diff --git a/OpenNest.Core/CNC/CuttingPlanning/LeadMaterialSnapshot.cs b/OpenNest.Core/CNC/CuttingPlanning/LeadMaterialSnapshot.cs
index de74850..8579d01 100644
--- a/OpenNest.Core/CNC/CuttingPlanning/LeadMaterialSnapshot.cs
+++ b/OpenNest.Core/CNC/CuttingPlanning/LeadMaterialSnapshot.cs
@@ -47,7 +47,7 @@ public sealed class LeadMaterialSnapshot
                 if (chain.Count > 0 && chain[^1].End.DistanceTo(curve.Start) > PostVerificationGeometry.Epsilon)
                     throw new ArgumentException("Material contour is discontinuous.");
                 chain.Add(curve);
-                if (PostVerificationGeometry.Closed(chain))
+                if (NominalContourClosure.IsClosed(chain[0].Start, chain[^1].End))
                     Finish();
             }
             Finish();
@@ -67,6 +67,15 @@ public sealed class LeadMaterialSnapshot
                             var b = rings[s][j];
                             var contacts = a.Contacts(b, out var overlap);
                             var adjacent = r == s && (j == i + 1 || (i == 0 && j == rings[r].Length - 1));
+                            var arcJoint = adjacent && a.IsFiniteArc && b.IsFiniteArc
+                                && (a.End.DistanceTo(b.Start) <= Tolerance.Epsilon
+                                    || a.Start.DistanceTo(b.End) <= Tolerance.Epsilon);
+                            // Native arc queries pad angles by 1e-5 radians, admitting
+                            // intersections on an extension (distance grows with radius).
+                            // At a shared arc joint require both actual finite spans;
+                            // overlap and genuine second intersections still refuse.
+                            if (arcJoint)
+                                contacts = contacts.Where(p => !a.IsOutsideArcSpan(p) && !b.IsOutsideArcSpan(p)).ToArray();
                             // Native contacts at rounded arc/line joints can drift from the
                             // authored endpoint. Use the shared geometry tolerance only to
                             // recognize that joint; overlaps and other contacts still refuse.
@@ -101,8 +110,13 @@ public sealed class LeadMaterialSnapshot
             {
                 if (chain.Count == 0)
                     return;
-                if (!PostVerificationGeometry.Closed(chain))
-                    throw new ArgumentException("Nominal material contour is open; tab gaps cannot be filled implicitly.");
+                if (!NominalContourClosure.IsClosed(chain[0].Start, chain[^1].End))
+                {
+                    var gap = chain[0].Start.DistanceTo(chain[^1].End);
+                    throw new ArgumentException(FormattableString.Invariant(
+                        $"Nominal material contour {rings.Count + 1} is open: endpoint gap {gap:G6} model units exceeds closure tolerance {NominalContourClosure.Tolerance:G6}.")
+                        + " Review the source contour in the drawing editor; gaps cannot be filled implicitly.");
+                }
                 rings.Add(chain.ToArray());
                 chain.Clear();
             }
diff --git a/OpenNest.Core/CNC/CuttingPlanning/LeadPathValidator.cs b/OpenNest.Core/CNC/CuttingPlanning/LeadPathValidator.cs
index 7ce0854..961fac3 100644
--- a/OpenNest.Core/CNC/CuttingPlanning/LeadPathValidator.cs
+++ b/OpenNest.Core/CNC/CuttingPlanning/LeadPathValidator.cs
@@ -113,7 +113,8 @@ public static class LeadPathValidator
                     return material.ContainsMaterial(move.Curve.Midpoint, token) ? "interior" : null;
                 }
             }
-            // Missing leads are the ReleasedContourState check's responsibility.
+            // No lead motion is valid for direct contour piercing. The caller still
+            // checks rapid travel and contour accounting for the complete program.
             return new(true, true, null);
         }
         catch (Exception ex) when (ex is ArgumentException or NotSupportedException)
diff --git a/OpenNest.Core/CNC/CuttingPlanning/NominalContourClosure.cs b/OpenNest.Core/CNC/CuttingPlanning/NominalContourClosure.cs
new file mode 100644
index 0000000..a232d03
--- /dev/null
+++ b/OpenNest.Core/CNC/CuttingPlanning/NominalContourClosure.cs
@@ -0,0 +1,20 @@
+using OpenNest.Geometry;
+
+namespace OpenNest.CNC.CuttingPlanning;
+
+/// <summary>Closure of source contours during planner material capture and preparation.</summary>
+internal static class NominalContourClosure
+{
+    internal const double Tolerance = 0.000001;
+
+    internal static bool IsClosed(Vector start, Vector end)
+    {
+        // Subtracting translated/rotated coordinates can put an exact boundary gap
+        // a few floating-point ulps above the limit. Bound that allowance to 1e-12.
+        var scale = System.Math.Max(1, System.Math.Max(
+            System.Math.Max(System.Math.Abs(start.X), System.Math.Abs(start.Y)),
+            System.Math.Max(System.Math.Abs(end.X), System.Math.Abs(end.Y))));
+        var roundoff = System.Math.Min(1e-12, 4 * 2.2204460492503131e-16 * scale);
+        return start.DistanceTo(end) <= Tolerance + roundoff;
+    }
+}
diff --git a/OpenNest.Core/CNC/CuttingPlanning/PreparedContours.cs b/OpenNest.Core/CNC/CuttingPlanning/PreparedContours.cs
index ef1e206..bda9d6a 100644
--- a/OpenNest.Core/CNC/CuttingPlanning/PreparedContours.cs
+++ b/OpenNest.Core/CNC/CuttingPlanning/PreparedContours.cs
@@ -74,7 +74,7 @@ public sealed class PreparedContours
             if (current.Entities.Count > 0 && End(current.Entities[^1]).DistanceTo(Start(entity)) > PostVerificationGeometry.Epsilon)
                 throw new ArgumentException("Discontinuous native contour.");
             current.Entities.Add(entity);
-            if (Start(current.Entities[0]).DistanceTo(End(entity)) <= PostVerificationGeometry.Epsilon)
+            if (NominalContourClosure.IsClosed(Start(current.Entities[0]), End(entity)))
                 FinishContour();
         }
         if (current.Entities.Count != 0 || contours.Count == 0)
diff --git a/OpenNest.Core/CNC/CuttingPlanning/ReleasedContourState.cs b/OpenNest.Core/CNC/CuttingPlanning/ReleasedContourState.cs
index 1c4400d..c10a81e 100644
--- a/OpenNest.Core/CNC/CuttingPlanning/ReleasedContourState.cs
+++ b/OpenNest.Core/CNC/CuttingPlanning/ReleasedContourState.cs
@@ -11,10 +11,20 @@ namespace OpenNest.CNC.CuttingPlanning;
 public sealed class ReleasedContourState
 {
     private readonly List<Obstacle> obstacles = new();
+    private readonly bool reportMissingLeadIns;
+
+    public ReleasedContourState() : this(true) { }
+
+    /// <param name="reportMissingLeadIns">Keep pre-post warnings by default. Planning
+    /// may pierce directly on a contour and checks travel without requiring a lead.</param>
+    public ReleasedContourState(bool reportMissingLeadIns)
+    {
+        this.reportMissingLeadIns = reportMissingLeadIns;
+    }
 
