Two-Part MDL for Inverse Program Synthesis from Short Tables with Discrete Cell Noise

We study inverse program synthesis from short numerical tables (six rows) when intermediate registers are unobserved and a fraction of cells are corrupted by discrete jumps (scale drift, dropped carry, arithmetic slip) rather than Gaussian noise. Candidate programs from a five-operator arithmetic DSL are enumerated exhaustively up to depth 2 and scored by a Two-Part MDL criterion with a frozen compositional prior and a five-channel discrete-jump likelihood. A program is accepted only if it compresses the table by 3 bits against a structureless Gaussian null. On a frozen benchmark of 5,000 tables from 20 generator families, the gate reaches table-level precision 97.2% (95% CI [96.0%, 98.1%]) and recall 45.7% ([43.5%, 47.8%]), with 0/500 false positives on white noise. Raising the enumeration depth to 3 lifts recall to 88.4% at precision 98.0%, showing that bounded recall is a search-depth ceiling. The study is synthetic and limited to the stated regime; it makes no claim of universal induction. Code, seeds and JSON artefacts are provided in the linked repository.