ILP<i64> rules declare bounds as constraints, so ILP<i64> → ILP<bool> always fails

[isPANN]

Summary

Every path of the form X → ILP<i64> → ILP<bool> → … (for example to QUBO or SpinGlass) fails on every instance for 41 of the 44 rules that produce ILP<i64>:

Error: concrete path N failed during reduction: ILP -> ILP: binary encoding requires a finite upper bound for every integer variable

This was 126 of the 128 errors in a sweep of pred path <variant> <target> <example.json> across all variants.

Root cause

• ILP::new (src/models/algebraic/ilp.rs) gives every i64 variable the default domain [0, +∞).
• Rules state variable bounds as constraint rows instead of variable domains. For example, minimumfeedbackarcset_ilp.rs adds o_v <= n - 1 as a LinearConstraint.
• ilp_i64_ilp_bool.rs needs variable.upper_bound() to be finite for its binary encoding, so it rejects the output.

Only 3 of the 44 ReduceTo<ILP<i64>> rules use ILP::with_variables: biconnectivityaugmentation_ilp, ilp_bool_ilp_i64 and openshopscheduling_ilp. biconnectivityaugmentation_ilp still fails, so some of its variables are left unbounded.

Reproduce

pred create MIS --graph 0-1,1-2,2-3,3-0,0-2 -o mis.json
pred path MIS QUBO mis.json   # path 5: … → MinimumFeedbackArcSet → ILP/i64 → ILP/bool → QUBO

Proposed fix

• For each ReduceTo<ILP<i64>> rule, declare the known variable intervals with ILP::with_variables (and IntegerVariable::new(Some(lo), Some(hi))) instead of, or in addition to, bound rows. Order/position variables, counts and flows almost always have a derivable finite bound.
• Where a variable is truly unbounded, document it. The ILP<i64> → ILP<bool> edge then correctly rejects those instances.
• Decide whether redundant bound constraints should be removed once they become variable domains. That affects num_constraints formulas and their tests.
• Add a test that runs each ILP<i64> rule's canonical example through ILP<i64> → ILP<bool> and checks that the encoding succeeds.
• Also check for a root-cause option: should ILP<i64> → ILP<bool> derive implied bounds from single-variable constraint rows?