{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZHDPKO6OYOHCW7CWSZUFYCE22S","short_pith_number":"pith:ZHDPKO6O","schema_version":"1.0","canonical_sha256":"c9c6f53bcec38e2b7c5696685c089ad498dc76df877d40547eb6efe7510e5c81","source":{"kind":"arxiv","id":"1404.0875","version":2},"attestation_state":"computed","paper":{"title":"Some quantitative results in $C^0$ symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Emmanuel Opshtein, Lev Buhovsky","submitted_at":"2014-04-03T12:19:20Z","abstract_excerpt":"This paper studies the action of symplectic homeomorphisms on smooth submanifolds, with a main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic homeomorphism may preserve and squeeze codimension $4$ symplectic submanifolds ($C^0$-flexibility), while this is impossible for codimension $2$ symplectic submanifolds ($C^0$-rigidity). We also discuss $C^0$-invariants of coistropic and Lagrangian submanifolds, proving some rigidity results and formulating some conjectures. We finally formulate an Eliashberg-"},"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":"1404.0875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-04-03T12:19:20Z","cross_cats_sorted":[],"title_canon_sha256":"a2b6c078e7ec0e620896b6ff424ca758454b8bd4155a9ddf586556dc046ad855","abstract_canon_sha256":"b6e7abe871c0c8d33beb28c1628c502dbeec6c3aa56243d0a3debad84644fccf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:53.448834Z","signature_b64":"swNXSpf/fs9wBILCne1dzlGcOcVRabKJDWiPMn4k9ODitQ6W5vr3ntHOtJRX/EAtQcrER0Q/FdpzfHt526o5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9c6f53bcec38e2b7c5696685c089ad498dc76df877d40547eb6efe7510e5c81","last_reissued_at":"2026-05-18T01:31:53.448415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:53.448415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some quantitative results in $C^0$ symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Emmanuel Opshtein, Lev Buhovsky","submitted_at":"2014-04-03T12:19:20Z","abstract_excerpt":"This paper studies the action of symplectic homeomorphisms on smooth submanifolds, with a main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic homeomorphism may preserve and squeeze codimension $4$ symplectic submanifolds ($C^0$-flexibility), while this is impossible for codimension $2$ symplectic submanifolds ($C^0$-rigidity). We also discuss $C^0$-invariants of coistropic and Lagrangian submanifolds, proving some rigidity results and formulating some conjectures. We finally formulate an Eliashberg-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0875","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":""},"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":"1404.0875","created_at":"2026-05-18T01:31:53.448478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.0875v2","created_at":"2026-05-18T01:31:53.448478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0875","created_at":"2026-05-18T01:31:53.448478+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZHDPKO6OYOHC","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZHDPKO6OYOHCW7CW","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZHDPKO6O","created_at":"2026-05-18T12:28:59.999130+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/ZHDPKO6OYOHCW7CWSZUFYCE22S","json":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S.json","graph_json":"https://pith.science/api/pith-number/ZHDPKO6OYOHCW7CWSZUFYCE22S/graph.json","events_json":"https://pith.science/api/pith-number/ZHDPKO6OYOHCW7CWSZUFYCE22S/events.json","paper":"https://pith.science/paper/ZHDPKO6O"},"agent_actions":{"view_html":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S","download_json":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S.json","view_paper":"https://pith.science/paper/ZHDPKO6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.0875&json=true","fetch_graph":"https://pith.science/api/pith-number/ZHDPKO6OYOHCW7CWSZUFYCE22S/graph.json","fetch_events":"https://pith.science/api/pith-number/ZHDPKO6OYOHCW7CWSZUFYCE22S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/action/storage_attestation","attest_author":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/action/author_attestation","sign_citation":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/action/citation_signature","submit_replication":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/action/replication_record"}},"created_at":"2026-05-18T01:31:53.448478+00:00","updated_at":"2026-05-18T01:31:53.448478+00:00"}