     public ReleasedContourState Copy()
     {
-        var copy = new ReleasedContourState();
+        var copy = new ReleasedContourState(reportMissingLeadIns);
         copy.obstacles.AddRange(obstacles);
         return copy;
     }
@@ -98,7 +108,7 @@ public sealed class ReleasedContourState
                 if (contour.Count == 0)
                 {
                     contourNumber++;
-                    if (!cutoff && !hasLead)
+                    if (reportMissingLeadIns && !cutoff && !hasLead)
                         findings.Add(new(PostVerificationKind.MissingLeadIn, plate, part, null,
                             $"Cutting contour {contourNumber} has no nonzero placed lead-in motion.")
                         { Location = move.Curve.Start });
diff --git a/OpenNest.Core/Diagnostics/PostVerificationGeometry.cs b/OpenNest.Core/Diagnostics/PostVerificationGeometry.cs
index db29e74..7dca378 100644
--- a/OpenNest.Core/Diagnostics/PostVerificationGeometry.cs
+++ b/OpenNest.Core/Diagnostics/PostVerificationGeometry.cs
@@ -201,6 +201,15 @@ internal static class PostVerificationGeometry
 
         internal bool Contains(Vector point) => nativeEntity.Value.ClosestPointTo(point).DistanceTo(point) <= Epsilon;
 
+        /// <summary>
+        /// Filters supporting-circle contacts against the actual finite arc span. The
+        /// native angular padding is larger and must not turn an arc extension into a
+        /// self-intersection at an adjacent nominal joint. This is not a radial test.
+        /// </summary>
+        internal bool IsOutsideArcSpan(Vector point) => Center.HasValue && !OnArc(point);
+
+        internal bool IsFiniteArc => Center.HasValue && System.Math.Abs(Sweep) < TwoPi;
+
         internal IReadOnlyList<Vector> Contacts(Curve other, out bool overlap)
         {
             var entity = nativeEntity.Value;
diff --git a/OpenNest.Engine/CuttingPlanning/BestEffortCuttingPlan.cs b/OpenNest.Engine/CuttingPlanning/BestEffortCuttingPlan.cs
index c168909..ffa1c16 100644
--- a/OpenNest.Engine/CuttingPlanning/BestEffortCuttingPlan.cs
+++ b/OpenNest.Engine/CuttingPlanning/BestEffortCuttingPlan.cs
@@ -28,7 +28,7 @@ internal static class BestEffortCuttingPlan
         var done = new HashSet<int>();
         var position = snapshot.StartPoint;
         var distance = 0.0;
-        var checker = new ReleasedContourState();
+        var checker = new ReleasedContourState(reportMissingLeadIns: false);
         try
         {
             while (order.Count < snapshot.Placements.Count)
diff --git a/OpenNest.Engine/CuttingPlanning/ContourEntryFeasibility.cs b/OpenNest.Engine/CuttingPlanning/ContourEntryFeasibility.cs
index 87ee195..95c9df3 100644
--- a/OpenNest.Engine/CuttingPlanning/ContourEntryFeasibility.cs
+++ b/OpenNest.Engine/CuttingPlanning/ContourEntryFeasibility.cs
@@ -31,8 +31,8 @@ public sealed record ContourFeasibilityVerdict(ContourFeasibilityStatus Status,
 /// candidate contour through the S06 diagnostic seam, reads it at the placement position,
 /// and certifies the emitted lead-in and lead-out against ALL placed material. It is not a
 /// new collision implementation and not a plan approval: a Clear verdict certifies this
-/// contour's emitted leads only — the missing-lead (NoLeadIn) check still runs later on the
-/// complete plan, and rapids/pierce clearance belong to their existing checkers. A
+/// contour's emitted leads only — NoLeadIn is supported, and the complete plan must
+/// still pass rapid travel and contour-accounting checks. A
 /// candidate rejected here is not proven infeasible by anything else: this adapter only
 /// reports what the validator reported.
 /// One instance is one captured planning attempt: verdicts cache per exact choice and node
diff --git a/OpenNest.Engine/CuttingPlanning/CuttingPlanBatch.cs b/OpenNest.Engine/CuttingPlanning/CuttingPlanBatch.cs
index a7b2353..01d3cbe 100644
--- a/OpenNest.Engine/CuttingPlanning/CuttingPlanBatch.cs
+++ b/OpenNest.Engine/CuttingPlanning/CuttingPlanBatch.cs
@@ -349,7 +349,7 @@ public sealed class CuttingPlanProposal
     public IReadOnlyList<string> Describe(string unit)
     {
         var lines = new List<string>();
-        var ready = Plates.Count(p => p.IsReady);
+        var blocked = Plates.Count(p => !p.CanApplyWithWarnings);
         if (IsCancelled)
             lines.Add("Planning was cancelled. Nothing has changed.");
         else if (CanApply)
@@ -360,7 +360,7 @@ public sealed class CuttingPlanProposal
             lines.Add("Best-effort plan available. Review the warnings and accept the unverified plan to apply. "
                 + "This is not approval to cut or post CNC output.");
         else
-            lines.Add($"Apply is unavailable: {Plates.Count - ready} of {Count(Plates.Count, "plate")} could not "
+            lines.Add($"Apply is unavailable: {blocked} of {Count(Plates.Count, "plate")} could not "
                 + "be planned. No plate changes until every plate is ready.");
 
