{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SUDMS5ALW47F6AEQCYGDXL2HIV","short_pith_number":"pith:SUDMS5AL","schema_version":"1.0","canonical_sha256":"9506c9740bb73e5f0090160c3baf474542e5edf1319aea7269b9869af14ae2b1","source":{"kind":"arxiv","id":"1208.1473","version":3},"attestation_state":"computed","paper":{"title":"Area-preserving diffeomorphisms of the torus whose rotation sets have non-empty interior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Salvador Addas-Zanata","submitted_at":"2012-08-07T17:35:13Z","abstract_excerpt":"In this paper we consider $C^{1+\\epsilon}$ area-preserving diffeomorphisms of the torus $f,$ either homotopic to the identity or to Dehn twists. We suppose that $f$ has a lift $\\widetilde{f}$ to the plane such that its rotation set has interior and prove, among other things that if zero is an interior point of the rotation set, then there exists a hyperbolic $\\widetilde{f}$-periodic point $\\widetilde{Q}$$\\in {\\rm I}\\negthinspace {\\rm R^2}$ such that $W^u(\\widetilde{Q})$ intersects $W^s(\\widetilde{Q}+(a,b))$ for all integers $(a,b)$, which implies that $\\bar{W^u(\\widetilde{Q})}$ is invariant un"},"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":"1208.1473","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-07T17:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"b3528a68ceec545dd986e47a63d89a615f0a501f3400cdb9c3dd1a732e7cb8fc","abstract_canon_sha256":"3df74cc8ac2d16e3594cf1e25c5bd4f3fafdba85cd90c3a15a19093ae1e0ef30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:54.189013Z","signature_b64":"y7fxYmP1ct7qYT3PeVI1AcotUIuJDJr7FOX57wiXX/VaU/aJs7L0PopeDOwK/UqoyPtzfWaFjnfHlGcv3nkwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9506c9740bb73e5f0090160c3baf474542e5edf1319aea7269b9869af14ae2b1","last_reissued_at":"2026-05-18T02:53:54.188042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:54.188042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Area-preserving diffeomorphisms of the torus whose rotation sets have non-empty interior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Salvador Addas-Zanata","submitted_at":"2012-08-07T17:35:13Z","abstract_excerpt":"In this paper we consider $C^{1+\\epsilon}$ area-preserving diffeomorphisms of the torus $f,$ either homotopic to the identity or to Dehn twists. We suppose that $f$ has a lift $\\widetilde{f}$ to the plane such that its rotation set has interior and prove, among other things that if zero is an interior point of the rotation set, then there exists a hyperbolic $\\widetilde{f}$-periodic point $\\widetilde{Q}$$\\in {\\rm I}\\negthinspace {\\rm R^2}$ such that $W^u(\\widetilde{Q})$ intersects $W^s(\\widetilde{Q}+(a,b))$ for all integers $(a,b)$, which implies that $\\bar{W^u(\\widetilde{Q})}$ is invariant un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1473","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":"1208.1473","created_at":"2026-05-18T02:53:54.188205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.1473v3","created_at":"2026-05-18T02:53:54.188205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1473","created_at":"2026-05-18T02:53:54.188205+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUDMS5ALW47F","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUDMS5ALW47F6AEQ","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUDMS5AL","created_at":"2026-05-18T12:27:23.164592+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/SUDMS5ALW47F6AEQCYGDXL2HIV","json":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV.json","graph_json":"https://pith.science/api/pith-number/SUDMS5ALW47F6AEQCYGDXL2HIV/graph.json","events_json":"https://pith.science/api/pith-number/SUDMS5ALW47F6AEQCYGDXL2HIV/events.json","paper":"https://pith.science/paper/SUDMS5AL"},"agent_actions":{"view_html":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV","download_json":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV.json","view_paper":"https://pith.science/paper/SUDMS5AL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.1473&json=true","fetch_graph":"https://pith.science/api/pith-number/SUDMS5ALW47F6AEQCYGDXL2HIV/graph.json","fetch_events":"https://pith.science/api/pith-number/SUDMS5ALW47F6AEQCYGDXL2HIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV/action/storage_attestation","attest_author":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV/action/author_attestation","sign_citation":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV/action/citation_signature","submit_replication":"https://pith.science/pith/SUDMS5ALW47F6AEQCYGDXL2HIV/action/replication_record"}},"created_at":"2026-05-18T02:53:54.188205+00:00","updated_at":"2026-05-18T02:53:54.188205+00:00"}