diff --git a/tests/kernel-cases/surfaces/cov-blend-between-coplanar-sheets-is-flat/expected.json b/tests/kernel-cases/surfaces/cov-blend-between-coplanar-sheets-is-flat/expected.json
new file mode 100644
index 0000000000..3555d3b30d
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-between-coplanar-sheets-is-flat/expected.json
@@ -0,0 +1,40 @@
+{
+ "sources": [],
+ "what": "a G1 blend across the 10 mm gap between two coplanar sheets, stitched to both: flat, filling the gap exactly",
+ "source": "analytic",
+ "method": "both ends' tangent planes are z = 0 and the edges face each other along x: every cross-section's Hermite lies in z = 0 from x = 10 to x = 20, so the blend is the 10 x 20 strip; stitched: one body, area 200 + 200 + 200 = 600, 6 free edges round the 30 x 20 outline (the blend's own sides counted, [6, 8]); seams at x = 10 and 20 at least G1",
+ "valid": false,
+ "body_count": 1,
+ "area_mm2": 600.0,
+ "boundary_edges": [
+  6,
+  8
+ ],
+ "bbox": {
+  "min": [
+   0,
+   0,
+   0
+  ],
+  "max": [
+   30,
+   20,
+   0
+  ]
+ },
+ "continuity": {
+  "order": "g1",
+  "edges": [
+   [
+    10,
+    10,
+    0
+   ],
+   [
+    20,
+    10,
+    0
+   ]
+  ]
+ }
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-between-coplanar-sheets-is-flat/recipe.json b/tests/kernel-cases/surfaces/cov-blend-between-coplanar-sheets-is-flat/recipe.json
new file mode 100644
index 0000000000..ddef4b4248
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-between-coplanar-sheets-is-flat/recipe.json
@@ -0,0 +1,125 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "A sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     0,
+     0
+    ],
+    "p1": [
+     10,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "A sketch",
+    "body_name": "A"
+   }
+  },
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "B sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     20,
+     0
+    ],
+    "p1": [
+     30,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "B sketch",
+    "body_name": "B"
+   }
+  },
+  {
+   "command": "surface.blend",
+   "params": {
+    "from": {
+     "body": "A",
+     "edges": [
+      [
+       10,
+       10,
+       0
+      ]
+     ]
+    },
+    "to": {
+     "body": "B",
+     "edges": [
+      [
+       20,
+       10,
+       0
+      ]
+     ]
+    },
+    "stitch": true,
+    "body_name": "Bridge"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-from-edges-that-do-not-chain-refused/expected.json b/tests/kernel-cases/surfaces/cov-blend-from-edges-that-do-not-chain-refused/expected.json
new file mode 100644
index 0000000000..e1a4902e1f
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-from-edges-that-do-not-chain-refused/expected.json
@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "a blend from two opposite sides of a sheet: they share no vertex, so they are no chain; refused",
+ "source": "invariants",
+ "method": "an end of a blend is one chain of edges, each running on from the last",
+ "outcome": "refused",
+ "refusal": "the picked edges do not run on from one another"
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-from-edges-that-do-not-chain-refused/recipe.json b/tests/kernel-cases/surfaces/cov-blend-from-edges-that-do-not-chain-refused/recipe.json
new file mode 100644
index 0000000000..3c2d6023e7
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-from-edges-that-do-not-chain-refused/recipe.json
@@ -0,0 +1,128 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "A sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     0,
+     0
+    ],
+    "p1": [
+     10,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "A sketch",
+    "body_name": "A"
+   }
+  },
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "B sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     20,
+     0
+    ],
+    "p1": [
+     30,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "B sketch",
+    "body_name": "B"
+   }
+  },
+  {
+   "command": "surface.blend",
+   "params": {
+    "from": {
+     "body": "A",
+     "edges": [
+      [
+       0,
+       10,
+       0
+      ],
+      [
+       10,
+       10,
+       0
+      ]
+     ]
+    },
+    "to": {
+     "body": "B",
+     "edges": [
+      [
+       20,
+       10,
+       0
+      ]
+     ]
+    }
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g1/expected.json b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g1/expected.json
new file mode 100644
index 0000000000..00c1719d75
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g1/expected.json
@@ -0,0 +1,24 @@
+{
+ "sources": [],
+ "what": "a G1 blend bridging a 10 mm step between two parallel sheets (z = 0 and z = 10), stitched to both: it meets each at G1",
+ "source": "invariants",
+ "method": "sheets x 0..10 at z = 0 and x 20..30 at z = 10, 20 wide; the blend leaves each edge in its sheet's tangent plane (and curvature, rate) as asked. Graded: the order at both seams as Continuity Analysis measures it, one body of 3 faces (each a different surface, so none merge)",
+ "valid": false,
+ "body_count": 1,
+ "faces": 3,
+ "continuity": {
+  "order": "g1",
+  "edges": [
+   [
+    10,
+    10,
+    0
+   ],
+   [
+    20,
+    10,
+    10
+   ]
+  ]
+ }
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g1/recipe.json b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g1/recipe.json
new file mode 100644
index 0000000000..7d7495ebb8
