{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:SICJSMIKTXH7GE3A5G7T65L6LI","short_pith_number":"pith:SICJSMIK","schema_version":"1.0","canonical_sha256":"920499310a9dcff31360e9bf3f757e5a01697708b0e51a165ee34e1b3ecb4bd1","source":{"kind":"arxiv","id":"1002.0318","version":3},"attestation_state":"computed","paper":{"title":"Entropy zero area preserving diffeomorphisms of $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"John Franks, Michael Handel","submitted_at":"2010-02-01T19:56:01Z","abstract_excerpt":"In this paper we formulate and prove a structure theorem for area preserving diffeomorphisms of genus zero surfaces with zero entropy. As an application we relate the existence of faithful actions of a finite index subgroup of the mapping class group of a closed surface $\\Sigma_g$ on $S^2$ by area preserving diffeomorphisms to the existence of finite index subgroups of bounded mapping class groups $MCG(S, \\partial S)$ with non-trivial first cohomology."},"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":"1002.0318","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-02-01T19:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"6033db08bd1d060eb0b4c7d19383831b38c80b6d5247fc245e5d7b4bb6dab503","abstract_canon_sha256":"5a115b2e2d175605dd212c454f6e921fc47668475e00492f3f3a902a73aeb428"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.633801Z","signature_b64":"h5PXRi7og+5ecC8uK38pTqs5MWdcmGnoge9G9d2Fbhr7SOuaUOe9ZbnZtxMTbNO4ucSky623woF+rtN0dCAQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"920499310a9dcff31360e9bf3f757e5a01697708b0e51a165ee34e1b3ecb4bd1","last_reissued_at":"2026-05-18T02:38:18.633157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.633157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy zero area preserving diffeomorphisms of $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"John Franks, Michael Handel","submitted_at":"2010-02-01T19:56:01Z","abstract_excerpt":"In this paper we formulate and prove a structure theorem for area preserving diffeomorphisms of genus zero surfaces with zero entropy. As an application we relate the existence of faithful actions of a finite index subgroup of the mapping class group of a closed surface $\\Sigma_g$ on $S^2$ by area preserving diffeomorphisms to the existence of finite index subgroups of bounded mapping class groups $MCG(S, \\partial S)$ with non-trivial first cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0318","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":"1002.0318","created_at":"2026-05-18T02:38:18.633255+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0318v3","created_at":"2026-05-18T02:38:18.633255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0318","created_at":"2026-05-18T02:38:18.633255+00:00"},{"alias_kind":"pith_short_12","alias_value":"SICJSMIKTXH7","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"SICJSMIKTXH7GE3A","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"SICJSMIK","created_at":"2026-05-18T12:26:13.927090+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/SICJSMIKTXH7GE3A5G7T65L6LI","json":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI.json","graph_json":"https://pith.science/api/pith-number/SICJSMIKTXH7GE3A5G7T65L6LI/graph.json","events_json":"https://pith.science/api/pith-number/SICJSMIKTXH7GE3A5G7T65L6LI/events.json","paper":"https://pith.science/paper/SICJSMIK"},"agent_actions":{"view_html":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI","download_json":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI.json","view_paper":"https://pith.science/paper/SICJSMIK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0318&json=true","fetch_graph":"https://pith.science/api/pith-number/SICJSMIKTXH7GE3A5G7T65L6LI/graph.json","fetch_events":"https://pith.science/api/pith-number/SICJSMIKTXH7GE3A5G7T65L6LI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI/action/storage_attestation","attest_author":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI/action/author_attestation","sign_citation":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI/action/citation_signature","submit_replication":"https://pith.science/pith/SICJSMIKTXH7GE3A5G7T65L6LI/action/replication_record"}},"created_at":"2026-05-18T02:38:18.633255+00:00","updated_at":"2026-05-18T02:38:18.633255+00:00"}