{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7FYAHAVDNMNHQNTGLXCJCOZ3OB","short_pith_number":"pith:7FYAHAVD","schema_version":"1.0","canonical_sha256":"f9700382a36b1a7836665dc4913b3b704f4a6132427f4a7366ae6bed2f1c26cb","source":{"kind":"arxiv","id":"1610.04552","version":1},"attestation_state":"computed","paper":{"title":"Generically Mane set supports uniquely ergodic measure for residual cohomology class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jianlu Zhang","submitted_at":"2016-10-14T17:43:55Z","abstract_excerpt":"In this paper, we proved that for generic Tonelli Lagrangian, there always exists a residual set $\\mathcal{G}\\subset H^1(M,\\mathbb{R})$ such that \\[ \\widetilde{\\mathcal{M}}(c)=\\widetilde{\\mathcal{A}}(c)=\\widetilde{\\mathcal{N}}(c),\\quad \\forall c\\in\\mathcal{G} \\] with $\\widetilde{\\mathcal{M}}(c)$ supports on a uniquely ergodic measure."},"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":"1610.04552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-14T17:43:55Z","cross_cats_sorted":[],"title_canon_sha256":"76e21187d30c2f04729a78aa28a8450a922560491b3883db638c0b1e75e95b02","abstract_canon_sha256":"b6c0ef6f80ac1b4ddb8017e72f79efee04b1ae93b322c18ac74019120bdc351a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:14.780483Z","signature_b64":"rdZjMbeUSUzQBcQ8IXMtE4T1D2sjTW4dHeuIXYsd5VTwwe67FES15V0yz1juclm0R6jyN78qaqlaauo04ul7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9700382a36b1a7836665dc4913b3b704f4a6132427f4a7366ae6bed2f1c26cb","last_reissued_at":"2026-05-18T01:02:14.779859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:14.779859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generically Mane set supports uniquely ergodic measure for residual cohomology class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jianlu Zhang","submitted_at":"2016-10-14T17:43:55Z","abstract_excerpt":"In this paper, we proved that for generic Tonelli Lagrangian, there always exists a residual set $\\mathcal{G}\\subset H^1(M,\\mathbb{R})$ such that \\[ \\widetilde{\\mathcal{M}}(c)=\\widetilde{\\mathcal{A}}(c)=\\widetilde{\\mathcal{N}}(c),\\quad \\forall c\\in\\mathcal{G} \\] with $\\widetilde{\\mathcal{M}}(c)$ supports on a uniquely ergodic measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04552","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":"1610.04552","created_at":"2026-05-18T01:02:14.779969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04552v1","created_at":"2026-05-18T01:02:14.779969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04552","created_at":"2026-05-18T01:02:14.779969+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FYAHAVDNMNH","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FYAHAVDNMNHQNTG","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FYAHAVD","created_at":"2026-05-18T12:30:04.600751+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/7FYAHAVDNMNHQNTGLXCJCOZ3OB","json":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB.json","graph_json":"https://pith.science/api/pith-number/7FYAHAVDNMNHQNTGLXCJCOZ3OB/graph.json","events_json":"https://pith.science/api/pith-number/7FYAHAVDNMNHQNTGLXCJCOZ3OB/events.json","paper":"https://pith.science/paper/7FYAHAVD"},"agent_actions":{"view_html":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB","download_json":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB.json","view_paper":"https://pith.science/paper/7FYAHAVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04552&json=true","fetch_graph":"https://pith.science/api/pith-number/7FYAHAVDNMNHQNTGLXCJCOZ3OB/graph.json","fetch_events":"https://pith.science/api/pith-number/7FYAHAVDNMNHQNTGLXCJCOZ3OB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB/action/storage_attestation","attest_author":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB/action/author_attestation","sign_citation":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB/action/citation_signature","submit_replication":"https://pith.science/pith/7FYAHAVDNMNHQNTGLXCJCOZ3OB/action/replication_record"}},"created_at":"2026-05-18T01:02:14.779969+00:00","updated_at":"2026-05-18T01:02:14.779969+00:00"}