Tests Reveal an Unstated Code: (N+1) Propagation Consistency for LLM Code Generation

Selecting LLM-generated code without ground-truth tests relies on LLM-generated test inputs and expected outputs. Yet whether the LLM-generated tests' expected outputs or the candidate codes are the more reliable signal varies sharply across tasks. Existing methods either trust the LLM-generated tests' expected outputs as ground truth or discard them in favor of cross-code consensus. To our knowledge, no prior framework unifies these two stances as endpoints of a principled, task-adaptive continuum; existing combinations remain heuristic. Our unifying insight: the LLM-generated tests' expected outputs are the input-output behavior of an unstated $(n+1)$-th candidate code implicit in the LLM's solution distribution, on equal footing with the $n$ explicit ones. Each of the $n+1$ codes defines an agreement view, and we identify codes that score consistently across all $n+1$ views. We propose $(N+1)$-Propagation Consistency (${\mathrm{N}}^{+}\mathrm{PC}$), which couples $n+1$ Laplacian propagations via a task-adaptive scalar $\kappa$ weighting the unstated-code view against the rest. At its two endpoints, ${\mathrm{N}}^{+}\mathrm{PC}$ reduces to each prior stance, making ${\mathrm{N}}^{+}\mathrm{PC}$ a principled unification rather than a heuristic mixture. ${\mathrm{N}}^{+}\mathrm{PC}$ consistently improves every inner baseline and advances the state-of-the-art Pass@$k$ among execution-only rerankers as a plug-and-play framework.