         foreach (var plate in Plates)
diff --git a/OpenNest.Engine/CuttingPlanning/CuttingPlanService.cs b/OpenNest.Engine/CuttingPlanning/CuttingPlanService.cs
index 03b1405..188b388 100644
--- a/OpenNest.Engine/CuttingPlanning/CuttingPlanService.cs
+++ b/OpenNest.Engine/CuttingPlanning/CuttingPlanService.cs
@@ -241,7 +241,7 @@ public static class CuttingPlanService
                 if (placement.Prepared != null)
                     continue; // An eligible old crossing is precisely what regeneration may repair.
                 // Ignore only the unknown incoming rapid. Every fixed internal motion is checked.
-                var findings = new ReleasedContourState().Check(placement.Execution, null,
+                var findings = new ReleasedContourState(reportMissingLeadIns: false).Check(placement.Execution, null,
                     placement.SourceOrdinal + 1, placement.IsCutOff, token);
                 fixedFindings.AddRange(Map(snapshot, findings));
             }
@@ -279,7 +279,7 @@ public static class CuttingPlanService
         if (snapshot.Dependencies.FirstViolation(order) is { } violation)
             return new(CuttingPlanStatus.InvalidInput,
                 findings: [DependencyFinding(snapshot, violation, "The proposed order")], expansions: expansions);
-        var checker = new ReleasedContourState();
+        var checker = new ReleasedContourState(reportMissingLeadIns: false);
         var position = snapshot.StartPoint;
         var distance = 0.0;
         var findings = new List<PostVerificationFinding>();
@@ -313,7 +313,7 @@ public static class CuttingPlanService
         if (snapshot.Dependencies.FirstViolation(order.Select(p => p.SourceOrdinal).ToArray()) is { } violation)
             return new(CuttingPlanStatus.InvalidInput,
                 findings: [DependencyFinding(snapshot, violation, "The proposed order")], expansions: expansions);
-        var checker = new ReleasedContourState();
+        var checker = new ReleasedContourState(reportMissingLeadIns: false);
         var position = snapshot.StartPoint;
         var distance = 0.0;
         var findings = new List<CuttingPlanFinding>();
diff --git a/OpenNest.Engine/CuttingPlanning/FixedProgramSearch.cs b/OpenNest.Engine/CuttingPlanning/FixedProgramSearch.cs
index 95208a7..06c9e7c 100644
--- a/OpenNest.Engine/CuttingPlanning/FixedProgramSearch.cs
+++ b/OpenNest.Engine/CuttingPlanning/FixedProgramSearch.cs
@@ -16,7 +16,7 @@ internal static class FixedProgramSearch
     internal static Outcome Run(CuttingPlanSnapshot snapshot, CancellationToken token)
     {
         var stack = new Stack<Frame>();
-        stack.Push(Create([], snapshot.StartPoint, new ReleasedContourState()));
+        stack.Push(Create([], snapshot.StartPoint, new ReleasedContourState(reportMissingLeadIns: false)));
         var rejected = new HashSet<PostVerificationFinding>();
         var expansions = 0;
         while (stack.Count != 0)
diff --git a/OpenNest.Engine/CuttingPlanning/JointCuttingPlanSearch.cs b/OpenNest.Engine/CuttingPlanning/JointCuttingPlanSearch.cs
index 466e370..6c644a6 100644
--- a/OpenNest.Engine/CuttingPlanning/JointCuttingPlanSearch.cs
+++ b/OpenNest.Engine/CuttingPlanning/JointCuttingPlanSearch.cs
@@ -191,7 +191,7 @@ internal static class JointCuttingPlanSearch
         /// </summary>
         internal Attempt Follow(int[] sequence, int? stall, Node resume, bool preferredOnly = false)
         {
-            var root = resume ?? new Node([], snapshot.StartPoint, new ReleasedContourState(), null, null);
+            var root = resume ?? new Node([], snapshot.StartPoint, new ReleasedContourState(reportMissingLeadIns: false), null, null);
             var attempt = new Attempt(sequence);
             var progressExpansions = Expansions;
             var stack = new Stack<Frame>();
diff --git a/OpenNest.Tests/CuttingPlanning/ContourEntryFeasibilityTests.cs b/OpenNest.Tests/CuttingPlanning/ContourEntryFeasibilityTests.cs
index 3ff8c63..9f432a4 100644
--- a/OpenNest.Tests/CuttingPlanning/ContourEntryFeasibilityTests.cs
+++ b/OpenNest.Tests/CuttingPlanning/ContourEntryFeasibilityTests.cs
@@ -126,7 +126,7 @@ public class ContourEntryFeasibilityTests
 
