CARVE: Certified Affordable Repair of Vetoed Maneuvers via Envelopes for Interactive Driving

The critical question after a correct driving veto is not only whether a maneuver is unsafe, but whether the blocked interaction admits a lawful, auditable, and responsibility-bounded repair. Prediction and game-theoretic planners can suggest plausible cooperation, yet they do not return a proof that the repair respects hard rules, right-of-way, cost allocation, and ego fallback. We introduce CARVE, Certified Affordable Repair of Vetoed maneuvers via Envelopes, a certificate architecture for prediction-free interactive repair. Given a vetoed maneuver, CARVE constructs a finite repair lattice and emits a structured certificate recording the binding rule, selected joint repair, right-of-way-scaled cooperation envelope, responsibility-weighted cost split, and ego-only fallback. This certificate view reveals the algorithmic bottleneck: multi-owner repair induces a product lattice $M = \prod_j |\mathcal{A}_j|$. We therefore introduce CARVE-Q, a verifier-shielded quantum-AI search layer that applies quantum minimum finding only to this black-box lattice while leaving all safety authority classical. In the conservative verifier-oracle model, exact classical minimum finding requires $Θ(M)$ queries in the worst case, whereas Durr-Hoyer/Grover minimum finding uses $O(\sqrt{M})$ oracle queries with high probability. We prove verifier-shielded certificate soundness, priority non-elicitation, black-box query separation, and finite-precision reversible-oracle constructibility. We then demonstrate state-vector minimum finding on CARVE repair oracles up to 65,536 assignments and validate certificate preservation on Lanelet2-grounded INTERACTION replay with 100% right-of-way respect, 100% blame consistency, and zero priority false positives. The result is a trust-bounded quantum-AI pattern for certified autonomy: quantum proposes; CARVE certifies.

Autonomous driving stacks must pick one trajectory from a multi-modal candidate set; choosing by model confidence ignores safety, traffic-law, and comfort constraints. We present \textsc{RECTOR} (Rule-Enforced Constrained Trajectory Orchestrator), a post-generation reranking layer that scores candidates against a tiered rulebook (Safety~$\succ$Legal$\succ$Road$\succ$Comfort) via differentiable proxies and a scene-conditioned applicability mechanism, then selects with a deterministic $\varepsilon$-lexicographic rule that preserves cross-tier priority by construction -- without retraining the predictor. On the Waymo Open Motion Dataset \texttt{validation_interactive} split (43{,}219 augmented instances, $K{=}6$), under ProtocolB (28-rule proxy catalog, oracle applicability) rule-aware selection cuts Safety+Legal violations from 28.58% to 20.42% and Total from 40.32% to 32.41% versus confidence-only on the same candidates. A uniform-weight weighted-sum baseline matches binary compliance on this benchmark -- the empirical lift comes from rule-aware ranking, while the lexicographic guarantee is the structural differentiator no weight calibration can replicate. Under adversarial confidence corruption, confidence-only selection fails in 100% of scenarios while both rule-aware selectors reject the injected mode in $\sim$96%. All figures are proxy-evaluator results (not a safety certificate), open-loop, 5,s horizon, U.S.\ rules, validation split.

Large language models (LLMs) are promising for autonomous driving, but semantics-only decision policies can yield physically unsafe behavior in dynamic traffic. Existing methods either perform online language reasoning without explicit dynamics verification or use world models mainly in offline pipelines, leaving a gap between semantic intent and physical feasibility at decision time. We propose Reason--Imagine--Act (RIA), a closed-loop framework that couples an LLM reasoner with an action-conditioned world model for online safety verification. At each step, the LLM proposes an action template and candidate sub-actions, the world model performs short-horizon rollouts, and a safety scorer selects the safest executable action with feedback to the next reasoning step. Under a unified CARLA point-goal protocol (1000 episodes), RIA achieves 80.05% route completion, 51.10% arrival rate, and 0.20% collision rate. Under the same closed-loop interface, RIA consistently outperforms training-free baselines, including CARLA TM and MADA, on core closed-loop metrics. For reproducibility, code is available at https://github.com/pku-smart-city/source_code/tree/main/RIA.