[bal7hazar]

Summary

Lot L1 of origami_hexmap: the default pathfinder.

• Bfs::search(grid, width, height, from, to) -> Span<u8>: shortest path (unit cost, 6 neighbours), from the target (included) to the start (excluded), empty when unreachable or from == to. One hex dilation per layer on two u128 limbs with a local bitwise triple, layers stored, then backtracking with the neighbour mask of the current tile. Deterministic.
• Endpoints are handled outside the loop: the first layer is the start neighbourhood, and the loop stops on the layer that touches the target neighbourhood. Open edge tiles (Digger entrances) can be endpoints; paths never cross another edge tile.
• The hex distance between the endpoints lets the first layers skip the target test. Boards of at most 128 bits run on a single limb. Loops are unrolled ×4.
• New Bfs::distance(..) -> Option<u8>: the forward pass only, ~70% of search.
• Bfs::reachable and Bfs::tiles_within_range (movement range with obstacles): open edge tiles are included when a path ends on them.
• Panics: Asserter: invalid dimension, Asserter: position not inside, Bfs: position not walkable.

Gas (17x14, sierra gas, minus the 15_040 fixture baseline)

Fixture (far)	Path	Library	Target	Status
EMPTY	19	554_993	500_000	+11 %, not met
CAVE	24	691_095	650_000	+6 %, not met
MAZE	53	1_504_486	1_400_000	+7 %, not met
SERPENTINE	90	2_517_050	2_400_000	+5 %, not met
UNREACHABLE	0	248_280	< flooding the component (reachable 276_581, keep_component 283_755)	met

• Per unit: ~19.3k per layer, ~8.4k per backtracking step, ~55k fixed cost. On 7x7 boards: 9.9k per layer and 6.4k per step.
• origami_map for reference: its BFS medium test (4x4, path of 6) costs 1_608_464; the hex 7x7 EMPTY far search (path of 6) costs 131_733.
• Baseline to beat: the scalar queue BFS is 3–35× more expensive on every fixture.
• reachable: −4 % to −8 % against Caver::keep_component on 17x14, about −40 % on 7x7.

Every variant listed in the brief is implemented test-only in bench_bfs.cairo and measured in GAS.md: layer storage, backtracking step, target test, bidirectional search, the single-limb path, the corelib operators and the scalar baseline. GAS.md also covers the iteration history (v1 to v12) and the Sierra code size of the close variants.

Test plan

• snforge test -p origami_hexmap: 538 passed, 0 failed, 3 ignored.
• Checked against a scalar queue BFS oracle on:
  • the fixture pairs, and sampled pairs on the fixtures and on random caves and mazes (7x7, 17x14, 19x13);
  • boards 3x3, 8x16, 9x15, 25x10, 83x3 and 3x83;
  • edge entrances, corners, adjacent edge tiles, the no-shortcut-through-the-edge case and Digger corridors and mazes.
• Every returned path is valid: consecutive tiles adjacent, walkable interior tiles only, and the same path on a second call.
• reachable equals Caver::keep_component on caves; tiles_within_range checked for every radius.
• CI Test origami_hexmap (green, 8m23s).

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