         // Nothing to certify means the validator passes vacuously — the emitted program
         // carries no lead motion at all, so this verdict certifies no lead and the
-        // complete-plan missing-lead check still has to run later. The adapter must not
+        // complete-plan rapid/contour checks still have to run later. The adapter must not
         // silently drop the distinction: consumers can see it is vacuous by counting leads.
         Assert.True(verdict.IsClear);
         var motions = ExecutionMotionReader.Read(prepared.Emit(new[] { choice }), At, null, default).Motions;
diff --git a/OpenNest.Tests/CuttingPlanning/CuttingPlanBatchTests.cs b/OpenNest.Tests/CuttingPlanning/CuttingPlanBatchTests.cs
index 2a990de..d0b6329 100644
--- a/OpenNest.Tests/CuttingPlanning/CuttingPlanBatchTests.cs
+++ b/OpenNest.Tests/CuttingPlanning/CuttingPlanBatchTests.cs
@@ -45,7 +45,9 @@ public class CuttingPlanBatchTests
         var nest = new Nest();
         var ready = Plate(nest, Clean("open", 1, 1));
         var locked = Clean("locked", 1, 1);
-        locked.LeadInsLocked = true; // Locked programs never regenerate: no lead-in is a conflict.
+        var crossing = OwnedProgramCopy.Copy(locked.Program);
+        crossing.MoveTo(5, 5); // Rapid enters the already completed square.
+        Assert.True(locked.RestoreLeadInProgram(crossing, true));
         var blocked = Plate(nest, locked);
         var readyProgram = ready.Parts[0].Program;
 
@@ -314,7 +316,9 @@ public class CuttingPlanBatchTests
         var nest = new Nest();
         var ready = Plate(nest, Clean("a", 1, 1));
         var locked = Clean("locked", 1, 1);
-        locked.LeadInsLocked = true;
+        var crossing = OwnedProgramCopy.Copy(locked.Program);
+        crossing.MoveTo(5, 5); // Rapid enters the already completed square.
+        Assert.True(locked.RestoreLeadInProgram(crossing, true));
         var blocked = Plate(nest, locked);
         var proposal = CuttingPlanBatch.Capture([ready, blocked], ExplicitContourTests.Parameters(), false).Plan();
         Assert.True(proposal.Plates[0].IsReady);
diff --git a/OpenNest.Tests/CuttingPlanning/CuttingPlanMessageTests.cs b/OpenNest.Tests/CuttingPlanning/CuttingPlanMessageTests.cs
index 5992e23..d13d5dd 100644
--- a/OpenNest.Tests/CuttingPlanning/CuttingPlanMessageTests.cs
+++ b/OpenNest.Tests/CuttingPlanning/CuttingPlanMessageTests.cs
@@ -8,77 +8,91 @@ namespace OpenNest.Tests.CuttingPlanning;
 
 public class CuttingPlanMessageTests
 {
+    [Fact]
+    public void Describe_MixedBestEffortAndOpenContour_CountsOnlyBlockedPlateAndExplainsGap()
+    {
+        var open = new OpenNest.CNC.Program();
+        open.MoveTo(0, 0);
+        open.LineTo(10, 0);
+        open.LineTo(10, 10);
+        open.LineTo(0, 10);
+        open.LineTo(0, 0.000002);
+        var part = new Part(new Drawing("open perimeter", open));
+        var original = OwnedProgramCopy.Copy(part.BaseDrawing.Program);
+        var plates = new[]
+        {
+            BestEffortCuttingPlanTests.Plate(BestEffortCuttingPlanTests.TouchingContours()),
+            BestEffortCuttingPlanTests.Plate(part),
+        };
+
+        var proposal = CuttingPlanBatch.Capture(plates, ExplicitContourTests.Parameters(), false).Plan();
+        var text = string.Join("\n", proposal.Describe("in"));
+
+        Assert.StartsWith("Apply is unavailable: 1 of 2 plates could not be planned.", text);
+        Assert.Contains("Plate 1: best-effort, unverified.", text);
+        Assert.Contains("Plate 2: blocked:", text);
+        Assert.Contains("contour 1 is open: endpoint gap 2E-06 model units", text);
+        Assert.Contains("closure tolerance 1E-06", text);
+        Assert.Contains("Review the source contour in the drawing editor", text);
+        Assert.False(proposal.CanApplyWithWarnings);
+        Assert.Equal(CuttingCommitStatus.InvalidInput, proposal.Apply(true).Status);
+        Assert.True(ProgramContent.Equal(original, part.BaseDrawing.Program));
+        Assert.All(plates.SelectMany(p => p.Parts), p => Assert.False(p.HasManualLeadIns));
+    }
+
     [Theory]
     [InlineData(false, false)]
     [InlineData(false, true)]
     [InlineData(true, false)]
     [InlineData(true, true)]
-    public void Describe_MissingOrZeroLengthLead_ExplainsSettingsWithoutBlamingSearch(bool keepOrder, bool zeroLength)
+    public void Describe_NoneIsSupportedButDegenerateLeadMotionStillRefuses(bool keepOrder, bool zeroLength)
     {
         var part = new Part(new Drawing("sample", ExplicitContourTests.Square(false)), new Vector(1, 1));
-        var plate = new Nest().CreatePlate();
-        plate.Size = new Size(100, 100);
-        plate.Parts.Add(part);
-        var program = part.Program;
-        var original = OwnedProgramCopy.Copy(program);
+        var plate = BestEffortCuttingPlanTests.Plate(part);
+        var original = OwnedProgramCopy.Copy(part.Program);
         var settings = new CuttingParameters();
         if (zeroLength)
             settings.ExternalLeadIn = new LineLeadIn { Length = 0, ApproachAngle = 90 };
 
         var proposal = CuttingPlanBatch.Capture([plate], settings, keepOrder).Plan();
 
-        Assert.False(proposal.CanApply);
-        var result = Assert.Single(proposal.Plates).Result;
-        Assert.Equal(CuttingPlanStatus.NoSolutionWithinBudget, result.Status);
-        Assert.Contains(result.Findings, f => f.Kind == PostVerificationKind.MissingLeadIn);
-        var text = string.Join("\n", proposal.Describe("in"));
-        Assert.Contains("Plate 1: blocked: missing or zero-length lead-in.", text);
-        Assert.Contains("Open Cutting Settings...", text);
-        Assert.Contains("other than None", text);
-        Assert.Contains("nonzero length", text);
-        Assert.Contains("Part 1 (sample):", text);
-        Assert.Contains("Cutting contour 1", text);
-        Assert.DoesNotContain("search limit", text);
-        Assert.Equal(CuttingCommitStatus.InvalidInput, proposal.Apply().Status);
-        Assert.Same(program, part.Program);
-        Assert.True(ProgramContent.Equal(original, part.Program));
-        Assert.Null(plate.CuttingParameters);
-        Assert.False(part.HasManualLeadIns);
+        if (zeroLength)
+        {
+            Assert.False(proposal.CanApply);
+            Assert.Contains("Lead motion is missing, degenerate or inconsistent", string.Join("\n", proposal.Describe("in")));
+            Assert.True(ProgramContent.Equal(original, part.Program));
+            return;
+        }
 
