5 problems
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Tensor-product conjecture for the full Hofstadter energy trans-series
Tensor-product conjecture. The full energy trans-series can be written as a tensor product of the minimal trans-series and the medium, namely
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The Hermite-identity conjecture for the critical flux sequence
Let be coprime flux parameters with . Let denote the critical integer in the sequence approaching the critical flux from above. Let…
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The subsequence conjecture for critical flux in the three-dimensional Hofstadter model
Let and define the subsequence . Let be the upper critical sequence of integers associated with the critical flux. Subsequence conjecture.…
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The first critical-sequence conjecture for the three-dimensional Hofstadter model
First critical-sequence conjecture. The intercept satisfies
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Validity of Theorem 5.11 for small constant magnetic fields
Conjecture on Theorem 5.11. Theorem 5.11 should remain valid for perturbations by small constant fields .