{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4EKB7GRQGPOGIKJC7MY6GRVYDE","short_pith_number":"pith:4EKB7GRQ","canonical_record":{"source":{"id":"1803.10453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-03-28T08:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"d410bed6f88342d4b708200a520d2d199615b7dabc2bb2e4e6679fd75cb71609","abstract_canon_sha256":"e6f79cda7299928663475d3baeab95f2ba19f361a8deaad9e8e2d376fd7086d5"},"schema_version":"1.0"},"canonical_sha256":"e1141f9a3033dc642922fb31e346b819225595ff78088e0d9da72a636c984feb","source":{"kind":"arxiv","id":"1803.10453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10453","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10453v1","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10453","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"4EKB7GRQGPOG","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EKB7GRQGPOGIKJC","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EKB7GRQ","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4EKB7GRQGPOGIKJC7MY6GRVYDE","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-03-28T08:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"d410bed6f88342d4b708200a520d2d199615b7dabc2bb2e4e6679fd75cb71609","abstract_canon_sha256":"e6f79cda7299928663475d3baeab95f2ba19f361a8deaad9e8e2d376fd7086d5"},"schema_version":"1.0"},"canonical_sha256":"e1141f9a3033dc642922fb31e346b819225595ff78088e0d9da72a636c984feb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:38.753062Z","signature_b64":"4f6ofITsNmoWhZI9koIUolaQ2MfB/YP+xnqchXh36hagaLkkHyW93bSbG/RYa/BKto84mot3ZNCNUsNEeMvmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1141f9a3033dc642922fb31e346b819225595ff78088e0d9da72a636c984feb","last_reissued_at":"2026-05-17T23:55:38.752598Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:38.752598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10453","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":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PVWoR0XTHq7M+RaTM3JgLVs8VzcHJqvVQOv3d1MpJvOnFfXUjRfjaEanNF93qVEs8C56HFr3lm9tj8x5bx5ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:16:36.841915Z"},"content_sha256":"1cda5fbdddce4b9100aaf7d555861594295548853bcae7aa58be49df5dc2079a","schema_version":"1.0","event_id":"sha256:1cda5fbdddce4b9100aaf7d555861594295548853bcae7aa58be49df5dc2079a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4EKB7GRQGPOGIKJC7MY6GRVYDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic cohomologies and deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Adriano Tomassini, Nicoletta Tardini","submitted_at":"2018-03-28T08:21:54Z","abstract_excerpt":"In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-K\\\"ahler manifolds $(X,J,g,\\omega)$ with $J$ $\\mathcal{C}^\\infty$-pure and full the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. Furthermore, we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10453","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":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2DYfYr7wEc+YSXzB7jWeqyucsTndrBA2Zd1BOOt3dF/mJIK14tSC/avZ7c6uNlTQcNSQC2V2+UrSflGn7OkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:16:36.842253Z"},"content_sha256":"ea328a2b7fccc0121b56380fe5d5ae5e694a28afef8a3204cc76e4ee85c31b30","schema_version":"1.0","event_id":"sha256:ea328a2b7fccc0121b56380fe5d5ae5e694a28afef8a3204cc76e4ee85c31b30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE/bundle.json","state_url":"https://pith.science/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE/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":"2026-06-03T18:16:36Z","links":{"resolver":"https://pith.science/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE","bundle":"https://pith.science/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE/bundle.json","state":"https://pith.science/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EKB7GRQGPOGIKJC7MY6GRVYDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4EKB7GRQGPOGIKJC7MY6GRVYDE","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":"e6f79cda7299928663475d3baeab95f2ba19f361a8deaad9e8e2d376fd7086d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-03-28T08:21:54Z","title_canon_sha256":"d410bed6f88342d4b708200a520d2d199615b7dabc2bb2e4e6679fd75cb71609"},"schema_version":"1.0","source":{"id":"1803.10453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10453","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10453v1","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10453","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"4EKB7GRQGPOG","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EKB7GRQGPOGIKJC","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EKB7GRQ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:ea328a2b7fccc0121b56380fe5d5ae5e694a28afef8a3204cc76e4ee85c31b30","target":"graph","created_at":"2026-05-17T23:55:38Z","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":"In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-K\\\"ahler manifolds $(X,J,g,\\omega)$ with $J$ $\\mathcal{C}^\\infty$-pure and full the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. Furthermore, we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms.","authors_text":"Adriano Tomassini, Nicoletta Tardini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-03-28T08:21:54Z","title":"Symplectic cohomologies and deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10453","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":"sha256:1cda5fbdddce4b9100aaf7d555861594295548853bcae7aa58be49df5dc2079a","target":"record","created_at":"2026-05-17T23:55:38Z","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":"e6f79cda7299928663475d3baeab95f2ba19f361a8deaad9e8e2d376fd7086d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-03-28T08:21:54Z","title_canon_sha256":"d410bed6f88342d4b708200a520d2d199615b7dabc2bb2e4e6679fd75cb71609"},"schema_version":"1.0","source":{"id":"1803.10453","kind":"arxiv","version":1}},"canonical_sha256":"e1141f9a3033dc642922fb31e346b819225595ff78088e0d9da72a636c984feb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1141f9a3033dc642922fb31e346b819225595ff78088e0d9da72a636c984feb","first_computed_at":"2026-05-17T23:55:38.752598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:38.752598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4f6ofITsNmoWhZI9koIUolaQ2MfB/YP+xnqchXh36hagaLkkHyW93bSbG/RYa/BKto84mot3ZNCNUsNEeMvmCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:38.753062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cda5fbdddce4b9100aaf7d555861594295548853bcae7aa58be49df5dc2079a","sha256:ea328a2b7fccc0121b56380fe5d5ae5e694a28afef8a3204cc76e4ee85c31b30"],"state_sha256":"a6e26a7f08402969287f499c944df21fa56aafbd694479fd71b815a0e149bc6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7b1hTWZV9qLT0TszPmb0PiNM08faFW3em0M3UYcFtEaPYeAG11kB2RhS04B64rf4sGG17y1HVj5cElSobmIDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:16:36.844113Z","bundle_sha256":"e2ccf45cc3e12a89934ba2d2c246950b78a734bc10161021c168aab94548d783"}}