Test-time compute is the second lever, after training, that can close the open/closed gap on coding benchmarks. The question is whether it can be deployed at bounded cost. Naive best-of-N sampling gets expensive fast, and many published test-time search protocols either fail to generalize past their demo benchmarks or require hidden scaffolding that doesn't survive reproduction.

This axiom forces the cost bound to be explicit. The solver delivers a test-time protocol — best-of-N, tree search, verifier-guided sampling, iterative refinement, or any combination — that, applied to a reference base model scoring 40% on SWE-bench Verified, lifts the score to at least 65% on the same held-out slice. Inference cost per task, measured including all draft rollouts, verifier calls, and auxiliary compute, must not exceed 10× the baseline single-pass cost. At baseline $0.04 per task, this caps the accelerated configuration at $0.40 per task.

Verification is a two-stage replay. First, the baseline: the protocol confirms that the unmodified reference model scores within tolerance of 40% on the held-out slice. Second, the accelerated run: the submitted protocol is applied end-to-end, score and per-task cost are measured. Axiom passes when score ≥65% and mean cost per task ≤$0.40.

This axiom and AX-00004 are complementary. AX-00004 reduces the cost per decoded token; AX-00005 uses the resulting headroom to buy accuracy back. Together they make the GP-gate's budget achievable.