Resolution Cost of Structured Inquiry States Under a SAT Kernel: Results of a Preregistered Four-Run Campaign

This paper reports the results of a preregistered campaign with three analytic runs and one exact repetition measuring the physical energy cost of resolving structured question-states encoded as boolean satisfiability instances. A question-state over the six interrogative dimensions (WHO, WHAT, WHERE, WHEN, HOW, WHY) was encoded in CNF so that interrogative entropy equals the free-variable count, making the solver's work the resolution of the question rather than arbitrary work attached to it. The headline result is apparatus-level and replicated: resolving a structured question-state has measurable physical cost, that cost tracks resolution difficulty (r(conflicts, CPU energy) = +0.9905 on the clean channel, permutation p = 0.001), it peaks at the satisfiability phase transition, and the marginal constant fell inside its preregistered band in both clean measurements (0.033 to 0.043 mJ per satisfaction check). The campaign's negative control detected GPU-channel contamination in Run A, a CPU-only recomputation quantified the contamination at roughly two thirds of the shipped combined energy, and Run B replicated the full result on a corrected instrument. A registered anomaly (P-W: harder instances appeared to run at lower CPU package power) reproduced across two runs and was then resolved by a targeted composition-controlled test (Run C) to an artifact of batching: measurement windows mix high-power solver setup with lower-power search, and the search share rises with hardness. An exact repetition (Run D: identical code, seeds, and conditions) returned every headline value inside its registered band, with the deterministic quantities bit-identical and the constants within three percent. The claim ceiling, fixed in advance, holds at the apparatus level: resolution of a structured question-state is physically instantiated, and its energetic cost tracks resolution difficulty through duration. No result points above that ceiling.