{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7MNDE7R2ZH6UK4VDPLUZB7BNFE","short_pith_number":"pith:7MNDE7R2","schema_version":"1.0","canonical_sha256":"fb1a327e3ac9fd4572a37ae990fc2d291bc0ce0a68fbb28d5b7b4df9b0949fef","source":{"kind":"arxiv","id":"1501.06551","version":1},"attestation_state":"computed","paper":{"title":"On the odd girth and the circular chromatic number of generalized Petersen graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amir Daneshgar, Meysam Madani","submitted_at":"2015-01-26T20:34:37Z","abstract_excerpt":"A class of simple graphs such as ${\\cal G}$ is said to be {\\it odd-girth-closed} if for any positive integer $g$ there exists a graph $G \\in {\\cal G}$ such that the odd-girth of $G$ is greater than or equal to $g$. An odd-girth-closed class of graphs ${\\cal G}$ is said to be {\\it odd-pentagonal} if there exists a positive integer $g^*$ depending on ${\\cal G}$ such that any graph $G \\in {\\cal G}$ whose odd-girth is greater than $g^*$ admits a homomorphism to the five cycle (i.e. is $C_{_{5}}$-colorable).\n  In this article, we show that finding the odd girth of generalized Petersen graphs can be"},"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":"1501.06551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-26T20:34:37Z","cross_cats_sorted":[],"title_canon_sha256":"c39c0f471abb2e91f6fcd475c9276ef3b1e6363b129e762d8310e3099f1234a3","abstract_canon_sha256":"11e949e164b128f1ae925f30ac5b289986b01bc33209b1947763f655f78f3b4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:41.097860Z","signature_b64":"YmoDlCmod6fxxJ8qpJzvsJs28AbN5J8M2pYFDvmy8MF+saICIiodJ5gn3T9v8KS0eNC94Cf1Y/IN1evF8LiwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1a327e3ac9fd4572a37ae990fc2d291bc0ce0a68fbb28d5b7b4df9b0949fef","last_reissued_at":"2026-05-18T02:28:41.097426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:41.097426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the odd girth and the circular chromatic number of generalized Petersen graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amir Daneshgar, Meysam Madani","submitted_at":"2015-01-26T20:34:37Z","abstract_excerpt":"A class of simple graphs such as ${\\cal G}$ is said to be {\\it odd-girth-closed} if for any positive integer $g$ there exists a graph $G \\in {\\cal G}$ such that the odd-girth of $G$ is greater than or equal to $g$. An odd-girth-closed class of graphs ${\\cal G}$ is said to be {\\it odd-pentagonal} if there exists a positive integer $g^*$ depending on ${\\cal G}$ such that any graph $G \\in {\\cal G}$ whose odd-girth is greater than $g^*$ admits a homomorphism to the five cycle (i.e. is $C_{_{5}}$-colorable).\n  In this article, we show that finding the odd girth of generalized Petersen graphs can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06551","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.06551","created_at":"2026-05-18T02:28:41.097488+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06551v1","created_at":"2026-05-18T02:28:41.097488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06551","created_at":"2026-05-18T02:28:41.097488+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MNDE7R2ZH6U","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MNDE7R2ZH6UK4VD","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MNDE7R2","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE","json":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE.json","graph_json":"https://pith.science/api/pith-number/7MNDE7R2ZH6UK4VDPLUZB7BNFE/graph.json","events_json":"https://pith.science/api/pith-number/7MNDE7R2ZH6UK4VDPLUZB7BNFE/events.json","paper":"https://pith.science/paper/7MNDE7R2"},"agent_actions":{"view_html":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE","download_json":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE.json","view_paper":"https://pith.science/paper/7MNDE7R2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06551&json=true","fetch_graph":"https://pith.science/api/pith-number/7MNDE7R2ZH6UK4VDPLUZB7BNFE/graph.json","fetch_events":"https://pith.science/api/pith-number/7MNDE7R2ZH6UK4VDPLUZB7BNFE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE/action/storage_attestation","attest_author":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE/action/author_attestation","sign_citation":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE/action/citation_signature","submit_replication":"https://pith.science/pith/7MNDE7R2ZH6UK4VDPLUZB7BNFE/action/replication_record"}},"created_at":"2026-05-18T02:28:41.097488+00:00","updated_at":"2026-05-18T02:28:41.097488+00:00"}