{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:6F4IVB7XZGBQTO5WTQLX5IMWEK","short_pith_number":"pith:6F4IVB7X","canonical_record":{"source":{"id":"0810.0164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-01T13:32:11Z","cross_cats_sorted":[],"title_canon_sha256":"a21defff1712893b9aac6e2b86717b0f66fbd63204aecb960c2517aaaa93876b","abstract_canon_sha256":"aa74be1278bc7be99b31fadda619769f5189a6b98d77ef389c0baee969efb342"},"schema_version":"1.0"},"canonical_sha256":"f1788a87f7c98309bbb69c177ea19622a6d199a09dd64e9712be1baa471f3f3a","source":{"kind":"arxiv","id":"0810.0164","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0164","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0164v2","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0164","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"pith_short_12","alias_value":"6F4IVB7XZGBQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6F4IVB7XZGBQTO5W","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6F4IVB7X","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:6F4IVB7XZGBQTO5WTQLX5IMWEK","target":"record","payload":{"canonical_record":{"source":{"id":"0810.0164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-01T13:32:11Z","cross_cats_sorted":[],"title_canon_sha256":"a21defff1712893b9aac6e2b86717b0f66fbd63204aecb960c2517aaaa93876b","abstract_canon_sha256":"aa74be1278bc7be99b31fadda619769f5189a6b98d77ef389c0baee969efb342"},"schema_version":"1.0"},"canonical_sha256":"f1788a87f7c98309bbb69c177ea19622a6d199a09dd64e9712be1baa471f3f3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:56.612300Z","signature_b64":"2IRla4DLUcfY3Wjk3t98e9gloyPULjJhdjuBs4tagBlGXz9sR0a9d5oE6lfDuJHcguN50KB34Iil+zlXTfTOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1788a87f7c98309bbb69c177ea19622a6d199a09dd64e9712be1baa471f3f3a","last_reissued_at":"2026-05-17T23:56:56.611814Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:56.611814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.0164","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":"2026-05-17T23:56:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BWnJg+tH3Fv66N+uV6rk2+UfSkhE+p8Tezae5DQREUDGHiHjiEy63a4je0HjYl8stbfakCuLSsCJnX/I3FmDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:33:33.675942Z"},"content_sha256":"3e58d549bb05b820b127b6cd81ec9b9e08aaa84ad6e8d3348dc9d31be6cc5d20","schema_version":"1.0","event_id":"sha256:3e58d549bb05b820b127b6cd81ec9b9e08aaa84ad6e8d3348dc9d31be6cc5d20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:6F4IVB7XZGBQTO5WTQLX5IMWEK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hermitian Laplace Operator on Nearly K\\\"ahler Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrei Moroianu (CMLS-EcolePolytechnique), Uwe Semmelmann (UNI KOELN)","submitted_at":"2008-10-01T13:32:11Z","abstract_excerpt":"The moduli space NK of infinitesimal deformations of a nearly K\\\"ahler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1,1) forms. Using the Hermitian Laplace operator and some representation theory, we compute the space NK on all 6-dimensional homogeneous nearly K\\\"ahler manifolds. It turns out that the nearly K\\\"ahler structure is rigid except for the flag manifold F(1,2)=SU_3/T^2, which carries an 8-dimensional moduli space of infinitesimal nearly K\\\"ahler deformations, modeled on the Lie algebra su_3 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0164","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":"2026-05-17T23:56:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0JVVmGBY1u/nlxlwG383AKexGhlogX9jh48frvaXLWZ5P7JaiJ/yOvg/1U1+AusK4/yo4e6can/8pboaJldmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:33:33.676500Z"},"content_sha256":"9563bb19577a1b36cebc0bba42973f3c137d534566ec769f815d3e3dbd29e015","schema_version":"1.0","event_id":"sha256:9563bb19577a1b36cebc0bba42973f3c137d534566ec769f815d3e3dbd29e015"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK/bundle.json","state_url":"https://pith.science/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK/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":"2026-06-22T21:33:33Z","links":{"resolver":"https://pith.science/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK","bundle":"https://pith.science/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK/bundle.json","state":"https://pith.science/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6F4IVB7XZGBQTO5WTQLX5IMWEK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:6F4IVB7XZGBQTO5WTQLX5IMWEK","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":"aa74be1278bc7be99b31fadda619769f5189a6b98d77ef389c0baee969efb342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-01T13:32:11Z","title_canon_sha256":"a21defff1712893b9aac6e2b86717b0f66fbd63204aecb960c2517aaaa93876b"},"schema_version":"1.0","source":{"id":"0810.0164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0164","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0164v2","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0164","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"pith_short_12","alias_value":"6F4IVB7XZGBQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6F4IVB7XZGBQTO5W","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6F4IVB7X","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9563bb19577a1b36cebc0bba42973f3c137d534566ec769f815d3e3dbd29e015","target":"graph","created_at":"2026-05-17T23:56:56Z","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 moduli space NK of infinitesimal deformations of a nearly K\\\"ahler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1,1) forms. Using the Hermitian Laplace operator and some representation theory, we compute the space NK on all 6-dimensional homogeneous nearly K\\\"ahler manifolds. It turns out that the nearly K\\\"ahler structure is rigid except for the flag manifold F(1,2)=SU_3/T^2, which carries an 8-dimensional moduli space of infinitesimal nearly K\\\"ahler deformations, modeled on the Lie algebra su_3 ","authors_text":"Andrei Moroianu (CMLS-EcolePolytechnique), Uwe Semmelmann (UNI KOELN)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-01T13:32:11Z","title":"The Hermitian Laplace Operator on Nearly K\\\"ahler Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0164","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":"sha256:3e58d549bb05b820b127b6cd81ec9b9e08aaa84ad6e8d3348dc9d31be6cc5d20","target":"record","created_at":"2026-05-17T23:56:56Z","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":"aa74be1278bc7be99b31fadda619769f5189a6b98d77ef389c0baee969efb342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-01T13:32:11Z","title_canon_sha256":"a21defff1712893b9aac6e2b86717b0f66fbd63204aecb960c2517aaaa93876b"},"schema_version":"1.0","source":{"id":"0810.0164","kind":"arxiv","version":2}},"canonical_sha256":"f1788a87f7c98309bbb69c177ea19622a6d199a09dd64e9712be1baa471f3f3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1788a87f7c98309bbb69c177ea19622a6d199a09dd64e9712be1baa471f3f3a","first_computed_at":"2026-05-17T23:56:56.611814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:56.611814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2IRla4DLUcfY3Wjk3t98e9gloyPULjJhdjuBs4tagBlGXz9sR0a9d5oE6lfDuJHcguN50KB34Iil+zlXTfTOAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:56.612300Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.0164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e58d549bb05b820b127b6cd81ec9b9e08aaa84ad6e8d3348dc9d31be6cc5d20","sha256:9563bb19577a1b36cebc0bba42973f3c137d534566ec769f815d3e3dbd29e015"],"state_sha256":"1ff698e1d59269ea51074a2e8789997e7f835eab3d6ef950ccd3dfef877e89a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xj1s18lLJgJXPXIyv5s2cxSrTEjRSy/yE0PFpNGU2M9YssCYCwfXdSQeD84T+0gxS+7N3p0TVFylWr84T95NAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:33:33.679086Z","bundle_sha256":"91f86738d2a0ba8edef160d421b90a65294dc6eaf8b6867ad8c5b5cfb8c12968"}}