{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NQHDTTBB44JY2MMIAPTFDKKFO3","short_pith_number":"pith:NQHDTTBB","canonical_record":{"source":{"id":"1605.02792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-09T21:37:30Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b465bb5bfca7818cb0da9e7c816bffffd96960135308a5b5f9e5fe57400623cf","abstract_canon_sha256":"1f7ea855c90031287ea519df89f1eb5d8c713230ca1d905c50722ae2c0adcee0"},"schema_version":"1.0"},"canonical_sha256":"6c0e39cc21e7138d318803e651a94576f8e1dea4d3adc592bb25a0b203a6f200","source":{"kind":"arxiv","id":"1605.02792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02792","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02792v1","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02792","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"NQHDTTBB44JY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NQHDTTBB44JY2MMI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NQHDTTBB","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NQHDTTBB44JY2MMIAPTFDKKFO3","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-09T21:37:30Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b465bb5bfca7818cb0da9e7c816bffffd96960135308a5b5f9e5fe57400623cf","abstract_canon_sha256":"1f7ea855c90031287ea519df89f1eb5d8c713230ca1d905c50722ae2c0adcee0"},"schema_version":"1.0"},"canonical_sha256":"6c0e39cc21e7138d318803e651a94576f8e1dea4d3adc592bb25a0b203a6f200","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.081605Z","signature_b64":"HYm4QFt8V12NLBa5ICJt1YOsNyM0bCCdkJ8FT3jfK95EQ/vZhepBKzAwV2IOE/ASYPzKcMpYLiTB+ghrJqWbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c0e39cc21e7138d318803e651a94576f8e1dea4d3adc592bb25a0b203a6f200","last_reissued_at":"2026-05-17T23:54:27.081067Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.081067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02792","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EteotkelLKbQqaqVWiSCj72zsBjGw6cuqWUMJee8d9kkAZmh4toyuYFgxSPpp9f0+etg8YmUCl2M5vmUB4e/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:35:05.419568Z"},"content_sha256":"eb8408fb1f205b1722d35e33d2edac6e7b5e47839130e79fcd05a4cf30010356","schema_version":"1.0","event_id":"sha256:eb8408fb1f205b1722d35e33d2edac6e7b5e47839130e79fcd05a4cf30010356"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NQHDTTBB44JY2MMIAPTFDKKFO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vaisman nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Giovanni Bazzoni","submitted_at":"2016-05-09T21:37:30Z","abstract_excerpt":"We prove that if a compact nilmanifold $\\Gamma\\backslash G$ is endowed with a Vaisman structure, then $G$ is isomorphic to the Cartesian product of the Heisenberg group with $\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02792","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5UAYBpJ0RH2ZZ6zBI+JTIn5qkGSSFl0KN/wv93dLajZ4UbbVU8Hs54Zqvu/8nkyBJeuJdoR7FsqTjUEiY6YDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:35:05.419915Z"},"content_sha256":"6ac01d15ad7cbddf2158333ebf568ec45adc762b445aa54ab08bb29cdbcc00ac","schema_version":"1.0","event_id":"sha256:6ac01d15ad7cbddf2158333ebf568ec45adc762b445aa54ab08bb29cdbcc00ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQHDTTBB44JY2MMIAPTFDKKFO3/bundle.json","state_url":"https://pith.science/pith/NQHDTTBB44JY2MMIAPTFDKKFO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQHDTTBB44JY2MMIAPTFDKKFO3/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":"2026-06-09T14:35:05Z","links":{"resolver":"https://pith.science/pith/NQHDTTBB44JY2MMIAPTFDKKFO3","bundle":"https://pith.science/pith/NQHDTTBB44JY2MMIAPTFDKKFO3/bundle.json","state":"https://pith.science/pith/NQHDTTBB44JY2MMIAPTFDKKFO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQHDTTBB44JY2MMIAPTFDKKFO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NQHDTTBB44JY2MMIAPTFDKKFO3","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":"1f7ea855c90031287ea519df89f1eb5d8c713230ca1d905c50722ae2c0adcee0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-09T21:37:30Z","title_canon_sha256":"b465bb5bfca7818cb0da9e7c816bffffd96960135308a5b5f9e5fe57400623cf"},"schema_version":"1.0","source":{"id":"1605.02792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02792","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02792v1","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02792","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"NQHDTTBB44JY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NQHDTTBB44JY2MMI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NQHDTTBB","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:6ac01d15ad7cbddf2158333ebf568ec45adc762b445aa54ab08bb29cdbcc00ac","target":"graph","created_at":"2026-05-17T23:54:27Z","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":"We prove that if a compact nilmanifold $\\Gamma\\backslash G$ is endowed with a Vaisman structure, then $G$ is isomorphic to the Cartesian product of the Heisenberg group with $\\mathbb{R}$.","authors_text":"Giovanni Bazzoni","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-09T21:37:30Z","title":"Vaisman nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02792","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:eb8408fb1f205b1722d35e33d2edac6e7b5e47839130e79fcd05a4cf30010356","target":"record","created_at":"2026-05-17T23:54:27Z","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":"1f7ea855c90031287ea519df89f1eb5d8c713230ca1d905c50722ae2c0adcee0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-05-09T21:37:30Z","title_canon_sha256":"b465bb5bfca7818cb0da9e7c816bffffd96960135308a5b5f9e5fe57400623cf"},"schema_version":"1.0","source":{"id":"1605.02792","kind":"arxiv","version":1}},"canonical_sha256":"6c0e39cc21e7138d318803e651a94576f8e1dea4d3adc592bb25a0b203a6f200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c0e39cc21e7138d318803e651a94576f8e1dea4d3adc592bb25a0b203a6f200","first_computed_at":"2026-05-17T23:54:27.081067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:27.081067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYm4QFt8V12NLBa5ICJt1YOsNyM0bCCdkJ8FT3jfK95EQ/vZhepBKzAwV2IOE/ASYPzKcMpYLiTB+ghrJqWbAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:27.081605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb8408fb1f205b1722d35e33d2edac6e7b5e47839130e79fcd05a4cf30010356","sha256:6ac01d15ad7cbddf2158333ebf568ec45adc762b445aa54ab08bb29cdbcc00ac"],"state_sha256":"a5c3c48646cdb6c2e5b02acd27f5b3d1b90856823ebf88d357f9d3d66a4fffd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ler3u2QylCKmhg82bXCc6/yzVb8dy5Yum/iY0yR9ZyU6v6yviKZ7o6P5f40ZN3LXzjq660tE0dWJQ4RMn5BkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:35:05.421933Z","bundle_sha256":"766493e7e1c73925ebf3ae38c0615b47fff30c92cb07b7482660910a4fa649a1"}}