{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6XFHNKLUVEPZYOEOON4J3UQWO4","short_pith_number":"pith:6XFHNKLU","canonical_record":{"source":{"id":"1210.0395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-01T13:33:11Z","cross_cats_sorted":[],"title_canon_sha256":"3317eee460ef342acce6442a86cf386df40f21c3b47a89c0eaec8a24977476aa","abstract_canon_sha256":"beec1a14b416663cfebb69d38d298063d0faa2c6b4d888dd412aff83915a0640"},"schema_version":"1.0"},"canonical_sha256":"f5ca76a974a91f9c388e73789dd2167733a5b374f880bb35c24da2016b2f55ef","source":{"kind":"arxiv","id":"1210.0395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0395","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0395v1","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0395","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"6XFHNKLUVEPZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6XFHNKLUVEPZYOEO","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6XFHNKLU","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6XFHNKLUVEPZYOEOON4J3UQWO4","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-01T13:33:11Z","cross_cats_sorted":[],"title_canon_sha256":"3317eee460ef342acce6442a86cf386df40f21c3b47a89c0eaec8a24977476aa","abstract_canon_sha256":"beec1a14b416663cfebb69d38d298063d0faa2c6b4d888dd412aff83915a0640"},"schema_version":"1.0"},"canonical_sha256":"f5ca76a974a91f9c388e73789dd2167733a5b374f880bb35c24da2016b2f55ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:22.560979Z","signature_b64":"+22NVw99TW4RRvzY45Z9ZhoIRB5cnJnDpeRtT1tMDD6HfcHjMtuOCff/XsfU4JWoSBZYGNrzDKfbj1hFSiY9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5ca76a974a91f9c388e73789dd2167733a5b374f880bb35c24da2016b2f55ef","last_reissued_at":"2026-05-18T03:44:22.560342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:22.560342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0395","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":"2026-05-18T03:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tl8F4Y9r4xMTrsAu54OK8OJgSC1L0v/71ndXCVm5ooY2QJ1rCgsfSY0WcBDsejDblonuS1q58bLuVBit8898BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:47:31.548761Z"},"content_sha256":"e5549a4713f2e19e013bb0f34b7628008ec6bc930557c088a4bb58df78a48dcd","schema_version":"1.0","event_id":"sha256:e5549a4713f2e19e013bb0f34b7628008ec6bc930557c088a4bb58df78a48dcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6XFHNKLUVEPZYOEOON4J3UQWO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Bott-Chern cohomology and balanced Hermitian nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adela Latorre, Luis Ugarte, Raquel Villacampa","submitted_at":"2012-10-01T13:33:11Z","abstract_excerpt":"The Bott-Chern cohomology of 6-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the $\\partial \\bar\\partial$-lemma condition and defined in terms of the Bott-Chern cohomology, and show that the vanishing of some of these invariants is not a closed property under holomorphic deformations. In the balanced case, we determine the spaces that parametrize deformations in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0395","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":"2026-05-18T03:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VGqU7QRcUZBeGUg1blarqGOW2T3//EoGgAhShpnfxsk7Yl805ZVLgGxj0BZTAIWZKxINCEoSZizXMLW87CGyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:47:31.549104Z"},"content_sha256":"b4b49e4ea4e3013846ebb1051f531866b02e5b82839733a184b9543092232c76","schema_version":"1.0","event_id":"sha256:b4b49e4ea4e3013846ebb1051f531866b02e5b82839733a184b9543092232c76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XFHNKLUVEPZYOEOON4J3UQWO4/bundle.json","state_url":"https://pith.science/pith/6XFHNKLUVEPZYOEOON4J3UQWO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XFHNKLUVEPZYOEOON4J3UQWO4/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":"2026-06-25T05:47:31Z","links":{"resolver":"https://pith.science/pith/6XFHNKLUVEPZYOEOON4J3UQWO4","bundle":"https://pith.science/pith/6XFHNKLUVEPZYOEOON4J3UQWO4/bundle.json","state":"https://pith.science/pith/6XFHNKLUVEPZYOEOON4J3UQWO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XFHNKLUVEPZYOEOON4J3UQWO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6XFHNKLUVEPZYOEOON4J3UQWO4","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":"beec1a14b416663cfebb69d38d298063d0faa2c6b4d888dd412aff83915a0640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-01T13:33:11Z","title_canon_sha256":"3317eee460ef342acce6442a86cf386df40f21c3b47a89c0eaec8a24977476aa"},"schema_version":"1.0","source":{"id":"1210.0395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0395","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0395v1","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0395","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"6XFHNKLUVEPZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6XFHNKLUVEPZYOEO","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6XFHNKLU","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:b4b49e4ea4e3013846ebb1051f531866b02e5b82839733a184b9543092232c76","target":"graph","created_at":"2026-05-18T03:44:22Z","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":"The Bott-Chern cohomology of 6-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the $\\partial \\bar\\partial$-lemma condition and defined in terms of the Bott-Chern cohomology, and show that the vanishing of some of these invariants is not a closed property under holomorphic deformations. In the balanced case, we determine the spaces that parametrize deformations in t","authors_text":"Adela Latorre, Luis Ugarte, Raquel Villacampa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-01T13:33:11Z","title":"On the Bott-Chern cohomology and balanced Hermitian nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0395","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:e5549a4713f2e19e013bb0f34b7628008ec6bc930557c088a4bb58df78a48dcd","target":"record","created_at":"2026-05-18T03:44:22Z","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":"beec1a14b416663cfebb69d38d298063d0faa2c6b4d888dd412aff83915a0640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-01T13:33:11Z","title_canon_sha256":"3317eee460ef342acce6442a86cf386df40f21c3b47a89c0eaec8a24977476aa"},"schema_version":"1.0","source":{"id":"1210.0395","kind":"arxiv","version":1}},"canonical_sha256":"f5ca76a974a91f9c388e73789dd2167733a5b374f880bb35c24da2016b2f55ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5ca76a974a91f9c388e73789dd2167733a5b374f880bb35c24da2016b2f55ef","first_computed_at":"2026-05-18T03:44:22.560342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:22.560342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+22NVw99TW4RRvzY45Z9ZhoIRB5cnJnDpeRtT1tMDD6HfcHjMtuOCff/XsfU4JWoSBZYGNrzDKfbj1hFSiY9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:22.560979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5549a4713f2e19e013bb0f34b7628008ec6bc930557c088a4bb58df78a48dcd","sha256:b4b49e4ea4e3013846ebb1051f531866b02e5b82839733a184b9543092232c76"],"state_sha256":"e2feec9380fe5784ce8d6f78f5086cd906817a0dbd97957774f81298696a1b6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCBFbFev95B/j515chnCtMPz9Cpqbq1pGmdEjkE/csuwkZn0dufWM9w0kUPb7fQyPo04kfl6dgIVtWE55y5fCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:47:31.551651Z","bundle_sha256":"6cfa59903ba11a0e409b80cccf53597ba5b9fa30613bd6aa3cb6e405c6c49c04"}}