2 problems

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Local uniqueness conjecture for discrete nonlinear Schrödinger bound states
Local-uniqueness conjecture. The $2^d$ solutions are locally unique for each $\sigma$ up to lattice translations: $J^{\alpha,\sigma}$ must be centered about $\sigma+M$ for some…
Conjectureopendiscrete-nonlinear-schrodinger lattice-bound-states uniquenessarXiv posted 2 days ago
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Conjecture on exponential smallness of the Peierls–Nabarro barrier
Exponential-smallness conjecture. The Peierls–Nabarro barrier quantities obey
Conjectureopendiscrete-nonlinear-schrodinger lattice-bound-states peierls-nabarro-barrierarXiv posted 2 days ago

Local uniqueness conjecture for discrete nonlinear Schrödinger bound states