Generating structurally valid synthetic tabular data remains difficult: outputs with high statistical fidelity and downstream utility can still violate semantically meaningful domain constraints. We study the discovery and enforcement of three complementary inter-column constraint families---equations, linear inequalities, and logical dependencies. Our unified tool-grounded workflow represents all three as machine-executable hypotheses and applies a common interface for full-table validation, deterministic diagnosis, and counterexample-guided revision. A generator-agnostic postprocessor coordinates family-specific repairs on outputs from unchanged tabular generators. Across curated behavioral audits and end-to-end evaluations, the complete workflow improves held-out violation detection over one-shot direct prompting, while postprocessing yields zero measured violations for every retained, applicable constraint, improves downstream utility on most datasets, and largely preserves univariate marginals.
A key challenge in multimodal reasoning is determining which visual dependencies become relevant under a specific task, rather than merely recognizing visible content. We study this through edit-induced constraint discovery in text-in-image editing, a controlled diagnostic setting where a local text change can activate secondary consistency constraints: given a valid editing instruction and an image, can a model identify the secondary regions that must also change? Across 461 diagnostic cases, four MLLMs, and 19 constraint subtypes, models recover only 46% case-level macro recall under unguided prompting versus 94% when constraints are explicitly provided, suggesting that a substantial portion of the failure arises when models must decide which unstated dependencies to surface. Oracle-field decomposition shows that case-specific causal explanations are the most effective partial guidance (0.782 recall), above region names (0.610) or type labels (0.646), suggesting that edit-specific causal cues account for much of the oracle gain. A downstream experiment further shows that higher self-discovery recall does not necessarily improve task performance: unverified self-discovery introduces false positives that offset recall gains, motivating precision-aware constraint elicitation.