{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EILV2UIKU2TCAN3XKHBHXQSRXD","short_pith_number":"pith:EILV2UIK","canonical_record":{"source":{"id":"1901.09708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-28T14:51:28Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"3133cc2faa277f329550a1ca34cda1ae1e6e1bd5ab0f1b08e4d195d958e4fbea","abstract_canon_sha256":"9fc09798ae7707ad86af7f024d2f946f793b9b4cc748bb36b5a57d28c028d37f"},"schema_version":"1.0"},"canonical_sha256":"22175d510aa6a620377751c27bc251b8eba1f1ffa3c820e98d829c002256747e","source":{"kind":"arxiv","id":"1901.09708","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09708","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09708v1","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09708","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"EILV2UIKU2TC","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EILV2UIKU2TCAN3X","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EILV2UIK","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EILV2UIKU2TCAN3XKHBHXQSRXD","target":"record","payload":{"canonical_record":{"source":{"id":"1901.09708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-28T14:51:28Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"3133cc2faa277f329550a1ca34cda1ae1e6e1bd5ab0f1b08e4d195d958e4fbea","abstract_canon_sha256":"9fc09798ae7707ad86af7f024d2f946f793b9b4cc748bb36b5a57d28c028d37f"},"schema_version":"1.0"},"canonical_sha256":"22175d510aa6a620377751c27bc251b8eba1f1ffa3c820e98d829c002256747e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:24.018332Z","signature_b64":"naIkw8g2L0wGRq+b7xHkuql2sjmIAWWNZTTQNQcJ5IuFMzltcbHYxRCgw1uGpLjyMGnBi0No1MtPwnKrwX48Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22175d510aa6a620377751c27bc251b8eba1f1ffa3c820e98d829c002256747e","last_reissued_at":"2026-05-17T23:55:24.017723Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:24.017723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.09708","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e+p17YyVt25M8VIb5l24DubIh7ck8U1CDnd1ZjzcTD48BSgSgn3WA0RUQ5ZlJ/qBXgtVxxep5q0yR5PWGka1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:07:19.301810Z"},"content_sha256":"1077bb302639fc676ac5fa5d652c7e2bdbb9a613479b6fab6f338233f331b062","schema_version":"1.0","event_id":"sha256:1077bb302639fc676ac5fa5d652c7e2bdbb9a613479b6fab6f338233f331b062"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EILV2UIKU2TCAN3XKHBHXQSRXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fukaya's conjecture on $S^1$-equivariant de Rham complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Ziming Nikolas Ma","submitted_at":"2019-01-28T14:51:28Z","abstract_excerpt":"Getzler-Jones-Petrack introduced $A_\\infty$ structures on the equivariant complex for manifold $M$ with smooth $\\mathbb{S}^1$ action, motivated by geometry of loop spaces. Applying Witten's deformation by Morse functions followed by homological perturbation we obtained a new set of $A_\\infty$ structures. We extend and prove Fukaya's conjecture relating this Witten's deformed equivariant de Rham complexes, to a new Morse theoretical $A_\\infty$ complexes defined by counting gradient trees with jumping which are closely related to the $\\mathbb{S}^1$ equivariant symplectic cohomology proposed by S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09708","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SE5WO2oaqEcoQrIo6ZFeeyHMG9j6m9wG0vHOfFOWDrSkpdlwL8HGS91+ZgrSZaEplLJSAGd4Doj563bS7PE1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:07:19.302150Z"},"content_sha256":"d83378fc2afa3c8a04f009a8931414d35afe81e81d7f5cbd10619718a50c0831","schema_version":"1.0","event_id":"sha256:d83378fc2afa3c8a04f009a8931414d35afe81e81d7f5cbd10619718a50c0831"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EILV2UIKU2TCAN3XKHBHXQSRXD/bundle.json","state_url":"https://pith.science/pith/EILV2UIKU2TCAN3XKHBHXQSRXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EILV2UIKU2TCAN3XKHBHXQSRXD/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":"2026-06-01T12:07:19Z","links":{"resolver":"https://pith.science/pith/EILV2UIKU2TCAN3XKHBHXQSRXD","bundle":"https://pith.science/pith/EILV2UIKU2TCAN3XKHBHXQSRXD/bundle.json","state":"https://pith.science/pith/EILV2UIKU2TCAN3XKHBHXQSRXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EILV2UIKU2TCAN3XKHBHXQSRXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EILV2UIKU2TCAN3XKHBHXQSRXD","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":"9fc09798ae7707ad86af7f024d2f946f793b9b4cc748bb36b5a57d28c028d37f","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-28T14:51:28Z","title_canon_sha256":"3133cc2faa277f329550a1ca34cda1ae1e6e1bd5ab0f1b08e4d195d958e4fbea"},"schema_version":"1.0","source":{"id":"1901.09708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09708","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09708v1","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09708","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"EILV2UIKU2TC","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EILV2UIKU2TCAN3X","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EILV2UIK","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:d83378fc2afa3c8a04f009a8931414d35afe81e81d7f5cbd10619718a50c0831","target":"graph","created_at":"2026-05-17T23:55:24Z","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":"Getzler-Jones-Petrack introduced $A_\\infty$ structures on the equivariant complex for manifold $M$ with smooth $\\mathbb{S}^1$ action, motivated by geometry of loop spaces. Applying Witten's deformation by Morse functions followed by homological perturbation we obtained a new set of $A_\\infty$ structures. We extend and prove Fukaya's conjecture relating this Witten's deformed equivariant de Rham complexes, to a new Morse theoretical $A_\\infty$ complexes defined by counting gradient trees with jumping which are closely related to the $\\mathbb{S}^1$ equivariant symplectic cohomology proposed by S","authors_text":"Ziming Nikolas Ma","cross_cats":["math-ph","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-28T14:51:28Z","title":"Fukaya's conjecture on $S^1$-equivariant de Rham complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09708","kind":"arxiv","version":1},"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":"sha256:1077bb302639fc676ac5fa5d652c7e2bdbb9a613479b6fab6f338233f331b062","target":"record","created_at":"2026-05-17T23:55:24Z","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":"9fc09798ae7707ad86af7f024d2f946f793b9b4cc748bb36b5a57d28c028d37f","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-28T14:51:28Z","title_canon_sha256":"3133cc2faa277f329550a1ca34cda1ae1e6e1bd5ab0f1b08e4d195d958e4fbea"},"schema_version":"1.0","source":{"id":"1901.09708","kind":"arxiv","version":1}},"canonical_sha256":"22175d510aa6a620377751c27bc251b8eba1f1ffa3c820e98d829c002256747e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22175d510aa6a620377751c27bc251b8eba1f1ffa3c820e98d829c002256747e","first_computed_at":"2026-05-17T23:55:24.017723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:24.017723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"naIkw8g2L0wGRq+b7xHkuql2sjmIAWWNZTTQNQcJ5IuFMzltcbHYxRCgw1uGpLjyMGnBi0No1MtPwnKrwX48Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:24.018332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.09708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1077bb302639fc676ac5fa5d652c7e2bdbb9a613479b6fab6f338233f331b062","sha256:d83378fc2afa3c8a04f009a8931414d35afe81e81d7f5cbd10619718a50c0831"],"state_sha256":"87ac44bd9253dae735a171ca43c22e5eb80466bedc9bcdcb4ba9d1262bb4cca8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7uSZC+Ijf2ktwOec7S/VaFVgvSLzc9y+pyxEUbnmnl/Jtu2NWxwaEzKWdLTi8yYzYP8Rcd3rePQfMlU38I6BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:07:19.304011Z","bundle_sha256":"5e9e689666fb5be1f785a7d1192100f74c356453fef7082bfea5691588b70e73"}}