[Bug] HC → StackerCrane reduction produces incorrect result

[isPANN]

Summary

The reduction HamiltonianCircuit → StackerCrane → ILP returns Or(false) on the prism graph, which has a valid Hamiltonian circuit. All other 2-step HC→ILP paths return Or(true).

Reproduction

pred create --example HamiltonianCircuit -o hc.json
pred reduce hc.json --to StackerCrane | pred solve -
# Returns Or(false) — should be Or(true)

The prism graph (6 vertices, 9 edges) has Hamiltonian circuit [0, 1, 4, 3, 5, 2].

Root cause

The StackerCrane solver returns Min(6) with solution [1, 2, 3, 0, 5, 4]. After extract_solution maps it back to HC, the same config [1, 2, 3, 0, 5, 4] is returned. However, this is not a valid Hamiltonian circuit — edges 2→3 and 0→5 do not exist in the prism graph:

  1 → 2  ✅
  2 → 3  ❌  (not an edge in prism graph)
  3 → 0  ✅
  0 → 5  ❌  (not an edge in prism graph)
  5 → 4  ✅
  4 → 1  ✅

This means either HC → StackerCrane reduce_to() constructs an incorrect StackerCrane instance, or extract_solution() incorrectly maps the StackerCrane solution back to HC.

Comparison with other paths

Path	Result	Solution	Valid HC?
HC → HamiltonianPath → ILP	Or(true)	[0, 1, 4, 3, 5, 2]	✅
HC → TravelingSalesman → ILP	Or(true)	[0, 1, 2, 5, 4, 3]	✅
HC → RuralPostman → ILP	Or(true)	[0, 3, 5, 4, 1, 2]	✅
HC → QuadraticAssignment → ILP	Or(true)	[0, 1, 2, 5, 4, 3]	✅
HC → StrongConnectivityAugmentation → ILP	Or(true)	[0, 3, 5, 4, 1, 2]	✅
HC → BottleneckTravelingSalesman → ILP	Or(true)	[0, 1, 2, 5, 4, 3]	✅
HC → BiconnectivityAugmentation → ILP	Or(true)	[0, 2, 1, 4, 5, 3]	✅
HC → StackerCrane → ILP	Or(false)	[1, 2, 3, 0, 5, 4]	❌

Files to investigate

• src/rules/hamiltoniancircuit_stackercrane.rs — reduce_to() and extract_solution()
• src/rules/stackercrane_ilp.rs — StackerCrane → ILP reduction