A Retention-Gated Self-Evolving Memory for LLM Agents: Pre-Registered Backward-Transfer Evidence and Design Rules

We implement inference-time recursive self-improvement for an LLM agent — a persistent natural-language memory the agent rewrites from its own graded attempts, no weight updates — and add the retention mechanism such loops lack: a gate admitting an edit set only if a rehearsal anchor from families the agent is not practising still holds. Claims, arms, metrics, refutation criteria and rival mechanisms were pre-registered before any data existed, with a length-matched neutral-memory control and a round-0-vs-round-0 noise floor; a mid-run integrity check caught a seed-inert temperature setting and discarded every measurement it had touched. A Llama-3.2-3B agent evolves memory on GSM8K for 3 rounds under a self-judged (ungated) and the gated accept rule — the arms differ only in that rule — and is re-scored on GSM8K, ARC-Challenge and CommonsenseQA over fixed items and 6 paired seeds (extended post hoc from 3; both are tabulated). Both pre-registered claims are refuted at six seeds. Ungated evolution moved held-out accuracy by -0.036111 on ARC and -0.033333 on CommonsenseQA, both intervals now containing zero and both inside the measured noise floor, so we report inference-time self-evolution as stability-safe at this scale; and the gate’s advantage, which three seeds put at +0.033333, falls to +0.011111 [−0.016667, 0.033333] and no longer separates from zero. What survives is the declared falsifier, which fires harder with more data: a neutral memory — irrelevant text, no evolved content — degrades more than the evolved memory (by −0.033333 on ARC, bootstrap and t intervals both excluding zero), so the dominant retention cost here is context occupancy, not content interference. We also show the three-seed intervals that licensed the stronger reading were degenerate: an n=3 percentile bootstrap is exactly [min, max] of the per-seed values and cannot contain zero once the seeds agree in sign. Every interval here carries its n, a paired-t interval and a sign-flip p. Three design rules follow.