-        // Choosing valid settings fixes the refusal; reporting never changes settings or bypasses checks.
-        var ready = CuttingPlanBatch.Capture([plate], ExplicitContourTests.Parameters(), keepOrder).Plan();
-        Assert.True(ready.CanApply, string.Join("\n", ready.Describe("in")));
-        Assert.True(Assert.Single(ready.Plates).Result.IndependentlyReplayed);
-        Assert.DoesNotContain("missing or zero-length", string.Join("\n", ready.Describe("in")));
-        Assert.Same(program, part.Program);
+        Assert.True(proposal.CanApply, string.Join("\n", proposal.Describe("in")));
+        var result = Assert.Single(proposal.Plates).Result;
+        Assert.True(result.IndependentlyReplayed);
+        Assert.DoesNotContain(result.Findings, f => f.Kind == PostVerificationKind.MissingLeadIn);
+        Assert.Contains("Plate 1: ready.", string.Join("\n", proposal.Describe("in")));
+        var output = Assert.Single(result.ProposedOrder).CopyProgram();
+        Assert.DoesNotContain(ExecutionMotionReader.ReadSupported(output, part.Location, null).Motions,
+            m => m.Layer == OpenNest.CNC.LayerType.Leadin && m.Length > 0);
         Assert.True(ProgramContent.Equal(original, part.Program));
+        Assert.Equal(CuttingCommitStatus.Applied, proposal.Apply().Status);
     }
 
     [Fact]
-    public void Describe_LockedProgramWithoutLead_ExplainsThatSettingsCannotRegenerateIt()
+    public void Describe_LockedProgramWithoutLead_IsReadyAndKeepsItsProgram()
     {
         var part = new Part(new Drawing("locked sample", ExplicitContourTests.Square(false)), new Vector(1, 1))
         {
             LeadInsLocked = true,
         };
-        var plate = new Nest().CreatePlate();
-        plate.Size = new Size(100, 100);
-        plate.Parts.Add(part);
+        var plate = BestEffortCuttingPlanTests.Plate(part);
         var program = part.Program;
-
         var proposal = CuttingPlanBatch.Capture([plate], ExplicitContourTests.Parameters(), false).Plan();
 
-        Assert.Equal(CuttingPlanStatus.ConstraintConflict, Assert.Single(proposal.Plates).Result.Status);
-        Assert.False(proposal.CanApply);
-        var text = string.Join("\n", proposal.Describe("in"));
-        Assert.Contains("missing or zero-length lead-in", text);
-        Assert.Contains("If the affected part is locked, edit its lead-ins or unlock it before replanning.", text);
-        Assert.Contains("Part 1 (locked sample):", text);
-        Assert.Equal(CuttingCommitStatus.InvalidInput, proposal.Apply().Status);
+        Assert.True(proposal.CanApply, string.Join("\n", proposal.Describe("in")));
+        Assert.False(Assert.Single(proposal.Plates[0].Result.ProposedOrder).IsRegenerated);
+        Assert.Equal(CuttingCommitStatus.Applied, proposal.Apply().Status);
         Assert.True(part.LeadInsLocked);
         Assert.Same(program, part.Program);
     }
-
     [Fact]
     public void Describe_LeadHitsNeighbour_SuggestsSpacingOrShorterLeadWithoutAllowingApply()
     {
diff --git a/OpenNest.Tests/CuttingPlanning/CuttingPlanServiceTests.cs b/OpenNest.Tests/CuttingPlanning/CuttingPlanServiceTests.cs
index ec4313c..3afaa09 100644
--- a/OpenNest.Tests/CuttingPlanning/CuttingPlanServiceTests.cs
+++ b/OpenNest.Tests/CuttingPlanning/CuttingPlanServiceTests.cs
@@ -126,9 +126,24 @@ public class CuttingPlanServiceTests
         Assert.Equal(beforeCodes, program.Codes?.ToArray());
     }
 
+    [Fact]
+    public void FixedProgramWithoutLead_IsReadyAndReplayed()
+    {
+        var part = Fixture()[0];
+        part.Program.Codes.RemoveAt(1);
+        ((RapidMove)part.Program.Codes[0]).EndPoint = new Vector(4, 2);
+        var unchanged = Unchanged([part]);
+
+        var result = CuttingPlanService.Plan(new CuttingPlanRequest([part]));
+
+        Assert.Equal(CuttingPlanStatus.Ready, result.Status);
+        Assert.True(result.IndependentlyReplayed);
+        Assert.False(Assert.Single(result.ProposedOrder).IsRegenerated);
+        unchanged();
+    }
+
     [Theory]
     [InlineData("suppressed")]
-    [InlineData("missing-lead")]
     [InlineData("retention-unknown")]
     [InlineData("cutoff")]
     public void Plan_UnsupportedOrIncompleteStateIsRefused(string fault)
@@ -138,10 +153,6 @@ public class CuttingPlanServiceTests
         switch (fault)
         {
             case "suppressed": ((Motion)part.Program.Codes[2]).Suppressed = true; break;
-            case "missing-lead":
-                part.Program.Codes.RemoveAt(1);
-                ((RapidMove)part.Program.Codes[0]).EndPoint = new Vector(4, 2);
-                expected = CuttingPlanStatus.ConstraintConflict; break;
             case "retention-unknown": ((LinearMove)part.Program.Codes[^2]).EndPoint = new Vector(4, 2.25); break;
             case "cutoff": part.BaseDrawing.IsCutOff = true; break;
         }
diff --git a/OpenNest.Tests/CuttingPlanning/JointCuttingPlanTests.cs b/OpenNest.Tests/CuttingPlanning/JointCuttingPlanTests.cs
index 15469c0..a289325 100644
--- a/OpenNest.Tests/CuttingPlanning/JointCuttingPlanTests.cs
+++ b/OpenNest.Tests/CuttingPlanning/JointCuttingPlanTests.cs
@@ -4,11 +4,55 @@ using OpenNest.CNC.CuttingStrategy;
 using OpenNest.Diagnostics;
 using OpenNest.Engine.CuttingPlanning;
 using OpenNest.Geometry;
+using OpenNest.IO;
 
