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We show that, when the genus of the surface is $g\\ge 2$, almost every locally Hamiltonian flow with 2g-2 non-degenerate simple saddles is such that any distinct two rational rescalings $(\\varphi_{\\kappa t})_{t\\in \\mathbb{R}}$ and $(\\varphi_{\\kappa' t})_{t\\in \\mathbb{R}}$ with $\\kappa="},"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":"2606.10714","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-09T11:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"ad9a1c0d6893108f517514149fe51ecf28c0f2d45079730d98d686eb03e4e133","abstract_canon_sha256":"8d54ed283c643b13f8ff77907434d97b8f98efd5a9bc1ce24cff2af82b788999"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:35.974041Z","signature_b64":"Q+aUwTaZA/OI5zHtlRQHRTZUjCzQ6FBnPwWcuALeFpErFwocFxUjMAT9F0NBe25yVzRN00YPl2xTSm6jeszSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ad1795cbadc6cd78ecc8b8ce533257a1acdd9d5440672346469f7f469b0cc3a","last_reissued_at":"2026-06-10T01:10:35.973254Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:35.973254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Disjointness of rescalings of smooth area preserving flows on surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Corinna Ulcigrai, Przemys{\\l}aw Berk","submitted_at":"2026-06-09T11:21:52Z","abstract_excerpt":"We consider the problem of \\emph{disjointness of rescalings} $(\\varphi_{\\kappa t})_{t\\in \\mathbb{R}}$, $\\kappa\\in\\mathbb{R}$ of a flow $(\\varphi_{t})_{t\\in \\mathbb{R}}$ in the context of smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces. We show that, when the genus of the surface is $g\\ge 2$, almost every locally Hamiltonian flow with 2g-2 non-degenerate simple saddles is such that any distinct two rational rescalings $(\\varphi_{\\kappa t})_{t\\in \\mathbb{R}}$ and $(\\varphi_{\\kappa' t})_{t\\in \\mathbb{R}}$ with $\\kappa="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10714","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10714/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":"2606.10714","created_at":"2026-06-10T01:10:35.973397+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10714v1","created_at":"2026-06-10T01:10:35.973397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10714","created_at":"2026-06-10T01:10:35.973397+00:00"},{"alias_kind":"pith_short_12","alias_value":"NLIXSXF23RWN","created_at":"2026-06-10T01:10:35.973397+00:00"},{"alias_kind":"pith_short_16","alias_value":"NLIXSXF23RWNPDWM","created_at":"2026-06-10T01:10:35.973397+00:00"},{"alias_kind":"pith_short_8","alias_value":"NLIXSXF2","created_at":"2026-06-10T01:10:35.973397+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/NLIXSXF23RWNPDWMROGOKMZFPI","json":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI.json","graph_json":"https://pith.science/api/pith-number/NLIXSXF23RWNPDWMROGOKMZFPI/graph.json","events_json":"https://pith.science/api/pith-number/NLIXSXF23RWNPDWMROGOKMZFPI/events.json","paper":"https://pith.science/paper/NLIXSXF2"},"agent_actions":{"view_html":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI","download_json":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI.json","view_paper":"https://pith.science/paper/NLIXSXF2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10714&json=true","fetch_graph":"https://pith.science/api/pith-number/NLIXSXF23RWNPDWMROGOKMZFPI/graph.json","fetch_events":"https://pith.science/api/pith-number/NLIXSXF23RWNPDWMROGOKMZFPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI/action/storage_attestation","attest_author":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI/action/author_attestation","sign_citation":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI/action/citation_signature","submit_replication":"https://pith.science/pith/NLIXSXF23RWNPDWMROGOKMZFPI/action/replication_record"}},"created_at":"2026-06-10T01:10:35.973397+00:00","updated_at":"2026-06-10T01:10:35.973397+00:00"}