# Audit the Scaffold, Not the Checkpoint: A Stationarity Dichotomy for Recursive Self-Improvement in Agentic Coding

arXiv: https://arxiv.org/abs/2609.34924 · HTML: https://mlsanity.com/paper/2609.34924/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 21 of 21)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Defining and Characterizing Reward Hacking](https://mlsanity.com/paper/2209.13085/) (2022)
- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)
- [Self-Adapting Language Models](https://mlsanity.com/paper/2506.10943/) (2025)
- [Measuring the Algorithmic Efficiency of Neural Networks](https://mlsanity.com/paper/2005.04305/) (2020)
- [Efficiently Learning at Test-Time: Active Fine-Tuning of LLMs](https://mlsanity.com/paper/2410.08020/) (2024)
- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Optimal and Adaptive Algorithms for Online Boosting](https://mlsanity.com/paper/1502.02651/) (2015)
- [RTTC: Reward-Guided Collaborative Test-Time Compute](https://mlsanity.com/paper/2508.10024/) (2025)
- [Rethinking Self-Evolving Agents: Do We Still Need Prescribed Optimization Pipelines?](https://mlsanity.com/paper/2608.09629/) (2026)
- [Predicting Acceptance and Review Effort in Human and Agent Pull Requests](https://mlsanity.com/paper/2607.12057/) (2026)

## Abstract (arXiv)

An auditor who checks whether a system's weights are frozen is checking the wrong thing. Our stationarity dichotomy says that iterative self-modification hits strict diminishing returns whenever the agent's reachable set of edits stays fixed, and can escape only if that set expands. Rewriting scaffolding (tools, verifiers, decomposition) expands what an agent reaches without touching a weight, so frozen weights buy an eventual ceiling but no stationarity along the way. The criterion also separates three regimes usually merged: search within a fixed class, test-time training that raises the ceiling itself, and scaffold rewriting between them. Audit the scaffold, not the checkpoint. The same ceiling binds sideways. Best-of-k orchestration realizes the best worker's ceiling exactly: width buys rate, not budget. Re-consulting a fixed pool has a horizon computable in advance, decided by the pool alone, and the one arrangement that would beat it, a weighted vote, needs diversity real workers lack: on 30 same-family workers the failure overlap sits at its maximum, and a majority fails 23/55 (42%) of tasks. We obtain the criterion by reading refinement as gradient boosting on the residual error between draft and target, a patch or git diff, and then measuring where that reading breaks: patches compose instead of standing beside each other to be voted on, and failures overlap. What we measure is saturation. Per-round improvement decays toward zero on SWE-bench, and churn decays geometrically across 401 production sessions, a shape shared with a pre-AI human baseline that establishes the regime without identifying its cause. Both breaks are engineering choices rather than laws about code, so together they specify a harness worth building.