Update app.py

app.py

@@ -23,6 +23,62 @@ DEFAULTS = {
 
 # ---------- Hypercube utilities ----------
 
+def cycle_edge_dims(cycle: List[int], d: int) -> List[int] | None:
+    """
+    cycle is vertex list WITHOUT repeating start at end.
+    Returns list of edge dimensions around the cycle (length n),
+    or None if any step is non-adjacent.
+    """
+    n = len(cycle)
+    dims = []
+    for i in range(n):
+        a = cycle[i]
+        b = cycle[(i + 1) % n]
+        dim = edge_dimension(a, b)
+        if dim is None:
+            return None
+        dims.append(dim)
+    return dims
+
+
+def is_symmetric_coil(path: List[int], d: int, allow_reverse: bool = True) -> bool:
+    """
+    A "doubled coil": valid coil whose second half repeats the structure of the first half.
+    We detect this via the cyclic edge-dimension sequence.
+
+    allow_reverse=True also accepts that the second half is the reverse traversal
+    of the first half (often happens depending on where you cut the cycle).
+    """
+    if not path or len(path) < 4:
+        return False
+    if path[0] != path[-1]:
+        return False  # must be explicitly closed
+
+    cycle = path[:-1]
+    n = len(cycle)
+    if n % 2 != 0:
+        return False
+
+    dims = cycle_edge_dims(cycle, d)
+    if dims is None:
+        return False
+
+    half = n // 2
+    first = dims[:half]
+    second = dims[half:]
+
+    if second == first:
+        return True
+
+    if allow_reverse:
+        # If the second half traverses the "same structure" but reversed,
+        # edge-dim sequence matches reversed order.
+        if second == list(reversed(first)):
+            return True
+
+    return False
+
+
 def index_in_path(path: List[int], vid: int):
     """Return the index of vid in path (first occurrence), or None."""
     try:
@@ -124,6 +180,9 @@ def classify_path(path, d: int):
 
     if is_closed:
         # distinct, consecutive adjacent, closed by an edge, no chords
+        # If it is also a doubled coil, label it as symmetric coil
+        if is_symmetric_coil(path, d, allow_reverse=True):
+            return "symmetric coil", True
         return "coil", True
 
     # Open path, induced
@@ -1022,6 +1081,7 @@ def path_info(d, path):
     color = {
         "snake": "green",
         "coil": "green",
+        "symmetric coil": "green",
         "almost coil": "green",
         "not snake": "red",
     }[label]