# 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.

Card: https://integralmanagement.ch/atlas-reader/fichas/N1817/
Source publication: https://jubap.net/xseil-quantum-formulation-companion-paper/

RELATIONSHIPS
xSeil quantum formulation. Companion paper → Admisibilidad contextual
documenta el concepto. 
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-3/#r-06e70479d80b60b9
Other card: https://integralmanagement.ch/atlas-reader/conceptos/C15/

xSeil quantum formulation. Companion paper → Contabilidad de recursos cuánticos
documenta el concepto. 
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-9/#r-7b6cc0208040308c
Other card: https://integralmanagement.ch/atlas-reader/conceptos/C48/

xSeil quantum formulation. Companion paper → Estado de una afirmación
documenta el concepto. 
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-10/#r-ed30bad008c45280
Other card: https://integralmanagement.ch/atlas-reader/conceptos/C50/

Regime-Aware Semantic Windows: Proposal for Mathematical Assessment and Empirical Validation → xSeil quantum formulation. Companion paper
hypothesis. Context qualification can define a research instance, but does not remove the cost of state preparation or establish quantum advantage.
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-36/#r-b51c9c96553d3f18
Other card: https://integralmanagement.ch/atlas-reader/fichas/T1513/

xSeil quantum formulation. Companion paper → Annex 9 — Claims and Evidence Appendix
candidate transfer. Oracle definitions, resource estimates and demonstrated results should carry separate evidence labels rather than sharing a single quantum-performance claim.
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-37/#r-5748a6cb0612e782
Other card: https://integralmanagement.ch/atlas-reader/fichas/T2814/

xSeil quantum formulation. Companion paper 2 → xSeil quantum formulation. Companion paper
editorial comparison. For a complementary reading, see [Quantum objects, oracles and resource accounting](https://jubap.net/xseil-quantum-formulation-companion-paper/).
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-43/#r-79fd34ea44887508
Other card: https://integralmanagement.ch/atlas-reader/fichas/N1819/

xSeil quantum formulation. Companion paper → xSeil VRP
editorial comparison. For a complementary reading, see [The classical routing problem and baselines](https://jubap.net/xseil-vrp/).
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-43/#r-3a639aa6574ff6cb
Other card: https://integralmanagement.ch/atlas-reader/fichas/N1803/

xSeil quantum formulation. Companion paper → Regime-Aware Semantic Windows: Proposal for Mathematical Assessment and Empirical Validation
editorial comparison. For a complementary reading, see [The semantic-window validation proposal](https://tegrity.ai/regime-aware-semantic-windows-mathematical-validation/).
Relationship: https://integralmanagement.ch/atlas-reader/relaciones/pagina-43/#r-a2cc9040882f2be6
Other card: https://integralmanagement.ch/atlas-reader/fichas/T1513/