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g1/recipe.json
@@ -0,0 +1,129 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "A sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     0,
+     0
+    ],
+    "p1": [
+     10,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "A sketch",
+    "body_name": "A"
+   }
+  },
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      10
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "Bs"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     20,
+     0
+    ],
+    "p1": [
+     30,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "Bs",
+    "body_name": "B"
+   }
+  },
+  {
+   "command": "surface.blend",
+   "params": {
+    "from": {
+     "body": "A",
+     "edges": [
+      [
+       10,
+       10,
+       0
+      ]
+     ]
+    },
+    "to": {
+     "body": "B",
+     "edges": [
+      [
+       20,
+       10,
+       10
+      ]
+     ]
+    },
+    "continuity": [
+     "g1",
+     "g1"
+    ],
+    "stitch": true,
+    "body_name": "Bridge"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g2/expected.json b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g2/expected.json
new file mode 100644
index 0000000000..ca0733547f
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g2/expected.json
@@ -0,0 +1,24 @@
+{
+ "sources": [],
+ "what": "a G2 blend bridging a 10 mm step between two parallel sheets (z = 0 and z = 10), stitched to both: it meets each at G2",
+ "source": "invariants",
+ "method": "sheets x 0..10 at z = 0 and x 20..30 at z = 10, 20 wide; the blend leaves each edge in its sheet's tangent plane (and curvature, rate) as asked. Graded: the order at both seams as Continuity Analysis measures it, one body of 3 faces (each a different surface, so none merge)",
+ "valid": false,
+ "body_count": 1,
+ "faces": 3,
+ "continuity": {
+  "order": "g2",
+  "edges": [
+   [
+    10,
+    10,
+    0
+   ],
+   [
+    20,
+    10,
+    10
+   ]
+  ]
+ }
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g2/recipe.json b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g2/recipe.json
new file mode 100644
index 0000000000..0b1e82e2cc
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g2/recipe.json
@@ -0,0 +1,129 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "A sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     0,
+     0
+    ],
+    "p1": [
+     10,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "A sketch",
+    "body_name": "A"
+   }
+  },
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      10
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "Bs"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     20,
+     0
+    ],
+    "p1": [
+     30,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "Bs",
+    "body_name": "B"
+   }
+  },
+  {
+   "command": "surface.blend",
+   "params": {
+    "from": {
+     "body": "A",
+     "edges": [
+      [
+       10,
+       10,
+       0
+      ]
+     ]
+    },
+    "to": {
+     "body": "B",
+     "edges": [
+      [
+       20,
+       10,
+       10
+      ]
+     ]
+    },
+    "continuity": [
+     "g2",
+     "g2"
+    ],
+    "stitch": true,
+    "body_name": "Bridge"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g3/expected.json b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g3/expected.json
new file mode 100644
index 0000000000..b701a91cac
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g3/expected.json
@@ -0,0 +1,24 @@
+{
+ "sources": [],
+ "what": "a G3 blend bridging a 10 mm step between two parallel sheets (z = 0 and z = 10), stitched to both: it meets each at G3",
+ "source": "invariants",
+ "method": "sheets x 0..10 at z = 0 and x 20..30 at z = 10, 20 wide; the blend leaves each edge in its sheet's tangent plane (and curvature, rate) as asked. Graded: the order at both seams as Continuity Analysis measures it, one body of 3 faces (each a different surface, so none merge)",
+ "valid": false,
+ "body_count": 1,
+ "faces": 3,
+ "continuity": {
+  "order": "g3",
+  "edges": [
+   [
+    10,
+    10,
+    0
+   ],
+   [
+    20,
+    10,
+    10
+   ]
+  ]
+ }
+}
diff --git a/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g3/recipe.json b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g3/recipe.json
new file mode 100644
index 0000000000..167e2b25da
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-blend-step-between-offset-sheets-g3/recipe.json
@@ -0,0 +1,129 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "A sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     0,
+     0
+    ],
+    "p1": [
+     10,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "A sketch",
+    "body_name": "A"
+   }
+  },
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      10
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "Bs"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     20,
+     0
+    ],
+    "p1": [
+     30,
+     20
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "Bs",
+    "body_name": "B"
+   }
+  },
+  {
+   "command": "surface.blend",
+   "params": {
+    "from": {
+     "body": "A",
+     "edges": [
+      [
+       10,
+       10,
+       0
+      ]
+     ]
+    },
+    "to": {
+     "body": "B",
+     "edges": [
+      [
+       20,
+       10,
+       10
+      ]
+     ]
+    },
+    "continuity": [
+     "g3",
+     "g3"
+    ],
+    "stitch": true,
+    "body_name": "Bridge"
+   }
+  }
+ ]
+}