test(solver): assert the max_outer contract instead of a magic outer count

[tschm]

Addresses #47.

Audit first

I audited every iteration-count / trajectory assertion in the two files the issue names. Most were already compliant:

• tests/test_paper/test_results.py — already fully behavioural: res.outer < 10 (bound), res.fallback == 0 (dormant-fallback claim), growth < envelope (relative √κ bound), res.free support checks. Unchanged.
• .inner assertions in test_solver.py — already relative/bounded (r_pcg.inner <= 0.7 * r_cg.inner, warm.inner < cold.inner).
• Warm-start outer == 1 — documented single-outer-step guarantees (warm start from an already-optimal free set converges in one step); exact by design, not implementation drift.
• Trajectory equalities (r_cg.traj == r_ex.traj) — compare two solvers to each other (the inexactness lemma), not a golden internal sequence.
• _CountingOperator call-counts — justified white-box regressions for Exact inner solver recomputes rcond_free p+1 times per free set in solve_eq (regression of #18) #30/Exact inner solver: unconditional rcond_free eigendecomposition dominates the direct-solve cost (~3.6x the solve it guards) #32; those call patterns aren't observable through Result, so they stay.

What changed

The one genuinely brittle pattern was the two cap tests hard-coding res.outer == 1 for max_outer=1 — a magic expected count. Each is now a contract test:

full = ActiveSetSolver(inner=CG()).solve(op, b).outer   # uncapped, measured not hard-coded
assert full > 1
for cap in range(1, full):                              # every cap short of convergence
    res = ...solve(..., config=ActiveSetConfig(max_outer=cap))
    assert not res.converged
    assert res.outer == cap                             # stops at exactly the cap

This is strictly stronger than the original (covers every cap below convergence, not just 1), reads only the public Result surface, and is robust to backend-dependent iteration-count drift because the reference count is measured, not pinned.

Verification

Check	Result
make test	102 passed, 100% coverage
make fmt	all hooks pass

Acceptance criterion (#47): iteration-count assertions reference only the public Result surface and express contracts/bounds rather than exact internal state; the paper's claims are still enforced; suite green at 100% coverage.

🤖 Generated with Claude Code

[Copilot]

Pull request overview

This PR updates the solver test suite to avoid brittle, hard-coded outer-iteration counts by asserting the public Result.outer / Result.converged max_outer contract instead of expecting a specific outer == 1 outcome for max_outer=1.

Changes:

• Reworked the bound-constrained max_outer cap test to measure the uncapped outer count and verify truncation behavior for every smaller cap.
• Reworked the equality-constrained max_outer cap test in the same way.
• Expanded docstrings to explain why the new assertions are more robust to backend-dependent iteration drift.

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