Fix render_braiding.rs: transitive for wire endpoints, direct for surface boundaries

Wire endpoints and surface boundaries require different computation methods:

- Wire endpoints: TRANSITIVE reachability to vertices
  A strand spans between vertices even if poset path has intermediate points.
  Most wires connect both v₀ and v₁; only wire 14 is a self-loop.

- Surface boundary_wires: DIRECT covering relations only
  The immediate boundary of a surface is its direct predecessor/successor wires.
  Surfaces have 1-3 boundary wires (was 1-7 with transitive).

Updated:
- examples/render_braiding.rs: restored reachable_from for wire endpoints
- fixtures/half_braid_geometry.json: correct wire endpoints + direct surface boundaries
- web/zigzag-renderer.jsx: updated embedded geometry data

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

examples/render_braiding.rs

@@ -126,7 +126,7 @@ fn main() {
         predecessors[upper].push(lower);
     }
 
-    // Helper: find all reachable points
+    // Helper: find all transitively reachable points (for wire→vertex connections)
     let reachable_from = |start: usize, adj: &[Vec<usize>]| -> HashSet<usize> {
         let mut visited = HashSet::new();
         let mut queue = VecDeque::new();
@@ -166,7 +166,8 @@ fn main() {
     for (i, &idx) in wire_indices.iter().enumerate() {
         let point = &pts.elements()[idx];
 
-        // Find connected vertices
+        // Find connected vertices via TRANSITIVE reachability
+        // A wire (strand) spans between vertices even if the poset path has intermediate points
         let reachable_up = reachable_from(idx, &successors);
         let reachable_down = reachable_from(idx, &predecessors);
 
@@ -213,12 +214,11 @@ fn main() {
     for (i, &idx) in surface_indices.iter().enumerate() {
         let point = &pts.elements()[idx];
 
-        // Find connected wires (boundary)
-        let reachable_up = reachable_from(idx, &successors);
-        let reachable_down = reachable_from(idx, &predecessors);
-
-        let mut boundary_wires: Vec<usize> = reachable_up
-            .union(&reachable_down)
+        // Find boundary wires via DIRECT covering relations only
+        // Surface (geom_dim=2) connects to wires (geom_dim=1) via single covers
+        let mut boundary_wires: Vec<usize> = successors[idx]
+            .iter()
+            .chain(predecessors[idx].iter())
             .filter(|v| wire_set.contains(v))
             .copied()
             .collect();

fixtures/half_braid_geometry.json

@@ -223,12 +223,7 @@
       ],
       "boundary_wires": [
         5,
-        8,
-        14,
-        15,
-        18,
-        19,
-        20
+        18
       ]
     },
     {
@@ -242,9 +237,7 @@
       ],
       "boundary_wires": [
         5,
-        15,
-        19,
-        20
+        19
       ]
     },
     {
@@ -258,11 +251,7 @@
       ],
       "boundary_wires": [
         8,
-        14,
-        15,
-        18,
-        19,
-        20
+        18
       ]
     },
     {
@@ -276,9 +265,7 @@
       ],
       "boundary_wires": [
         8,
-        15,
-        19,
-        20
+        19
       ]
     },
     {
@@ -292,7 +279,6 @@
       ],
       "boundary_wires": [
         14,
-        15,
         18
       ]
     },
@@ -306,11 +292,8 @@
         2.0
       ],
       "boundary_wires": [
-        5,
-        8,
         14,
         15,
-        18,
         19
       ]
     },
@@ -324,12 +307,7 @@
         2.0
       ],
       "boundary_wires": [
-        5,
-        8,
-        14,
         15,
-        18,
-        19,
         20
       ]
     },
@@ -343,11 +321,7 @@
         1.0
       ],
       "boundary_wires": [
-        14,
-        15,
-        18,
-        19,
-        20
+        18
       ]
     },
     {

web/zigzag-renderer.jsx

@@ -29,14 +29,14 @@ const GEOMETRY_DATA = {
       "endpoints": [21, 22], "endpoint_coords": [[1.0, 1.0, 1.0], [3.0, 1.0, 1.0]] }
   ],
   "surfaces": [
-    { "id": 3, "label": "surface_0", "point": "r0,s0,r0", "coords": [0.0, 1.0, 0.0], "boundary_wires": [5, 8, 14, 15, 18, 19, 20] },
-    { "id": 4, "label": "surface_1", "point": "r1,s0,r0", "coords": [2.0, 1.0, 0.0], "boundary_wires": [5, 15, 19, 20] },
-    { "id": 6, "label": "surface_2", "point": "r0,s1,r0", "coords": [0.0, 3.0, 0.0], "boundary_wires": [8, 14, 15, 18, 19, 20] },
-    { "id": 7, "label": "surface_3", "point": "r1,s1,r0", "coords": [2.0, 3.0, 0.0], "boundary_wires": [8, 15, 19, 20] },
-    { "id": 11, "label": "surface_4", "point": "r0,s0,r1", "coords": [0.0, 1.0, 2.0], "boundary_wires": [14, 15, 18] },
-    { "id": 12, "label": "surface_5", "point": "r1,s0,r1", "coords": [2.0, 1.0, 2.0], "boundary_wires": [5, 8, 14, 15, 18, 19] },
-    { "id": 13, "label": "surface_6", "point": "r2,s0,r1", "coords": [4.0, 1.0, 2.0], "boundary_wires": [5, 8, 14, 15, 18, 19, 20] },
-    { "id": 16, "label": "surface_7", "point": "r0,r0,s0", "coords": [0.0, 0.0, 1.0], "boundary_wires": [14, 15, 18, 19, 20] },
+    { "id": 3, "label": "surface_0", "point": "r0,s0,r0", "coords": [0.0, 1.0, 0.0], "boundary_wires": [5, 18] },
+    { "id": 4, "label": "surface_1", "point": "r1,s0,r0", "coords": [2.0, 1.0, 0.0], "boundary_wires": [5, 19] },
+    { "id": 6, "label": "surface_2", "point": "r0,s1,r0", "coords": [0.0, 3.0, 0.0], "boundary_wires": [8, 18] },
+    { "id": 7, "label": "surface_3", "point": "r1,s1,r0", "coords": [2.0, 3.0, 0.0], "boundary_wires": [8, 19] },
+    { "id": 11, "label": "surface_4", "point": "r0,s0,r1", "coords": [0.0, 1.0, 2.0], "boundary_wires": [14, 18] },
+    { "id": 12, "label": "surface_5", "point": "r1,s0,r1", "coords": [2.0, 1.0, 2.0], "boundary_wires": [14, 15, 19] },
+    { "id": 13, "label": "surface_6", "point": "r2,s0,r1", "coords": [4.0, 1.0, 2.0], "boundary_wires": [15, 20] },
+    { "id": 16, "label": "surface_7", "point": "r0,r0,s0", "coords": [0.0, 0.0, 1.0], "boundary_wires": [18] },
     { "id": 17, "label": "surface_8", "point": "r0,r1,s0", "coords": [0.0, 2.0, 1.0], "boundary_wires": [18] }
   ],
   "volumes": [