7 problems
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Equal tagging conjecture for Laplacian-invariant anti-synchrony subspaces
Equal tagging conjecture. Every -invariant anti-synchrony subspace is evenly tagged, not merely fully tagged.
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NSS6 equal-state-count conjecture for anti-synchrony subspaces
NSS6 equal-state-count conjecture. The number of cells in the common state must equal the number of cells in the opposite state.
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The Rigid Synchrony Conjecture for network periodic states
Rigid Synchrony Conjecture. Every rigid global synchrony pattern is balanced.
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The Rigid Phase Conjecture for network periodic states
Rigid Phase Conjecture. If
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The Rigidity Properties conjectures for network dynamics
Rigidity Properties conjectures. Every network has the corresponding property: RIP, RSP, RPP, and FOP.
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Persistence of balanced-coloring synchrony for hyperbolic periodic states
Persistence conjecture. The correspondence between balanced colorings and synchrony that persists under small perturbations of admissible ODEs should hold for all hyperbolic period…
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The hidden-symmetry conjecture for robust synchrony
Hidden-symmetry conjecture. Robust synchrony is always a consequence of hidden symmetry, even in networks with nontrivial symmetry groupoids.