Every flexible graph has a stable cut; this implies a characterization of minimally rigid graphs that admit flexible realizations with positive lengths via NAC-colourings.
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Constructs quantum filtered oracle for Valiant-Vazirani theorem reducing SAT to UNIQUE SAT, enabling polynomial-time NP solution via torsion nonlinearity in noise-free limit but not #P.
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Stable cuts, NAC-colourings and flexible realisations of graphs
Every flexible graph has a stable cut; this implies a characterization of minimally rigid graphs that admit flexible realizations with positive lengths via NAC-colourings.
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Quantum algorithm for Valiant-Vazirani reduction
Constructs quantum filtered oracle for Valiant-Vazirani theorem reducing SAT to UNIQUE SAT, enabling polynomial-time NP solution via torsion nonlinearity in noise-free limit but not #P.