = _com_pid_polyline("3E", (0.0, 0.0, 100.0, 0.0), payload)
+    poly.Length = 157.0796  # a semicircle: longer than the 100 mm chord walk
+    poly.GetBulge = lambda index: -1.0 if index == 0 else 0.0
+    backend = _fake_com(monkeypatch, [poly])
+    lines = await existing_pid_lines(backend)
+    assert lines[0]["vertices"] == [(0.0, 0.0), (100.0, 0.0)]
+    assert lines[0]["bulges"] == [-1.0, 0.0]
diff --git a/tests/test_pid_lines.py b/tests/test_pid_lines.py
index 9ccebe9..8cc4f75 100644
--- a/tests/test_pid_lines.py
+++ b/tests/test_pid_lines.py
@@ -3,6 +3,8 @@
 
 from __future__ import annotations
 
+import math
+
 import pytest
 
 from engineering.pid.lines import (
@@ -176,3 +178,41 @@ def test_route_refuses_non_axis_port_directions_with_a_value_error():
     # Equivalent angles and engine float drift still resolve to the axis.
     assert route((0, 0), -360.0, (50, 0), 540.0) == [(0.0, 0.0), (50.0, 0.0)]
     assert route((0, 0), 1e-9, (50, 0), 180.0 - 1e-9) == [(0.0, 0.0), (50.0, 0.0)]
+
+
+# ── Track A hardening (track E wave 0, Task 7): bulge flattening ─────────────
+
+
+@pytest.mark.parametrize("bulge", [1.0, -1.0, 0.5, -0.3, 2.0, 0.2])
+def test_flatten_bulges_matches_ezdxf_flattening(bulge):
+    """Pinned against ezdxf's own arc flattening: same vertex count, same points."""
+    from ezdxf.math import ConstructionArc, Vec2, bulge_to_arc
+
+    from engineering.pid.lines import FLATTEN_SAGITTA, flatten_bulges
+
+    a, b = (0.0, 0.0), (10.0, 0.0)
+    mine = flatten_bulges([a, b], [bulge])
+    centre, start_rad, end_rad, radius = bulge_to_arc(Vec2(a), Vec2(b), bulge)
+    arc = ConstructionArc(
+        center=centre,
+        radius=radius,
+        start_angle=math.degrees(start_rad),
+        end_angle=math.degrees(end_rad),
+    )
+    reference = [(p.x, p.y) for p in arc.flattening(FLATTEN_SAGITTA)]
+    assert len(mine) == len(reference)
+    assert mine[0] == a and mine[-1] == b
+    assert all(math.hypot(p[0] - centre.x, p[1] - centre.y) == pytest.approx(radius) for p in mine)
+    assert mine[len(mine) // 2] == pytest.approx(reference[len(reference) // 2])
+
+
+def test_flatten_bulges_passes_straight_edges_through_and_pads_short_bulge_lists():
+    from engineering.pid.lines import flatten_bulges
+
+    pts = [(0.0, 0.0), (10.0, 0.0), (10.0, 10.0)]
+    assert flatten_bulges(pts, []) == pts
+    assert flatten_bulges(pts, [0.0, 0.0, 0.0]) == pts
+    flat = flatten_bulges(pts, [0.0, 1.0])
+    assert flat[0] == (0.0, 0.0) and flat[1] == (10.0, 0.0) and flat[-1] == (10.0, 10.0)
+    assert len(flat) > 3, "the second edge became a semicircle of chords"
+    assert flatten_bulges([(1.0, 1.0)], [1.0]) == [(1.0, 1.0)]