 namespace OpenNest.Tests.CuttingPlanning;
 
 public class JointCuttingPlanTests
 {
+    [Fact]
+    public void JointSearch_NoLeads_RepairsRapidCrossings()
+    {
+        var (part, parameters) = Crossing();
+        parameters.ExternalLeadIn = new NoLeadIn();
+        parameters.InternalLeadIn = new NoLeadIn();
+        parameters.ArcCircleLeadIn = new NoLeadIn();
+        var unchanged = Unchanged(part, parameters);
+        var source = Read(part.Program, part.Location);
+        Assert.Contains(new ReleasedContourState(reportMissingLeadIns: false).Check(source, Vector.Zero, 1),
+            f => f.Kind == PostVerificationKind.RapidCrossing);
+
+        var result = CuttingPlanService.Plan(new CuttingPlanRequest([part], confirmedParameters: parameters));
+
+        Assert.True(result.Status == CuttingPlanStatus.Ready, Describe(result));
+        Assert.True(result.IndependentlyReplayed);
+        var output = Read(Assert.Single(result.ProposedOrder).CopyProgram(), part.Location);
+        Assert.DoesNotContain(output.Motions, m => m.Layer == LayerType.Leadin);
+        Assert.Empty(new ReleasedContourState(reportMissingLeadIns: false).Check(output, Vector.Zero, 1));
+        Assert.Contains(new ReleasedContourState().Check(output, Vector.Zero, 1),
+            f => f.Kind == PostVerificationKind.MissingLeadIn);
+        unchanged();
+    }
+
+    [Fact]
+    public void JointSearch_NoLeads_ChoosesDifferentPiercesForOppositeApproaches()
+    {
+        var part = new Part(new Drawing("direct pierce", ExplicitContourTests.Square(false)));
+        var settings = new CuttingParameters();
+        var pierces = new List<Vector?>();
+        foreach (var start in new[] { new Vector(-5, 5), new Vector(15, 5) })
+        {
+            var result = CuttingPlanService.Plan(new CuttingPlanRequest([part], start, confirmedParameters: settings));
+            Assert.True(result.Status == CuttingPlanStatus.Ready, Describe(result));
+            Assert.True(result.IndependentlyReplayed);
+            var output = Read(Assert.Single(result.ProposedOrder).CopyProgram(), part.Location);
+            Assert.DoesNotContain(output.Motions, m => m.Layer == LayerType.Leadin);
+            pierces.Add(output.Motions.First(m => !m.Rapid && m.Layer is LayerType.Cut or LayerType.Display).Start);
+            Assert.Empty(new ReleasedContourState(reportMissingLeadIns: false).Check(output, start, 1));
+        }
+        Assert.NotEqual(pierces[0], pierces[1]);
+    }
+
     [Fact]
     public void JointSearch_RepairsActualCompletedHoleCrossing_WithExactReplayAndNoMutation()
     {
@@ -46,7 +90,6 @@ public class JointCuttingPlanTests
     [Theory]
     [InlineData("locked")]
     [InlineData("ineligible")]
-    [InlineData("no-valid-entry")]
     [InlineData("unsupported")]
     public void JointSearch_RefusesWithoutInstallingFallbackOrMutating(string fault)
     {
@@ -55,12 +98,6 @@ public class JointCuttingPlanTests
         var expected = CuttingPlanStatus.ConstraintConflict;
         if (fault == "locked") part.LeadInsLocked = true;
         if (fault == "ineligible") eligible = [];
-        if (fault == "no-valid-entry")
-        {
-            parameters.ArcCircleLeadIn = new NoLeadIn();
-            parameters.InternalLeadIn = parameters.ArcCircleLeadIn;
-            expected = CuttingPlanStatus.NoSolutionWithinBudget;
-        }
         if (fault == "unsupported")
         {
             part.BaseDrawing.Program.Codes.AddRange(LeadPathValidationTests.Rectangle(30, 30, 40, 40).Codes);
@@ -418,7 +455,7 @@ public class JointCuttingPlanTests
         var manual = part.HasManualLeadIns;
         var bounds = part.BoundingBox;
         var quantity = part.BaseDrawing.Quantity.Nested;
-        var length = ((LineLeadIn)parameters.ExternalLeadIn).Length;
+        var settings = CuttingParametersSerializer.Serialize(parameters);
         return () =>
         {
             Assert.Same(program, part.Program); Assert.Same(clean, part.BaseDrawing.Program);
@@ -427,7 +464,7 @@ public class JointCuttingPlanTests
             Assert.Equal(locked, part.LeadInsLocked); Assert.Equal(manual, part.HasManualLeadIns);
             Assert.Same(bounds, part.BoundingBox); Assert.Same(parameters, part.CuttingParameters);
             Assert.Equal(quantity, part.BaseDrawing.Quantity.Nested);
-            Assert.Equal(length, ((LineLeadIn)parameters.ExternalLeadIn).Length);
+            Assert.Equal(settings, CuttingParametersSerializer.Serialize(parameters));
             foreach (var sub in subs)
             {
                 Assert.Same(sub.Program, sub.c.Program); Assert.Equal(sub.text, sub.c.Program.ToString());
diff --git a/OpenNest.Tests/CuttingPlanning/LeadMaterialSnapshotTests.cs b/OpenNest.Tests/CuttingPlanning/LeadMaterialSnapshotTests.cs
index 54a600f..4691147 100644
--- a/OpenNest.Tests/CuttingPlanning/LeadMaterialSnapshotTests.cs
+++ b/OpenNest.Tests/CuttingPlanning/LeadMaterialSnapshotTests.cs
@@ -6,6 +6,61 @@ namespace OpenNest.Tests.CuttingPlanning;
 
