This paper develops a symbolically effective contract calculus for semantic translation under gluing-coherent aspect semantics. Rather than treating translation correctness as a single predicate, it separates several distinct obligations: exact declared-state audit, exact accountability-state audit, accountability-state collapse-accountable audit, native collapse-accountable audit, and round-trip accountability. The framework models source semantics using finite component alphabets, closure-generated aspects, gluing-compatible summary spaces, aspectwise preorders, directed defects, and accountable classes with refinement and diameter structure. A translation package includes a forward map, a backward map, declared full-state envelopes, accountability-state channels, native target channels, and decoders back to source summaries or accountable source-side classes. The main constructive claim is symbolic effectivity: under declared semantic conditions, audit, bridge adequacy, budget feasibility, and local-to-global collapse checks can be reduced to decidable entailment in symbolic domains such as intervals, polyhedra, or other abstract-interpretation-style envelopes, with finite tabulation as a special case rather than the general method. The paper also develops a typed bridge-contract calculus for composition. Exact and accountability-state obligations compose through exact bridge stages, while native collapse composes through a bridge-induced accountable-class algebra with accumulated bridge budgets. A local-to-global theorem shows how symbolic subset semantics and gluing lift basiswise checks to whole-aspect native-collapse guarantees. At deployment time, the theory makes public observation and memory constraints explicit. A deployment bottleneck theorem yields cardinality, entropy, and shared-side-information rate-distortion lower bounds, with downstream consequences for reporting, scoring, thresholding, ranking, retrieval, and one-step control tasks. A detailed symbolic case study based on a Lipschitz quantized predictor illustrates how the framework supports accountable symbolic envelopes, accumulated collapse budgets, and deployable decision guarantees. Overall, the paper offers a first-principles, symbolically checkable theory of semantic translation that is narrower than unrestricted extraction from raw semantics, but substantially stronger than finite-table audit languages.
K. Takahashi (Thu,) studied this question.