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We construct independent sets of size $134753$ in $C_7^{10}$, $21909$ in $C_{11}^{6}$, and $62530$ in $C_{13}^{6}$, improving the best known lower bounds for the Shannon capacity of these graphs to $\\Theta(C_7)\\geq 134753^{1/10}>3.258020$, $\\Theta(C_{11})\\geq 21909^{1/6}>5.289773$, and $\\Theta(C_{13})\\geq 6"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.21517","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-07-23T17:01:36Z","cross_cats_sorted":["cs.AI","cs.DM","math.CO","math.IT"],"title_canon_sha256":"86a0a1357f4db95d703b0452fd9393d092fd4f2cb4d1e0ebbba4927053d2ba1b","abstract_canon_sha256":"f21bcb41ad46944db2f8431d50f670c890adf3f5d20d29cf3e643138681e6fc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T01:24:37.351520Z","signature_b64":"Cpnj+molrmxwlW4d3Yp6fdoltnpH/yZzOvso//l7bR77H6xw/TZ6R53rUud9eC/3FKIO6YvoNtrGH5VZWRJ1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebc24dd446d19bc984cb9c1a9c7146020d0704ef8353b3553dc28295703f8046","last_reissued_at":"2026-07-24T01:24:37.350645Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T01:24:37.350645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved lower bounds for the Shannon capacity of odd cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Chase Carstensen, Christopher D. 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