xSeil quantum formulation. Companion paper

This note reformulates four candidate quantum work packages grounded in a formal regime-awareness programme and in the preserved source code of xSeil, a deployed logistics-planning system. The candidates are: (Q1) amplitude estimation for candidate-origin scores that are explicitly defined as expectations over uncertainty; (Q2) amplitude amplification for rare, implicit structural targets in xSeil’s concordance space; (Q3) amplitude estimation of rollback or cascade probabilities using a finite deterministic planner kernel extracted from the production code; and (Q4) a snapshot QUBO benchmark over a frozen route pool. The note separates ideal query complexity from end-to-end cost, corrects the crossover mathematics, distinguishes bifurcations from basin boundaries, and removes unsupported claims about market equilibrium, pre-armed catastrophic scenarios, identical simulation code paths, and exact quantum fit. The principal recommendation is to begin with an end-to-end resource audit. A negative result remains scientifically useful because it establishes which apparent quadratic speedups survive state preparation, reversible-oracle construction, output requirements, and comparison with strong classical methods.

Executive finding. The research direction holds, but only as a formulation-and-resource-accounting programme. Q2 is the cleanest first reversible-circuit study; Q3 has the highest potential operational value but the most difficult oracle; Q1 becomes valid only after the candidate score is defined as a bounded expectation; Q4 is a useful benchmark and negative control, not evidence of optimization advantage.