LLMs increasingly generate workflow actions and repairs that may be well formed yet stale, infeasible, conflicting, or destructive of their own evidence. We introduce Agentic Transaction Processing (ATP), which treats generated actions as untrusted proposals until deterministic admission accepts them under an executable constraint set C. Its two-sided principle is: a proposal is not truth, and no proposal foresees every disruption. Anything may propose, but only the runtime admits and commits; unforeseen disruptions trigger bounded reactive repair whose output re-enters admission. Mnemosyne realizes ATP with an append-only transition log, effective-state projection, dependency-safe compensation, and active contract records. Under stated assumptions and relative to C, we prove four safety properties (authority separation, serial-equivalent generative admission, evidence-preserving repair, and obligation containment) and establish bounded reactive repair. Across nine safety benchmarks and a four-case Temporal SDK comparison, ATP rejects every targeted violation while admitting valid work. A matched data-size sweep measures 5.2-6.6% incremental throughput cost over the same local durable commit path and exposes local saturation. In a companion scheduling harness, local repair edits nearly an order of magnitude fewer operations than global recompute; a 12-scenario interruption stress test rejects every stale recovery candidate without losing observations or producing invalid commits. Two bounded pilots route 80 proposals from four heterogeneous LLMs through the same gate with zero invalid commits; 24 of 40 mid-execution proposals are admitted and 16 are rejected, including four explicit safety rejections.

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