Ladder: 016 and 018 refused, their r3 chain takes the vertical edge; 020 and 021 recorded

With the tangent chain on, 016's and 018's r3 runs on along the r5 round's end arc and down the
vertical edge, so the third pick (60, 40, 8) is 3 from both of that round's contact lines and
names no edge: refused, asking for a point along one edge. The corners they were made for are
020 and 021 (the r3 alone), whose golden entries are 016's and 018's (021 measured on f12a101).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DtL5M41G8Nua7HvuFPZkmJ

tests/kernel-cases/ladder/07-fillets/016-corner-three-sequential-r5-r3-r7/expected.json

@@ -1,8 +1,8 @@
 {
  "sources": [],
- "what": "rounds r5 and r3 on the two top edges at a corner, then r7 on the vertical edge under them: refused, the r7 cannot exist",
+ "what": "rounds r5 and r3 on the two top edges at a corner, the r3 with its tangent chain, then a round on the vertical edge under them: the r3 chain has rounded that edge, so the pick takes no edge: refused",
  "source": "invariants",
- "method": "the r7 runs on (tangent chain) up the side x=60 along its arc on the r5 round, a circle of radius 5 about the r5 axis: the r7's contact line on that face would be the arc offset 7 towards its centre, radius 5 - 7 < 0, so the blend passes through itself; and along the seam of the r5 and r3 rounds no ball over r3 fits the r3 round. No such round exists, so the right answer is a clean refusal (SMLib: no room for the rolling ball). 018 is the same corner with a radius that fits.",
+ "method": "box 60x40x20; the top edge y=40 rounded r5, then the top edge x=60 rounded r3 with its tangent chain: at (60, 35, 20) it runs on tangentially into the r5 round's end arc on x = 60 (a quarter circle about y = 35, z = 15, convex), which runs on at (60, 40, 15) into the vertical edge x=60, y=40, so the r3 rounds all three and the vertical edge is gone: its round is the cylinder r3 about (57, 37), z 0..15, meeting the faces along x=57, y=40 and x=60, y=37. The third pick (60, 40, 8) is 3 from each of those two lines and nearer no other edge: it names neither, and the right answer is a clean refusal asking for a point along one edge. The corner this case was made for, with the r3 on its edge alone, is ladder 07-fillets/020.",
  "outcome": "refused",
- "refusal": "the fillet is larger than the faces beside its edges allow"
+ "refusal": "give a point along one edge"
 }

tests/kernel-cases/ladder/07-fillets/018-corner-three-sequential-r5-r3-r2/expected.json

@@ -1,20 +1,8 @@
 {
  "sources": [],
- "what": "rounds r5 and r3 on the two top edges at a corner, then r2 on the vertical edge under them, run on up into the corner",
+ "what": "rounds r5 and r3 on the two top edges at a corner, the r3 with its tangent chain, then a round on the vertical edge under them: the r3 chain has rounded that edge, so the pick takes no edge: refused",
  "source": "invariants",
- "method": "as 016 with a radius that fits (r < 3, the smaller top round): the r2 runs up the vertical edge and on along the side's arc on the r5 round and the seam between the two rounds, tapering to a point where they become tangent. Faces: the box's 6 and the two top rounds, + 3 for the r2 (along the vertical edge, up the arc, along the seam); one valid body inside the box",
- "body_count": 1,
- "faces": 11,
- "bbox": {
-  "min": [
-   0,
-   0,
-   0
-  ],
-  "max": [
-   60,
-   40,
-   20
-  ]
- }
+ "method": "box 60x40x20; the top edge y=40 rounded r5, then the top edge x=60 rounded r3 with its tangent chain: at (60, 35, 20) it runs on tangentially into the r5 round's end arc on x = 60 (a quarter circle about y = 35, z = 15, convex), which runs on at (60, 40, 15) into the vertical edge x=60, y=40, so the r3 rounds all three and the vertical edge is gone: its round is the cylinder r3 about (57, 37), z 0..15, meeting the faces along x=57, y=40 and x=60, y=37. The third pick (60, 40, 8) is 3 from each of those two lines and nearer no other edge: it names neither, and the right answer is a clean refusal asking for a point along one edge. The corner this case was made for, with the r3 on its edge alone, is ladder 07-fillets/021.",
+ "outcome": "refused",
+ "refusal": "give a point along one edge"
 }

tests/kernel-cases/ladder/golden.json

@@ -1381,14 +1381,6 @@
       "status": "pass"
     },
     "ladder/07-fillets/018-corner-three-sequential-r5-r3-r2": {
-      "measured": {
-        "area_mm2": 8591.675008996122,
-        "body_count": 1,
-        "edges": 24,
-        "faces": 11,
-        "vertices": 15,
-        "volume_mm3": 47589.770467263734
-      },
       "seconds": 0.06135609,
       "status": "pass"
     },
@@ -1404,6 +1396,22 @@
       "seconds": 2.083591798,
       "status": "pass"
     },
+    "ladder/07-fillets/020-corner-three-sequential-r5-r3-r7-partial-chain": {
+      "seconds": 0.053107612,
+      "status": "pass"
+    },
+    "ladder/07-fillets/021-corner-three-sequential-r5-r3-r2-partial-chain": {
+      "measured": {
+        "area_mm2": 8591.674904919324,
+        "body_count": 1,
+        "edges": 24,
+        "faces": 11,
+        "vertices": 15,
+        "volume_mm3": 47589.7705835473
+      },
+      "seconds": 0.06135609,
+      "status": "pass"
+    },
     "ladder/08-chamfers/001-equal-5": {
       "measured": {
         "area_mm2": 8599.26406871193,
@@ -1993,5 +2001,5 @@
       "status": "pass"
     }
   },
-  "reason": "06/023 (1/2-14 NPT) passes: a taper thread's groove follows its crest cone, so no sliver of the flanks is left (volume 8226.4042 against the standard's 8226.4049); the other cases as recorded on SMLib 60b1c6a"
+  "reason": "07-fillets/016 and 018 round the r3 with its tangent chain, which takes the vertical edge their third round was to pick (refused: the pick names no edge); 020 and 021 are the same corners with the r3 alone, as 016 and 018 were recorded (021 measured on SMLib f12a101); 06/023 (1/2-14 NPT) passes: a taper thread's groove follows its crest cone, so no sliver of the flanks is left (volume 8226.4042 against the standard's 8226.4049); the other cases as recorded on SMLib 60b1c6a"
 }