 public class LeadMaterialSnapshotTests
 {
+    [Theory]
+    [InlineData(false, 0, 0, 0)]
+    [InlineData(true, 0, 0, 0)]
+    [InlineData(false, 0.7, 40, 20)]
+    [InlineData(true, 0.7, 40, 20)]
+    public void AdjacentArcs_IntersectionOnExtensionIsNotASelfIntersection(bool atSeam, double angle, double x, double y)
+    {
+        var program = ArcJoint(0.00005, false, atSeam);
+        program.Rotate(angle);
+        var location = new Vector(x, y);
+        var execution = ExecutionMotionReader.ReadSupported(program, location, null);
+        var arcs = execution.Motions.Where(m => m.Curve?.IsFiniteArc == true).Select(m => m.Curve!).ToArray();
+        var contacts = arcs[0].Contacts(arcs[1], out var overlap);
+        Assert.False(overlap);
+        Assert.Contains(contacts, p => arcs.Any(a => a.IsOutsideArcSpan(p)));
+
+        var material = LeadMaterialSnapshot.Capture(program, location);
+
+        Assert.True(material.IsComplete, material.Reason);
+    }
+
+    [Fact]
+    public void AdjacentArcs_RealSecondIntersectionRemainsRejected()
+    {
+        var program = ArcJoint(-0.00005, true, false);
+        var arcs = ExecutionMotionReader.ReadSupported(program, Vector.Zero, null).Motions
+            .Where(m => m.Curve?.IsFiniteArc == true).Select(m => m.Curve!).ToArray();
+        var contacts = arcs[0].Contacts(arcs[1], out var overlap);
+        Assert.False(overlap);
+        Assert.Contains(contacts, p => p.DistanceTo(Vector.Zero) > 0.00001
+            && !arcs[0].IsOutsideArcSpan(p) && !arcs[1].IsOutsideArcSpan(p));
+        var material = LeadMaterialSnapshot.Capture(program, Vector.Zero);
+
+        Assert.False(material.IsComplete);
+        Assert.Contains("Material boundaries", material.Reason);
+    }
+
+    private static Program ArcJoint(double centerOffset, bool reverseSecond, bool atSeam)
+    {
+        // Near-tangent circles meet at zero and about 0.000106 away. The native
+        // angular band of the radius-18 arc admits its extension beyond zero.
+        var first = new Vector(-18, 18);
+        var center = new Vector(centerOffset, 1);
+        var end = center + new Vector(center.DistanceTo(Vector.Zero), 0);
+        var program = new Program();
+        program.MoveTo(atSeam ? Vector.Zero : first);
+        if (!atSeam)
+            program.ArcTo(0, 0, 0, 18, RotationType.CCW);
+        program.ArcTo(end.X, end.Y, center.X, center.Y, reverseSecond ? RotationType.CW : RotationType.CCW);
+        program.LineTo(first);
+        if (atSeam)
+            program.ArcTo(0, 0, 0, 18, RotationType.CCW);
+        return program;
+    }
+
     [Theory]
     [InlineData(false)]
     [InlineData(true)]
diff --git a/OpenNest.Tests/CuttingPlanning/NominalContourClosureTests.cs b/OpenNest.Tests/CuttingPlanning/NominalContourClosureTests.cs
new file mode 100644
index 0000000..4abf313
--- /dev/null
+++ b/OpenNest.Tests/CuttingPlanning/NominalContourClosureTests.cs
@@ -0,0 +1,36 @@
+using OpenNest.CNC.CuttingPlanning;
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.CuttingPlanning;
+
+public class NominalContourClosureTests
+{
+    [Theory]
+    [InlineData(0.0000009, true)]
+    [InlineData(0.000001, true)]
+    [InlineData(0.00000101, false)]
+    [InlineData(0.000002, false)]
+    public void CaptureAndPreparation_AgreeAtClosureBoundary(double gap, bool accepted)
+    {
+        // Nonzero coordinates exercise roundoff at the inclusive boundary.
+        var program = new OpenNest.CNC.Program();
+        program.MoveTo(14, 3);
+        program.LineTo(24, 3);
+        program.LineTo(24, 13);
+        program.LineTo(14, 13);
+        program.LineTo(14, 3 + gap);
+        var original = OwnedProgramCopy.Copy(program);
+
+        var material = LeadMaterialSnapshot.Capture(program, new Vector(30, 20));
+
+        Assert.Equal(accepted, material.IsComplete);
+        if (accepted)
+            Assert.Equal(1, PreparedContours.Capture(program, ExplicitContourTests.Parameters()).Count);
+        else
+        {
+            Assert.Contains("closure tolerance 1E-06", material.Reason);
+            Assert.Throws<ArgumentException>(() => PreparedContours.Capture(program, ExplicitContourTests.Parameters()));
+        }
+        Assert.True(ProgramContent.Equal(original, program));
+    }
+}
diff --git a/OpenNest.WinForms.Tests/Forms/CuttingPlanFormTests.cs b/OpenNest.WinForms.Tests/Forms/CuttingPlanFormTests.cs
index 057e7b3..bffce19 100644
--- a/OpenNest.WinForms.Tests/Forms/CuttingPlanFormTests.cs
+++ b/OpenNest.WinForms.Tests/Forms/CuttingPlanFormTests.cs
@@ -49,7 +49,9 @@ public class CuttingPlanFormTests
     public void BlockedPlate_KeepsApplyDisabledAndShowsTheCurrentParts() => RunSta(() =>
     {
         var locked = Square("locked", 1, 1);
-        locked.LeadInsLocked = true; // A locked program is never regenerated: no lead-in blocks it.
+        var crossing = (OpenNest.CNC.Program)locked.Program.Clone();
+        crossing.MoveTo(5, 5); // A locked crossing cannot be repaired by regeneration.
+        Assert.True(locked.RestoreLeadInProgram(crossing, true));
         var (nest, view) = CreateView(locked);
         using var editor = view;
         using var form = new CuttingPlanForm(view, nest, allPlates: false, Parameters());
@@ -187,7 +189,9 @@ public class CuttingPlanFormTests
         first.Parts.Add(Square("open", 1, 1));
         var second = nest.CreatePlate();
         var locked = Square("locked", 1, 1);
-        locked.LeadInsLocked = true;
+        var crossing = (OpenNest.CNC.Program)locked.Program.Clone();
+        crossing.MoveTo(5, 5);
+        Assert.True(locked.RestoreLeadInProgram(crossing, true));
         second.Parts.Add(locked);
         nest.CreatePlate(); // An empty plate, like the editor's trailing plate.
         using var view = new PlateView { Plate = first };
diff --git a/docs/cutting-planner.md b/docs/cutting-planner.md
index 0ef7feb..9c31c87 100644
--- a/docs/cutting-planner.md
+++ b/docs/cutting-planner.md
@@ -57,8 +57,17 @@ Nominal material validation recognizes contacts at shared endpoints of adjacent
 contour segments using `OpenNest.Math.Tolerance.Epsilon` (0.00001 model units).
 This avoids false self-intersection warnings from rounding at arc/line joints,
 including the contour seam. Overlapping segments and contacts away from those
-joints or between separate contours still fail validation. Contour closure and
-the underlying native intersection queries retain their existing tolerances.
+joints or between separate contours still fail validation. For adjacent finite arcs
+with a shared endpoint, material validation filters native contacts against both
+actual arc spans: the native query's angular padding can otherwise report a
+supporting-circle intersection beyond one arc's endpoint. This does not increase
+the joint-distance tolerance, discard overlapping arcs, or waive a second intersection
+inside both spans. Lead and rapid checks keep their conservative contact queries.
+Source contour closure
+in material capture and emitter preparation accepts endpoint gaps up to 0.000001
+model units (inches for an inch nest), with a floating-point roundoff allowance
+capped at 1e-12. It does not rewrite source endpoints. Native intersections,
+executed-motion checks and pre-post verification retain their existing tolerances.
 
