Signed-Literal Boundary Discovery in Noncoherent Fault Trees: D-Wave Hybrid CQM Recovery and Consequences for PRA Metrics

Fault trees containing NOT logic can represent noncoherent structure functions, whose prime implicants may include or consist entirely of negated literals. A workflow that decodes candidate solutions as sets of positive basic events cannot express such an implicant at all, so the deficiency is representational rather than a shortfall of search effort. This paper asks whether a signed-literal constrained quadratic model can represent and retrieve that class, and what omitting it costs in downstream probabilistic risk assessment metrics. A complete De Morgan symbolic truth family was locked for a fixed 80-instance benchmark cohort before any signed-literal hybrid-solver submission in this study. Scoring existing positive-projection candidates against that authority left no unrecovered nonempty projection but isolated 99 all-negated signed implicants across 29 instances, for which existing artifacts supplied no hit. Those targets were preregistered, verified locally as minimal implicants, and encoded as a compact proof-tree model within 110 variables and 111 constraints per instance. Executed on a D-Wave Leap hybrid CQM solver with no target information supplied, the formulation returned exact signed-literal assignments for 73 of the 99 targets; preregistered target-conditioned submissions then closed the remaining cohort gaps at 99 of 99 exact and 99 of 99 superset under strict scoring, after an inflated earlier figure was corrected to 97 of 99. Over the complete state space the locked signed truth family reproduces the original Boolean function exactly, while a positive-only projection of it disagrees in every instance. The disagreement is directional: all 29 boundary instances carry false-negative states and underestimate the top-event probability for p at or below 0.1, whereas none of the 51 non-boundary comparison instances carries any. At an absolute sign tolerance of 1e-12, the exact model yields 855 resolved negative Birnbaum evaluations, whereas the positive-only surrogate yields none. No quantum advantage, speedup, isolated QPU contribution, family enumeration, or plant-specific risk estimate is claimed.