Quantum Observation Constraints on Pre-Solution Information in SAT

This paper introduces an observation-respecting computational principle that forbids the existence of pre-solution “cheat sheets” for canonical SAT instances. Classical complexity theory implicitly allows auxiliary information that encodes solution-relevant structure prior to solving, erasing any notion of causal or observational order. In contrast, physically grounded models of computation—motivated by quantum mechanics—permit classical information only as the irreversible outcome of explicit measurement. We formalize this distinction by introducing non-resolving preprocessing procedures, defined as polynomial-time processes that avoid satisfiability-correlated measurement. For a canonical non-uniform family of satisfiable SAT instances, we define a hierarchy of solution structures and show that no such preprocessing can significantly compress these structures prior to observation. The obstruction arises from a fundamental mismatch between distribution-level information available before measurement and realization-dependent information that emerges only after satisfiability is resolved. Rather than claiming a resolution of P versus NP in the classical Turing model, this work isolates a precise conceptual barrier: realization-dependent solution information cannot be generated in advance without violating observation-respecting constraints. The result provides a physically motivated explanation for persistent pre-solution information asymmetry in NP-complete problems and suggests new directions for examining computational hardness through the lens of information generation.