Asi möbius-path-filtering

Non-orientable topological filtering that eliminates self-revisiting paths before Navigator compilation

install

source · Clone the upstream repo

git clone https://github.com/plurigrid/asi

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/plurigrid/asi "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/m-bius-path-filtering" ~/.claude/skills/plurigrid-asi-mobius-path-filtering-86f072 && rm -rf "$T"

manifest: skills/m-bius-path-filtering/SKILL.md

source content

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

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