Shortest-path optimality does not guarantee that a memoryless graph generator preserves a prescribed source-target correspondence. We study whether reordering legal shortest edits can retain this correspondence without changing the pairing, mandatory edits, or sampling budget. Under a common Poisson clock, we establish an exact criterion for endpoint coupling recoverability: the source-blind Markov projection attains the unavoidable clock-error floor if and only if routes to distinct targets do not share graph states. Routes to the same target may merge without sacrificing endpoint fidelity. This characterization leads to an exact finite-state routing formulation and a legality-preserving scheduling procedure with recovery certificates. A marker-free construction demonstrates how shared edge structure can retain source distinctions, while a capacity-constrained family exhibits a sharp separation in paired error between edit orders with identical marginal error. Finally, a target-conditioned aliasing bound connects structural route design to the terminal fidelity of a learned graph-only generator. These results characterize when legal edit ordering can preserve a prescribed coupling under fixed operational costs.
Jinhu Qi, Minda Hu, Wentao Zhang, Zixing Song, Irwin King
AI assistants are increasingly asked to reason over a user's own web traces: group chats, community threads, activity logs and revision histories. On CL-bench Life, a benchmark of such real-life context learning, frontier LLMs solve fewer than one task in five. We find that the request is not the specification: over 80% of the benchmark's rubrics share less than 60% of their content words with the final request, as for a rule set two turns earlier or every record that meets the user's criterion, and LLMs answering directly pass only 67% of these implicit rubrics against 81% of the others. We propose QERA, a Question-driven Evidence Reasoning Architecture that asks before it answers. QERA first turns the request into a requirement checklist and typed information needs, filtered by code for faithfulness to the user's words; it then answers from the whole conversation, asks the same questions again with quotes verified by code, and applies a guarded local repair. It needs no training or rubrics and makes about four LLM calls per task. On all 405 tasks with four frontier LLMs, QERA attains the highest solving rate on every LLM (21.0% on average, against 18.2% for the strongest of three inference-time baselines and 14.6% for direct answering) and leads every baseline significantly when pooled across LLMs, while using fewer tokens than PSCI and 4-5% of the tokens of Ctx2Skill. Ablations on GPT-6-Luna show that the gain is settled before the answer, by a fixed answer protocol (+3.8 rubric points) and the request-specific questions (+1.6), and that it is concentrated on implicit rubrics, with checking afterwards refining mainly numeric requirements.