How Far Can Reasoning Alone Take You? Graph-Based Candidate Selection for Test-Time Scaling on Code

Large reasoning models spend most of their test-time compute on long chains of thought, and on competitive programming the quality of that reasoning — rather than implementation ability — is the dominant bottleneck. Given $N$ sampled candidates per problem, the question is which one to trust. We ask how much of that selection problem is solvable from the reasoning trace alone: no code execution, no answer consensus, no token probabilities. We condense each trace into a summary, lift the summary into a reasoning graph whose topology encodes steps, dependencies and case analysis, and train a graph neural network (GNN) to predict correctness from the graph. On LiveCodeBench-v6, under a leakage-free 10-fold cross-test protocol in which every problem is scored only by models that never saw it during training or checkpoint selection, per-fold ensembles recover 0.29 of the $\text{pass@1}\to \text{pass@64}$ gap (+9.5 points absolute over random selection), against 0.12 for a frontier judge reading the same traces and 0.16 for a topology-free MLP over the same summary embeddings; single models recover 0.19, so seed-ensembling — effective here because a small training set and aggressive dropout yield weakly correlated models — accounts for a third of the effect, and the worst of the ten folds still recovers 0.16. A comparison of seven checkpoint-selection rules shows that selecting on a smoothed validation curve dominates raw peak selection in both mean and worst-case usefulness. As a transfer example, on a harder LiveCodeBench-Pro subset the classifier–selector cascade recovers $0.22\pm 0.04$. We then characterize the ceiling of reasoning-only selection: 94.5% of incorrect candidates textually claim success, and most residual errors are near-ties where candidates share an algorithm and differ only in implementation details absent from the trace — so much so that the same judge, held fixed, recovers three times as much of the gap from the candidates' code as from their reasoning.