{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GZ2Z6DLMAYL2DL3WILIEMNJGOI","short_pith_number":"pith:GZ2Z6DLM","schema_version":"1.0","canonical_sha256":"36759f0d6c0617a1af7642d04635267239c78c802ebcf6d1de8ebe025cedeb72","source":{"kind":"arxiv","id":"1901.01524","version":1},"attestation_state":"computed","paper":{"title":"Rotation sets for graph maps of degree 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Llu\\'is Alsed\\`a, Sylvie Ruette","submitted_at":"2019-01-06T10:06:34Z","abstract_excerpt":"For a continuous map on a topological graph containing a loop $S$ it is possible to define the degree (with respect to the loop $S$) and, for a map of degree $1$, rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop $S$ then the set of rotation numbers of points in $S$ has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational $\\alpha$ in this interval there exists a periodic point of rotation number $\\alpha$.\n "},"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":"1901.01524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-06T10:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"6495e962100ee3b28f9606003080cbe8af7aa8acb94f4946bda68a8b0c1d9d46","abstract_canon_sha256":"e074f4b863f32c1ee77a443e07ed85ee5d0060c61b874d781124b9a897cc47a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:51.807394Z","signature_b64":"GbTaZDQ0bGJGxvg9s4UwDwsK1HYqD8QB+DqCoF4u61/wdV8TYxRkI7WKhRl1Bewwc1goTv+Xe/4nHEMPby9nDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36759f0d6c0617a1af7642d04635267239c78c802ebcf6d1de8ebe025cedeb72","last_reissued_at":"2026-05-17T23:56:51.807025Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:51.807025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotation sets for graph maps of degree 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Llu\\'is Alsed\\`a, Sylvie Ruette","submitted_at":"2019-01-06T10:06:34Z","abstract_excerpt":"For a continuous map on a topological graph containing a loop $S$ it is possible to define the degree (with respect to the loop $S$) and, for a map of degree $1$, rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop $S$ then the set of rotation numbers of points in $S$ has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational $\\alpha$ in this interval there exists a periodic point of rotation number $\\alpha$.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01524","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":"1901.01524","created_at":"2026-05-17T23:56:51.807082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01524v1","created_at":"2026-05-17T23:56:51.807082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01524","created_at":"2026-05-17T23:56:51.807082+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZ2Z6DLMAYL2","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZ2Z6DLMAYL2DL3W","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZ2Z6DLM","created_at":"2026-05-18T12:33:18.533446+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/GZ2Z6DLMAYL2DL3WILIEMNJGOI","json":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI.json","graph_json":"https://pith.science/api/pith-number/GZ2Z6DLMAYL2DL3WILIEMNJGOI/graph.json","events_json":"https://pith.science/api/pith-number/GZ2Z6DLMAYL2DL3WILIEMNJGOI/events.json","paper":"https://pith.science/paper/GZ2Z6DLM"},"agent_actions":{"view_html":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI","download_json":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI.json","view_paper":"https://pith.science/paper/GZ2Z6DLM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01524&json=true","fetch_graph":"https://pith.science/api/pith-number/GZ2Z6DLMAYL2DL3WILIEMNJGOI/graph.json","fetch_events":"https://pith.science/api/pith-number/GZ2Z6DLMAYL2DL3WILIEMNJGOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI/action/storage_attestation","attest_author":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI/action/author_attestation","sign_citation":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI/action/citation_signature","submit_replication":"https://pith.science/pith/GZ2Z6DLMAYL2DL3WILIEMNJGOI/action/replication_record"}},"created_at":"2026-05-17T23:56:51.807082+00:00","updated_at":"2026-05-17T23:56:51.807082+00:00"}