{"paper":{"title":"A Recursive Construction Improving the Lower Bound on the Shannon Capacity of $C_7$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Yu Gao","submitted_at":"2026-07-30T08:44:15Z","abstract_excerpt":"We give a recursive reformulation and extension of the independent set of size $134753$ in $C_7^{10}$ constructed by N. Itty, C. D. Rosin, C. Carstensen, and D. Reichman (arXiv:2607.21517v1). We prove a product lemma that combines gadgets of different dimensions while preserving the required independence conditions. Starting from the size-$367$ independent set in $C_7^5$ of S. C. Polak and A. Schrijver (Information Processing Letters 143 (2019), 37-40), the construction gives an explicitly specified independent set in $C_7^{200}$. Consequently, \\[ \\Theta(C_7)\\geq 3.2587891539086910161967650155"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27869","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/2607.27869/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"}