{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZHDPKO6OYOHCW7CWSZUFYCE22S","short_pith_number":"pith:ZHDPKO6O","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"},"canonical_sha256":"c9c6f53bcec38e2b7c5696685c089ad498dc76df877d40547eb6efe7510e5c81","source":{"kind":"arxiv","id":"1404.0875","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0875","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0875v2","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0875","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZHDPKO6OYOHC","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZHDPKO6OYOHCW7CW","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZHDPKO6O","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZHDPKO6OYOHCW7CWSZUFYCE22S","target":"record","payload":{"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"},"canonical_sha256":"c9c6f53bcec38e2b7c5696685c089ad498dc76df877d40547eb6efe7510e5c81","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"},"source_kind":"arxiv","source_id":"1404.0875","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9eqUr1+BvA5EtdkC+1gZ/JJtOZEOWLVf+M7bgrmmgxnz3+pKAwSXbK3WhMh2jDPz/TiRcf35xZL2OMrMp0iFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:21:14.301038Z"},"content_sha256":"3f995b69dd103cc8f6c90d9279e6abc7cd5d725def2ab4894dc8d3daf95a070c","schema_version":"1.0","event_id":"sha256:3f995b69dd103cc8f6c90d9279e6abc7cd5d725def2ab4894dc8d3daf95a070c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZHDPKO6OYOHCW7CWSZUFYCE22S","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPIuIQL/YPAx/VG0p1+9DNSjbkyyY/R3Kpibv0FwXhc+TXlHpfvCdkzmXZ/JmNd3rH5d/MqviI0FQQjTF+uRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:21:14.301389Z"},"content_sha256":"e8180b2c9fce06a1133b52e02c019549abdec87f320a8f3bc8bfc9421b062f3b","schema_version":"1.0","event_id":"sha256:e8180b2c9fce06a1133b52e02c019549abdec87f320a8f3bc8bfc9421b062f3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/bundle.json","state_url":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T08:21:14Z","links":{"resolver":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S","bundle":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/bundle.json","state":"https://pith.science/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHDPKO6OYOHCW7CWSZUFYCE22S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZHDPKO6OYOHCW7CWSZUFYCE22S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b6e7abe871c0c8d33beb28c1628c502dbeec6c3aa56243d0a3debad84644fccf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-04-03T12:19:20Z","title_canon_sha256":"a2b6c078e7ec0e620896b6ff424ca758454b8bd4155a9ddf586556dc046ad855"},"schema_version":"1.0","source":{"id":"1404.0875","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0875","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0875v2","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0875","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZHDPKO6OYOHC","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZHDPKO6OYOHCW7CW","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZHDPKO6O","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:e8180b2c9fce06a1133b52e02c019549abdec87f320a8f3bc8bfc9421b062f3b","target":"graph","created_at":"2026-05-18T01:31:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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-","authors_text":"Emmanuel Opshtein, Lev Buhovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-04-03T12:19:20Z","title":"Some quantitative results in $C^0$ symplectic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0875","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3f995b69dd103cc8f6c90d9279e6abc7cd5d725def2ab4894dc8d3daf95a070c","target":"record","created_at":"2026-05-18T01:31:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b6e7abe871c0c8d33beb28c1628c502dbeec6c3aa56243d0a3debad84644fccf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-04-03T12:19:20Z","title_canon_sha256":"a2b6c078e7ec0e620896b6ff424ca758454b8bd4155a9ddf586556dc046ad855"},"schema_version":"1.0","source":{"id":"1404.0875","kind":"arxiv","version":2}},"canonical_sha256":"c9c6f53bcec38e2b7c5696685c089ad498dc76df877d40547eb6efe7510e5c81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c6f53bcec38e2b7c5696685c089ad498dc76df877d40547eb6efe7510e5c81","first_computed_at":"2026-05-18T01:31:53.448415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:53.448415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"swNXSpf/fs9wBILCne1dzlGcOcVRabKJDWiPMn4k9ODitQ6W5vr3ntHOtJRX/EAtQcrER0Q/FdpzfHt526o5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:53.448834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0875","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f995b69dd103cc8f6c90d9279e6abc7cd5d725def2ab4894dc8d3daf95a070c","sha256:e8180b2c9fce06a1133b52e02c019549abdec87f320a8f3bc8bfc9421b062f3b"],"state_sha256":"604d24fe70c58dfada1bfa056ef74515661919a537896822a7f13af43c6da1c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqYE7RQ5qek6VrCGs2Ov7eczO70dEHybW7RtzyxMhdWEckqyQ/EufCGneCnMShx6evMdgdDeG1b7iM0utxPvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:21:14.303338Z","bundle_sha256":"17259a2fe392150c8c2355300f97ce526079f93f5ffddad4d1cd7a9a48d66d3b"}}