{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:DEJFQE2WTTIABTU56GV54CJT7B","short_pith_number":"pith:DEJFQE2W","schema_version":"1.0","canonical_sha256":"19125813569cd000ce9df1abde0933f84deb238bf282c48cbd4a76e55e775b6d","source":{"kind":"arxiv","id":"2110.13844","version":2},"attestation_state":"computed","paper":{"title":"A note on the existence of U-cyclic elements in periodic Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Boyu Zhang, Dan Cristofaro-Gardiner, Daniel Pomerleano, Rohil Prasad","submitted_at":"2021-10-26T16:43:47Z","abstract_excerpt":"Edtmair-Hutchings have recently defined, using periodic Floer homology, a U-cycle property for Hamiltonian isotopy classes of area-preserving diffeomorphisms of closed surfaces. They show that every Hamiltonian isotopy class satisfying the U-cycle property satisfies the smooth closing lemma and also satisfies a kind of Weyl law involving the actions of certain periodic points; they show that every rational isotopy class on the two-torus satisfies the U-cycle property. It seems that in general, not much is known about the U-module structure on PFH. Here we consider a version of Seiberg-Witten-F"},"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":"2110.13844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2021-10-26T16:43:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5f2d2cbb14dec4d4909054f49b7205b9e7aaf5336de854f24aa88cdac08e00a7","abstract_canon_sha256":"a0d4577719d25971e463cfd25aea1a60436eaa2da3fcdea9a38dbf19984efe85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:56:51.448717Z","signature_b64":"M/LQNJ0pxrNFXKo1ZT+zBpZmDQKezcEB1JXdFcnmUcNZ0pllLAp5TStz2Jp/9xcsL67PNKKpgrLpUWOdqK/fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19125813569cd000ce9df1abde0933f84deb238bf282c48cbd4a76e55e775b6d","last_reissued_at":"2026-07-05T03:56:51.448294Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:56:51.448294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the existence of U-cyclic elements in periodic Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Boyu Zhang, Dan Cristofaro-Gardiner, Daniel Pomerleano, Rohil Prasad","submitted_at":"2021-10-26T16:43:47Z","abstract_excerpt":"Edtmair-Hutchings have recently defined, using periodic Floer homology, a U-cycle property for Hamiltonian isotopy classes of area-preserving diffeomorphisms of closed surfaces. They show that every Hamiltonian isotopy class satisfying the U-cycle property satisfies the smooth closing lemma and also satisfies a kind of Weyl law involving the actions of certain periodic points; they show that every rational isotopy class on the two-torus satisfies the U-cycle property. It seems that in general, not much is known about the U-module structure on PFH. Here we consider a version of Seiberg-Witten-F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.13844","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/2110.13844/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":"2110.13844","created_at":"2026-07-05T03:56:51.448358+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.13844v2","created_at":"2026-07-05T03:56:51.448358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.13844","created_at":"2026-07-05T03:56:51.448358+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEJFQE2WTTIA","created_at":"2026-07-05T03:56:51.448358+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEJFQE2WTTIABTU5","created_at":"2026-07-05T03:56:51.448358+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEJFQE2W","created_at":"2026-07-05T03:56:51.448358+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":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B","json":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B.json","graph_json":"https://pith.science/api/pith-number/DEJFQE2WTTIABTU56GV54CJT7B/graph.json","events_json":"https://pith.science/api/pith-number/DEJFQE2WTTIABTU56GV54CJT7B/events.json","paper":"https://pith.science/paper/DEJFQE2W"},"agent_actions":{"view_html":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B","download_json":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B.json","view_paper":"https://pith.science/paper/DEJFQE2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.13844&json=true","fetch_graph":"https://pith.science/api/pith-number/DEJFQE2WTTIABTU56GV54CJT7B/graph.json","fetch_events":"https://pith.science/api/pith-number/DEJFQE2WTTIABTU56GV54CJT7B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B/action/storage_attestation","attest_author":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B/action/author_attestation","sign_citation":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B/action/citation_signature","submit_replication":"https://pith.science/pith/DEJFQE2WTTIABTU56GV54CJT7B/action/replication_record"}},"created_at":"2026-07-05T03:56:51.448358+00:00","updated_at":"2026-07-05T03:56:51.448358+00:00"}