{"paper":{"title":"Random-projector quantum diagnostics of Ramsey numbers and a prime-factor heuristic for $R(5,5)=45$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"Fabrizio Tamburini","submitted_at":"2025-08-22T03:28:43Z","abstract_excerpt":"We introduce a statistical framework for estimating Ramsey numbers by embedding two-color Ramsey instances into a $Z_2 \\times Z_2$-graded Majorana algebra. This approach replaces brute-force enumeration with two randomized spectral diagnostics applied to operators of a given dimension d associated with Ramsey numbers: a linear projector $P_{lin}$ and an exponential map $P_{exp}(\\alpha)$, suitable for both classical and quantum computation. In the diagonal case, both diagnostics identify R(5,5) at n=45. The quantum realizations act on a reduced module and therefore require only five data qubits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.16699","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.16699/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}