Lookahead Calculation Verification: Predicting Which Intermediate Calculations Are Most Likely to Contain Consequential Errors

Multi-step problem solving frequently involves intermediate calculations whose accuracy can influence subsequent reasoning and final outcomes. Although verifying every intermediate calculation may improve reliability, exhaustive verification introduces additional computational costs and may be unnecessary when some calculations have limited downstream influence. Conversely, failing to verify a consequential intermediate calculation may allow an error to propagate through multiple subsequent operations. This paper introduces Lookahead Calculation Verification (LCV), a conceptual framework for predicting which intermediate calculations are most likely to contain consequential errors and estimating whether verifying them before continuing the solution is worthwhile. Rather than assigning equal verification priority to all intermediate calculations, LCV evaluates candidate calculations according to their estimated error probability, downstream consequence, propagation potential, verification effectiveness, and verification cost. The proposed framework consists of five components: intermediate calculation identification, error-risk estimation, downstream consequence prediction, verification-value estimation, and adaptive verification scheduling. For each intermediate calculation, the framework estimates the expected loss associated with an undetected error and compares this quantity with the expected cost of verification. Calculations with high expected verification value receive priority, whereas low-risk calculations may be retained without immediate verification. A mathematical formulation is developed to represent calculation-level error risk, downstream propagation, verification effectiveness, and resource allocation. The paper also introduces a set of testable research hypotheses and a controlled experimental protocol for comparing LCV against exhaustive verification, random verification, uncertainty-based verification, and no-verification baselines. The framework is intended to investigate whether forward-looking estimates of calculation error consequences can improve the allocation of verification resources in multi-step reasoning tasks. No experimental superiority is claimed in this paper. The proposed framework requires empirical validation across mathematical reasoning, numerical computation, symbolic manipulation, and other multi-step problem-solving settings.