plurigrid Möbius Path Filtering
Rejects navigation paths that create "Möbius twists" — where traversal would revisit a position from a contradictory orientation. Runs before path compilation so invalid Navigators are never cached.
Orientation Tracking
Each path step carries a position and an orientation (forward/reverse). A path is valid iff no (position, orientation) pair is visited contradictorily.
| Step Type | Orientation Change |
|---|---|
ALL |
+0 (preserves) |
keypath(k) |
+0 (direct navigation) |
pred(f) |
+0 (filtering, no reorientation) |
INDEX(i) |
+0 (direct indexing) |
REVERSE |
+1 (flips orientation) |
| Nested navigation | Compound (sum orientations) |
Two flips = orientable (valid). Odd accumulated flips on a revisited position = Möbius twist (invalid).
API
Location of is_valid_path, validate_path, eliminate_invalid_paths is not confirmed in the current repo tree. Search for these function names or for MöbiusTwistError to locate the implementation.
is_valid_path(path_expr) :: Bool
is_valid_path([ALL, keypath("x")]) # => true
is_valid_path([REVERSE, ALL, REVERSE]) # => true (2 flips = orientable)
is_valid_path([ALL, REVERSE, ALL, REVERSE]) # => false (creates twist)
validate_path(path_expr) :: Result
Returns ValidResult or InvalidResult with diagnostic (e.g., "Orientation flip at step 3 creates non-orientable surface").
eliminate_invalid_paths(paths::Vector) :: Vector
Filters candidate paths, keeping only valid ones.
Integration with Specter Navigator
When coerce_nav(path_expr) is called, validation order is:
- Möbius filtering (this skill)
- Type inference
- 3-MATCH constraint checking
- Compilation (only if all pass)
No runtime overhead — filtering is compile-time, before caching.
Related Skills
- specter-navigator-gadget — uses Möbius filtering as early validation
- color-envelope-preserving — enforces color consistency alongside topological validity
- three-match — constraint satisfaction runs on Möbius-filtered paths only