{"paper":{"title":"Lean-verified lower bounds for the Shannon capacity of odd cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Jeroen Zuiddam, Pjotr Buys, Sven Polak","submitted_at":"2026-07-31T17:57:08Z","abstract_excerpt":"We give new lower bounds for the Shannon capacities of small odd cycles: $\\Theta(C_7)\\geq3.258805369885\\ldots$, $\\Theta(C_{11})\\geq5.294502522149\\ldots$, $\\Theta(C_{13})\\geq6.302455083464\\ldots$, $\\Theta(C_{15})\\geq7.301600534487\\ldots$, $\\Theta(C_{19})\\geq9.357192705918\\ldots$, $\\Theta(C_{21})\\geq10.342455853338\\ldots$, and $\\Theta(C_{23})\\geq11.328224257774\\ldots$. The bounds are obtained by an iterative procedure due to Gao (2026) which is based on a method by Itty, Rosin, Carstensen and Reichman (2026). The bounds are fully formalised in Lean."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29681","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29681/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"}