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

arXiv:2609.29636v2 Announce Type: replace-cross Abstract: 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 in eight of nine problems (one-sided 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 searches stall after closing 85-92% of the gap on the flagship problem, and a later analysis reads that plateau as a resolution limit: the reference value is a continuum limit and the unaided long-run finals already carry its family's structure. In the registered family-hint test the family named in words is adopted and loses; handed as code, it is optimized, but our best finite-grid encoding stays below the plateau reached unaided. We release the harness, every candidate, and the dated pre-registrations.