{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:S37DB7CQJ3AZ5ONJT53QOQFXZN","short_pith_number":"pith:S37DB7CQ","schema_version":"1.0","canonical_sha256":"96fe30fc504ec19eb9a99f770740b7cb622bb78ff0ac52312b98965969d84f60","source":{"kind":"arxiv","id":"1811.00184","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of a class of smooth singular flows on $\\mathbb T^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Changguang Dong","submitted_at":"2018-11-01T01:58:50Z","abstract_excerpt":"We study joining rigidity in the class of von Neumann flows with one singularity. They are given by a smooth vector field $\\mathcal{X}$ on $\\mathbb T^2\\setminus \\{a\\}$, where $\\mathcal{X}$ is not defined at $a\\in \\mathbb T^2$. It follows that the phase space can be decomposed into a (topological disc) $D_\\mathcal{X}$ and an ergodic component $E_\\mathcal{X}=\\mathbb T^2\\setminus D_\\mathcal{X}$. Let $\\omega_\\mathcal{X}$ be the 1-form associated to $\\mathcal{X}$. We show that if $|\\int_{E_{\\mathcal{X}_1}}d\\omega_{\\mathcal{X}_1}|\\neq |\\int_{E_{\\mathcal{X}_2}}d\\omega_{\\mathcal{X}_2}|$, then the corr"},"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":"1811.00184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-01T01:58:50Z","cross_cats_sorted":[],"title_canon_sha256":"e66df97c1e9354a861b924a32cc77df256f8f6dd6f82f12b81fddc3ba61e08c7","abstract_canon_sha256":"59e5a8aefb5c4d2d2fdaf5bb8cd0ec27effbde12a655673daf7536a8e74a0fb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.017936Z","signature_b64":"XvTphhh0sjzE2IORxQQ1YK6oU6EucSJs55obN02vYWCifrKYrbWVUmB+mP6CI/GKSWveLa0HHK40APFcMIQRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96fe30fc504ec19eb9a99f770740b7cb622bb78ff0ac52312b98965969d84f60","last_reissued_at":"2026-05-18T00:01:48.017429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.017429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of a class of smooth singular flows on $\\mathbb T^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Changguang Dong","submitted_at":"2018-11-01T01:58:50Z","abstract_excerpt":"We study joining rigidity in the class of von Neumann flows with one singularity. They are given by a smooth vector field $\\mathcal{X}$ on $\\mathbb T^2\\setminus \\{a\\}$, where $\\mathcal{X}$ is not defined at $a\\in \\mathbb T^2$. It follows that the phase space can be decomposed into a (topological disc) $D_\\mathcal{X}$ and an ergodic component $E_\\mathcal{X}=\\mathbb T^2\\setminus D_\\mathcal{X}$. Let $\\omega_\\mathcal{X}$ be the 1-form associated to $\\mathcal{X}$. We show that if $|\\int_{E_{\\mathcal{X}_1}}d\\omega_{\\mathcal{X}_1}|\\neq |\\int_{E_{\\mathcal{X}_2}}d\\omega_{\\mathcal{X}_2}|$, then the corr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00184","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":"1811.00184","created_at":"2026-05-18T00:01:48.017508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.00184v1","created_at":"2026-05-18T00:01:48.017508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00184","created_at":"2026-05-18T00:01:48.017508+00:00"},{"alias_kind":"pith_short_12","alias_value":"S37DB7CQJ3AZ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"S37DB7CQJ3AZ5ONJ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"S37DB7CQ","created_at":"2026-05-18T12:32:50.500415+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/S37DB7CQJ3AZ5ONJT53QOQFXZN","json":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN.json","graph_json":"https://pith.science/api/pith-number/S37DB7CQJ3AZ5ONJT53QOQFXZN/graph.json","events_json":"https://pith.science/api/pith-number/S37DB7CQJ3AZ5ONJT53QOQFXZN/events.json","paper":"https://pith.science/paper/S37DB7CQ"},"agent_actions":{"view_html":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN","download_json":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN.json","view_paper":"https://pith.science/paper/S37DB7CQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.00184&json=true","fetch_graph":"https://pith.science/api/pith-number/S37DB7CQJ3AZ5ONJT53QOQFXZN/graph.json","fetch_events":"https://pith.science/api/pith-number/S37DB7CQJ3AZ5ONJT53QOQFXZN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN/action/storage_attestation","attest_author":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN/action/author_attestation","sign_citation":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN/action/citation_signature","submit_replication":"https://pith.science/pith/S37DB7CQJ3AZ5ONJT53QOQFXZN/action/replication_record"}},"created_at":"2026-05-18T00:01:48.017508+00:00","updated_at":"2026-05-18T00:01:48.017508+00:00"}