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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17986838 |
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Table of Contents:
- <p>We have shown that the adjoint Collatz operator on L2(Nn 2) is Hilbert Schmidt, hence compact. This spectral fact explains Taos almost all result: the innite-dimensional decaying subspace H<1 corresponds to typical orbits, while any exceptions must lie in the finite-dimensional subspace H≥ 1-. The Collatz conjecture thus reduces from an innite search to a finite spectral computation: verify that all eigenvalues with Lamba ≥ 1 have eigen functions supported on the known cycle {1,2,4,} This does not prove the conjecture outright, but it completes Taos result by identifying exactly where exceptions could hide and proving that hiding place is finite-dimensional.</p>