# Operator Packages, Proposer Strength, and Construction-Family Plateaus in Office-Scale Verified Search

arXiv: https://arxiv.org/abs/2609.29636 · HTML: https://mlsanity.com/paper/2609.29636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 15 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [LoongFlow: Directed Evolutionary Search via a Cognitive Plan-Execute-Summarize Paradigm](https://mlsanity.com/paper/2512.24077/) (2025)
- [Mutation Without Variation: Convergence Dynamics in LLM-Driven Program Evolution](https://mlsanity.com/paper/2606.05408/) (2026)
- [Interrupting the Loop: Periodic Subject Changes Raise Judged Surprise and Connection in Base Language Models](https://mlsanity.com/paper/2608.19893/) (2026)
- [Memory-Guided Tree Search with Cross-Branch Knowledge Transfer for LLM Solver Synthesis](https://mlsanity.com/paper/2605.17539/) (2026)

## Abstract (arXiv)

Verified search, in which a language model proposes programs, a hard evaluator scores them, and selection keeps the best, has recently moved mathematical records; controlled ablations of the proposer-side components remain rare. We instrument a minimal FunSearch-style loop at office scale (a 30B local model on a laptop, 120-600 verified samples per run) with three operator packages: a schematic notebook the model writes and carries instead of verbatim elites, a named obstacle, and behavioural repulsion from constructions already found. On nine construction problems from a public repository, the complete 2^3 factorial with two replicates favours the primary contrast in a nominal two-stage analysis: the composition closes more of the seed-to-record gap (+0.196; nominal pooled p=0.023, stage-combination p~0.08; median per-problem effect +0.045). Repulsion raises construction-hash diversity everywhere (p=0.0039; partly a manipulation check). The factorial finds no positive memory-by-repulsion interaction (bounded to about +/-0.04); the gain decomposes additively, and memory+repulsion is the only arm that never collapses (0 of 18 runs), within 0.025 of the full composition. A frontier proposer under the identical loop reaches in tens of samples what the local model does not in hundreds; in single scoping runs its gains arrive without the operators. The search stalls after closing ~92% of the gap on the flagship problem, and the registered family-hint test gives the stall its first reading: named in words, the reference family is adopted and loses; handed as code, it is optimized, but our best finite-grid implementation remains below the plateau reached unaided. The loop transported and optimized the idea it was handed; no unaided run produced it. We release the harness, every candidate, and the dated pre-registrations.