{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XWMJMIY2WZZGT4JK6F7JVIDN5G","short_pith_number":"pith:XWMJMIY2","schema_version":"1.0","canonical_sha256":"bd9896231ab67269f12af17e9aa06de9990da6ad68004181539a4748e682542b","source":{"kind":"arxiv","id":"1603.01665","version":1},"attestation_state":"computed","paper":{"title":"New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Hieu Trung Do, Thomas A. Schmidt","submitted_at":"2016-03-05T01:10:25Z","abstract_excerpt":"We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech's construction of pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing Sah-Arnoux-Fathi invariant. In particular, we give new infinite families of such maps in genus 3."},"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":"1603.01665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-05T01:10:25Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4de3d3b30ffc2d8fa513628b4f9998fbeb0f29f36e6f61744bbe3dff68ac7259","abstract_canon_sha256":"9d46244085290ed168ae163979a31fa877ae2e5a4b83004d5e7a291f07d57f5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:05.064816Z","signature_b64":"9KgT1Cyqkm126y/6AH53/yZhqGUS81/6BhKt7kF9osqsCkuw8awNL/UDWlZ/H3S3ZUWAUnOANvIMYNXf9WaoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd9896231ab67269f12af17e9aa06de9990da6ad68004181539a4748e682542b","last_reissued_at":"2026-05-18T01:19:05.064336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:05.064336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Hieu Trung Do, Thomas A. Schmidt","submitted_at":"2016-03-05T01:10:25Z","abstract_excerpt":"We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech's construction of pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing Sah-Arnoux-Fathi invariant. In particular, we give new infinite families of such maps in genus 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01665","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":"1603.01665","created_at":"2026-05-18T01:19:05.064417+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01665v1","created_at":"2026-05-18T01:19:05.064417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01665","created_at":"2026-05-18T01:19:05.064417+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWMJMIY2WZZG","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWMJMIY2WZZGT4JK","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWMJMIY2","created_at":"2026-05-18T12:30:51.357362+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/XWMJMIY2WZZGT4JK6F7JVIDN5G","json":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G.json","graph_json":"https://pith.science/api/pith-number/XWMJMIY2WZZGT4JK6F7JVIDN5G/graph.json","events_json":"https://pith.science/api/pith-number/XWMJMIY2WZZGT4JK6F7JVIDN5G/events.json","paper":"https://pith.science/paper/XWMJMIY2"},"agent_actions":{"view_html":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G","download_json":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G.json","view_paper":"https://pith.science/paper/XWMJMIY2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01665&json=true","fetch_graph":"https://pith.science/api/pith-number/XWMJMIY2WZZGT4JK6F7JVIDN5G/graph.json","fetch_events":"https://pith.science/api/pith-number/XWMJMIY2WZZGT4JK6F7JVIDN5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G/action/storage_attestation","attest_author":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G/action/author_attestation","sign_citation":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G/action/citation_signature","submit_replication":"https://pith.science/pith/XWMJMIY2WZZGT4JK6F7JVIDN5G/action/replication_record"}},"created_at":"2026-05-18T01:19:05.064417+00:00","updated_at":"2026-05-18T01:19:05.064417+00:00"}