Case analysis is the deduction technique that splits a problem space into a finite, mutually exclusive, exhaustive set of cases, proves the conclusion for each case independently, and concludes the result holds universally. Two of those three properties — mutual exclusion, exhaustiveness — are where most attempts at case analysis quietly fail. A partition that overlaps lets the same input fall under two derivations, and a partition that is incomplete lets some inputs fall under no derivation at all. Both produce a conclusion that looks proven and is not.
Quantm's resolution stage treats partitions as typed objects with two compile-time checks. The mutual-exclusion check confirms that no input satisfies more than one case predicate. The exhaustiveness check confirms that every input in the declared domain satisfies at least one case predicate. Both checks must pass before the engine begins per-case derivation. A partition that fails either check is rejected at the structural layer rather than at the verification layer, because a flawed partition cannot be repaired by careful per-case work.
The payoff is that a Quantm case-analysis derivation is unconditionally sound against the declared domain. If every case derivation is sound and the partition is verified mutually exclusive and exhaustive, the universal conclusion follows by construction. The user does not have to audit the partition manually — the engine has already done so, and the audit trail records the verification. That is the operational definition of a trustworthy case-analysis result, and it is what separates a complete proof from a confident-looking one.