Proposal Collapse and Execution Fibers in Stochastic Program Generation

When a stochastic code generator (an LLM) proposes executable specifications in response to natural-language prompts, two distinct kinds of variation emerge. Surface-form variation produces syntactically different proposals that resolve to the same deterministic execution. Execution ambiguity produces proposals that resolve to different executions. The operational distinction between these two phenomena is induced by the deterministic execution system. We formalize this distinction through execution fibers -- the preimages of execution classes under a deterministic projection -- and measure its empirical structure using controlled perturbation experiments. Across 2,200 proposals (1,200 baseline, 1,000 controlled perturbations), we observe 28 execution classes with non-uniform fiber cardinality (Gini = 0.467). Synonym perturbations produce near-perfect intra-fiber stability (sigma = 0.992, rho = 0.985): surface rewording is absorbed by canonicalization. Metric and family substitutions produce zero same-fiber transition mass (rho = 0.000) with perfect per-variant stability (sigma = 1.000): they create clean transitions to different execution identities, not noisy instability. The execution adjacency graph is sparse (density = 0.095, 10 connected components), and prompt support correlates strongly with fiber cardinality (r = 0.925). These results demonstrate that deterministic execution semantics induces observable, measurable structure on the stochastic proposal space. The structure is discrete, finite, and made observable through the execution system's provenance structure.