{"paper":{"title":"Pauli graphs, Riemann hypothesis, Goldbach pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Fabio Anselmi (FEMTO-ST), Michel Planat (FEMTO-ST), Patrick Sol\\'e","submitted_at":"2011-03-14T09:26:03Z","abstract_excerpt":"Let consider the Pauli group $\\mathcal{P}_q=<X,Z>$ with unitary quantum generators $X$ (shift) and $Z$ (clock) acting on the vectors of the $q$-dimensional Hilbert space via $X|s> =|s+1>$ and $Z|s> =\\omega^s |s>$, with $\\omega=\\exp(2i\\pi/q)$. It has been found that the number of maximal mutually commuting sets within $\\mathcal{P}_q$ is controlled by the Dedekind psi function $\\psi(q)=q \\prod_{p|q}(1+\\frac{1}{p})$ (with $p$ a prime) \\cite{Planat2011} and that there exists a specific inequality $\\frac{\\psi (q)}{q}>e^{\\gamma}\\log \\log q$, involving the Euler constant $\\gamma \\sim 0.577$, that is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2608","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}