{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:D7EUHOPQMKJD3URAPNRL7J5KYK","short_pith_number":"pith:D7EUHOPQ","schema_version":"1.0","canonical_sha256":"1fc943b9f062923dd2207b62bfa7aac283f5e4e748ce335939c5224814bee6ab","source":{"kind":"arxiv","id":"2112.14601","version":2},"attestation_state":"computed","paper":{"title":"Generic equidistribution of periodic orbits for area-preserving surface maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Rohil Prasad","submitted_at":"2021-12-29T15:19:01Z","abstract_excerpt":"We prove that a $C^{\\infty}$-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem for area-preserving surface diffeomorphisms. The proof has two ingredients. The first is a \"Weyl law\" for PFH spectral invariants, which was used to prove the generic density theorem. The second is a variational argument inspired by the work of Marques-Neves-Song and Irie on equidistribution results for minimal hypersurfaces and three-dimensional Reeb flows, r"},"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":"2112.14601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2021-12-29T15:19:01Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a5ad8d0841244e3e7bfe62bf357da0f3752f9326656fbf3ff2a81d5550dfe64e","abstract_canon_sha256":"990885403c17f7ed683732b612a292dc971d0a706cd5b68b4d703765c1725ed7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:59:53.512376Z","signature_b64":"n/P40N2WN6xCn2Kw2rp5eeB+QxoCYnp98raRUkF3Si1hBtgzYtRUfqzLw6XNcfldOVHKnCg4NkRb3ivXtteDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fc943b9f062923dd2207b62bfa7aac283f5e4e748ce335939c5224814bee6ab","last_reissued_at":"2026-07-05T03:59:53.511909Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:59:53.511909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic equidistribution of periodic orbits for area-preserving surface maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Rohil Prasad","submitted_at":"2021-12-29T15:19:01Z","abstract_excerpt":"We prove that a $C^{\\infty}$-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem for area-preserving surface diffeomorphisms. The proof has two ingredients. The first is a \"Weyl law\" for PFH spectral invariants, which was used to prove the generic density theorem. The second is a variational argument inspired by the work of Marques-Neves-Song and Irie on equidistribution results for minimal hypersurfaces and three-dimensional Reeb flows, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14601","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.14601/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2112.14601","created_at":"2026-07-05T03:59:53.511965+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.14601v2","created_at":"2026-07-05T03:59:53.511965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.14601","created_at":"2026-07-05T03:59:53.511965+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7EUHOPQMKJD","created_at":"2026-07-05T03:59:53.511965+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7EUHOPQMKJD3URA","created_at":"2026-07-05T03:59:53.511965+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7EUHOPQ","created_at":"2026-07-05T03:59:53.511965+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.15429","citing_title":"Generic density of periodic orbits of area-preserving maps on punctured surfaces","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK","json":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK.json","graph_json":"https://pith.science/api/pith-number/D7EUHOPQMKJD3URAPNRL7J5KYK/graph.json","events_json":"https://pith.science/api/pith-number/D7EUHOPQMKJD3URAPNRL7J5KYK/events.json","paper":"https://pith.science/paper/D7EUHOPQ"},"agent_actions":{"view_html":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK","download_json":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK.json","view_paper":"https://pith.science/paper/D7EUHOPQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.14601&json=true","fetch_graph":"https://pith.science/api/pith-number/D7EUHOPQMKJD3URAPNRL7J5KYK/graph.json","fetch_events":"https://pith.science/api/pith-number/D7EUHOPQMKJD3URAPNRL7J5KYK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK/action/storage_attestation","attest_author":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK/action/author_attestation","sign_citation":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK/action/citation_signature","submit_replication":"https://pith.science/pith/D7EUHOPQMKJD3URAPNRL7J5KYK/action/replication_record"}},"created_at":"2026-07-05T03:59:53.511965+00:00","updated_at":"2026-07-05T03:59:53.511965+00:00"}