{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YAM7ODMNPYRIKPEFFOOTOLQPTU","short_pith_number":"pith:YAM7ODMN","schema_version":"1.0","canonical_sha256":"c019f70d8d7e22853c852b9d372e0f9d263d20f15b333e45b1ccb09d6685bac8","source":{"kind":"arxiv","id":"1108.2899","version":3},"attestation_state":"computed","paper":{"title":"Periods of orbits for maps on graphs homotopic to a constant map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adriana Johnson, Chris Bernhardt, Whitney Radil, Zach Gaslowitz","submitted_at":"2011-08-14T18:59:13Z","abstract_excerpt":"The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of $2^k$ then there must be a periodic point with period $2^k$. The second is that if $v=2^ks$ for odd $s>1$, then for all $r>s$ there exists a periodic point of minimum period $2^k r$. These results are then compared to the Sharkovsky ordering of the positive integers.\n  (The final version of this paper will appear in the Journal of Difference Equations and App"},"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":"1108.2899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-14T18:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"70fb4c5abf74b31dff83e27243c47be83303eb6e142f49a130a4ab5a63ec2e7c","abstract_canon_sha256":"38c384ff1e32239a7c05db7d7c8038fe653fb2da6fc6e074271a199e69ea9c12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:12.796374Z","signature_b64":"PRO3lWMLyLIao1b8WGc3CZAGngqt7LEEg6P0l/WsemxwK5N2a6Z7BwhotuyQCK7Z9CgscQZ5DQ5k+OLZaxuEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c019f70d8d7e22853c852b9d372e0f9d263d20f15b333e45b1ccb09d6685bac8","last_reissued_at":"2026-05-18T03:57:12.795928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:12.795928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periods of orbits for maps on graphs homotopic to a constant map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adriana Johnson, Chris Bernhardt, Whitney Radil, Zach Gaslowitz","submitted_at":"2011-08-14T18:59:13Z","abstract_excerpt":"The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of $2^k$ then there must be a periodic point with period $2^k$. The second is that if $v=2^ks$ for odd $s>1$, then for all $r>s$ there exists a periodic point of minimum period $2^k r$. These results are then compared to the Sharkovsky ordering of the positive integers.\n  (The final version of this paper will appear in the Journal of Difference Equations and App"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2899","kind":"arxiv","version":3},"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":"1108.2899","created_at":"2026-05-18T03:57:12.795989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2899v3","created_at":"2026-05-18T03:57:12.795989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2899","created_at":"2026-05-18T03:57:12.795989+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAM7ODMNPYRI","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAM7ODMNPYRIKPEF","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAM7ODMN","created_at":"2026-05-18T12:26:47.523578+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/YAM7ODMNPYRIKPEFFOOTOLQPTU","json":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU.json","graph_json":"https://pith.science/api/pith-number/YAM7ODMNPYRIKPEFFOOTOLQPTU/graph.json","events_json":"https://pith.science/api/pith-number/YAM7ODMNPYRIKPEFFOOTOLQPTU/events.json","paper":"https://pith.science/paper/YAM7ODMN"},"agent_actions":{"view_html":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU","download_json":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU.json","view_paper":"https://pith.science/paper/YAM7ODMN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2899&json=true","fetch_graph":"https://pith.science/api/pith-number/YAM7ODMNPYRIKPEFFOOTOLQPTU/graph.json","fetch_events":"https://pith.science/api/pith-number/YAM7ODMNPYRIKPEFFOOTOLQPTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU/action/storage_attestation","attest_author":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU/action/author_attestation","sign_citation":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU/action/citation_signature","submit_replication":"https://pith.science/pith/YAM7ODMNPYRIKPEFFOOTOLQPTU/action/replication_record"}},"created_at":"2026-05-18T03:57:12.795989+00:00","updated_at":"2026-05-18T03:57:12.795989+00:00"}