 Capture builds whole-part prerequisites from owned values, and both the search and
 the final replay enforce them:
@@ -232,7 +241,7 @@ Neither obtaining a proposal nor copying its programs installs them on live part
 ## Results and refusal
 
 `Ready` and `IndependentlyReplayed` describe the modeled proposal only. In the
-no-parameter fixed route, replay checks rapid crossings, missing leads and
+no-parameter fixed route, replay checks rapid crossings and
 incomplete retention; it does not add regeneration-mode material/lead checks.
 In regeneration mode, replay also checks actual lead paths and contour accounting
 against owned clean material. Neither mode certifies final NC, production cutting
@@ -317,10 +326,13 @@ plans every plate that has parts. Both open one dialog built on
   whole-part order; either change replans. The settings are confirmed parameters: every
   unlocked part's lead-ins are regenerated. Locked parts keep their exact programs;
   the strict route checks them, while any best-effort warnings require explicit review below.
-- A missing or zero-length lead-in is reported directly, rather than as a search-limit
-  failure. Open `Cutting Settings...`, choose a lead-in other than `None` with a nonzero
-  length on the affected `External`, `Internal`, or `Arc / Circle` tab, then replan.
-  Locked programs require manual lead editing or unlocking before regeneration.
+- Lead-ins are optional for planning. With `None` (or a style that emits no lead
+  motion), the emitter places the pierce directly on the selected contour point.
+  Unlocked contour starts can still move to improve travel; locked programs keep
+  their existing starts. Search and independent replay still check rapid crossings,
+  emitted lead paths when present, and contour accounting. The separate pre-post
+  missing-lead warning remains available for operator review; a ready plan does not
+  waive posting checks.
   When a lead hits another part, the finding suggests more spacing or a shorter lead;
   when no tested entry fits, it suggests reducing lead-in length and, if neighbours
   obstruct it, spacing the parts farther apart. These are suggestions, not guaranteed
@@ -360,7 +372,12 @@ plans every plate that has parts. Both open one dialog built on
   programs. Ready and best-effort proposals can be previewed only while the plate still
   matches capture. Best-effort previews are labelled `UNVERIFIED`. Refused program graphs
   are never copied, and changed plates require replanning.
-- Apply requires usable output for every plate and remains all or nothing. A ready batch
+- Apply requires usable output for every plate and remains all or nothing. The summary
+  counts best-effort proposals as usable when reporting how many plates block Apply;
+  their warnings still require acceptance. Open nominal contour findings identify the
+  contour number, endpoint gap in model units (the nest's linear units), and closure
+  tolerance, so the source can be reviewed in the drawing editor. Reporting never
+  closes gaps or changes the validation tolerance. A fully ready batch
   can apply immediately; an unverified batch requires the unchecked, per-proposal
   `I reviewed the warnings. Apply this unverified plan.` checkbox. Replanning clears it.
   Both use the same owned-program, freshness and rollback boundary. After it applies, each plate keeps its own copy of the
diff --git a/docs/post-verification.md b/docs/post-verification.md
index 4320c28..f143336 100644
--- a/docs/post-verification.md
+++ b/docs/post-verification.md
@@ -54,6 +54,8 @@ shows all three check categories, even when there are no findings:
 - **Missing lead-ins:** cutting contours without an actual, nonzero lead-in in the
   placed program. Applying a lead-in to only one contour does not clear the other
   contours. Scribe-only work and scrap cutoff lines do not require lead-ins here.
+  The cutting planner supports direct contour piercing without lead-ins; that does
+  not suppress this pre-post review warning or grant posting consent.
 - **Rapid crossings:** direct XY moves crossing closed, already-cut, untabbed
   contours in cutting order. This includes earlier holes within the same part and
   previously cut parts. A future cut is not an obstacle yet. Actual uncut gaps are