Refuse a schedule whose binaries came back off the integers

[andig]

Fixes the defect behind #127: an EV with c_min=4140 charging at a fifth of that in 14 of 192 slots, z_c sitting between 0.12 and 0.36, reported as Feasible.

What happens

_solve_preferences decides whether to keep its result by reading the variables back. A solve that runs out of clock before it finds an integer solution leaves the relaxation in them, and pulp reads that like any other result. It scores better on the preferences than any real schedule can — because it is one the model forbids — so improved is true, the first stage schedule is discarded, and problem.status is then forced to Optimal.

Reproduces on the split path at the default probe budget:

path=split  preference_stage=Not Solved  status=Feasible  5.70s
  slot   3: c=  615.46 gate= 1035.00  z_c=0.35678659
  ... 14 slots between 0.12 and 0.36

What changes

The acceptance test. Integrality joins the two conditions already checked there, for the reason the comment beside them gives: a solver that reports the wrong status must not be able to spend money, and it must not be able to hand back a schedule the model does not allow either. The stage now ends as Not Solved, kept the first stage and the first stage schedule survives.

A check before the result is built. Standing in for every stage above deciding correctly. A schedule that breaks the model is worse than no schedule — it looks like an answer and the caller charges a battery by it — so a fractional point is reported as no schedule rather than returned. One pass over the integer variables against a solve measured in seconds. It logs when it fires; a silent fallback is how this stayed invisible.

Note for anyone reading the check: pulp stores a binary as an integer bounded to 0 and 1, so LpBinary never survives on a variable and LpInteger is what the filter has to match. Getting that wrong makes the guard pass vacuously.

Tests

tests/test_fractional_solution.py, three cases, no captured request and no dependence on a timing race:

• a preference stage that returns without an integer solution is refused, first stage schedule intact
• a fractional point that reaches the result is reported as Not Solved with no schedule
• values inside CBC's own integer tolerance still pass, so the guard does not fire on rounding

Full suite passes (115).

Base

Branched off perf/two-stage-solve rather than main, since that is where _solve_preferences lives. #135 picks it up on its next merge. Worth deploying independently of the perf work — production currently runs the rollup, where this is reachable.

Related: the probe change measured alongside this hides the bug by keeping most requests on the joint path. It does not remove it, and this fix stands on its own.

[andig]

@ekkea on top of the 2-stage solve. Merging since that hasn't hit master yet.