{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MKFIKL42NNNA54ROMPBO4K2NML","short_pith_number":"pith:MKFIKL42","canonical_record":{"source":{"id":"1309.0975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-04T10:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"1de7e008a337d0d6bfabc9058b7001000201d476ed75d939e479e65154d5277b","abstract_canon_sha256":"70cf88fd8416f44f812c497bfe48e6222615cc42c417bd086147e7db35782adf"},"schema_version":"1.0"},"canonical_sha256":"628a852f9a6b5a0ef22e63c2ee2b4d62faffb04a3348e0ebf01292274ea39426","source":{"kind":"arxiv","id":"1309.0975","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0975","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0975v1","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0975","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"MKFIKL42NNNA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MKFIKL42NNNA54RO","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MKFIKL42","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MKFIKL42NNNA54ROMPBO4K2NML","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-04T10:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"1de7e008a337d0d6bfabc9058b7001000201d476ed75d939e479e65154d5277b","abstract_canon_sha256":"70cf88fd8416f44f812c497bfe48e6222615cc42c417bd086147e7db35782adf"},"schema_version":"1.0"},"canonical_sha256":"628a852f9a6b5a0ef22e63c2ee2b4d62faffb04a3348e0ebf01292274ea39426","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:21.310729Z","signature_b64":"yGGvS2e3xKBUVltFmxK2Vt3C2x60un1KQ8y6MNk+5HsqNeqTya906y6OKeK1dq8TbJinylK7BzefVQUAQo/aAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"628a852f9a6b5a0ef22e63c2ee2b4d62faffb04a3348e0ebf01292274ea39426","last_reissued_at":"2026-05-18T02:54:21.310297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:21.310297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0975","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixDZPM6xKMyRXORwJidqSt5ExFFA4lY5eDglkDUbY3pvNcThmLCXZKcupvkoLtYz8XLSB53WvJUj8n6wXYt5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:51:03.860254Z"},"content_sha256":"62c4ce2dbf74d1762c0a47ed3d1c4896eba64512a0ee82eaa1e8dc665bfbf41e","schema_version":"1.0","event_id":"sha256:62c4ce2dbf74d1762c0a47ed3d1c4896eba64512a0ee82eaa1e8dc665bfbf41e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MKFIKL42NNNA54ROMPBO4K2NML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypercomplex structures with Hermitian-Norden metrics on four-dimensional Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mancho Manev","submitted_at":"2013-09-04T10:57:52Z","abstract_excerpt":"Integrable hypercomplex structures with Hermitian and Norden metrics on Lie groups of dimension 4 are considered. The corresponding five types of invariant hypercomplex structures with hyper-Hermitian metric, studied by M.L. Barberis, are constructed here. The different cases regarding the signature of the basic pseudo-Riemannian metric are considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0975","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnRqC93djYNNzNgiv9otbhIww88097bTaMN5n3kO6oQ4L6sXTWZ3fE8uBEx0pnKPsjdn/0IEFQk5nAObTF/uBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:51:03.860627Z"},"content_sha256":"e5014c77393b7f55d6d29d8c9f5c161078bfe520611d809f9b634418f205f09c","schema_version":"1.0","event_id":"sha256:e5014c77393b7f55d6d29d8c9f5c161078bfe520611d809f9b634418f205f09c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKFIKL42NNNA54ROMPBO4K2NML/bundle.json","state_url":"https://pith.science/pith/MKFIKL42NNNA54ROMPBO4K2NML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKFIKL42NNNA54ROMPBO4K2NML/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":"2026-07-04T15:51:03Z","links":{"resolver":"https://pith.science/pith/MKFIKL42NNNA54ROMPBO4K2NML","bundle":"https://pith.science/pith/MKFIKL42NNNA54ROMPBO4K2NML/bundle.json","state":"https://pith.science/pith/MKFIKL42NNNA54ROMPBO4K2NML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKFIKL42NNNA54ROMPBO4K2NML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MKFIKL42NNNA54ROMPBO4K2NML","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":"70cf88fd8416f44f812c497bfe48e6222615cc42c417bd086147e7db35782adf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-04T10:57:52Z","title_canon_sha256":"1de7e008a337d0d6bfabc9058b7001000201d476ed75d939e479e65154d5277b"},"schema_version":"1.0","source":{"id":"1309.0975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0975","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0975v1","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0975","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"MKFIKL42NNNA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MKFIKL42NNNA54RO","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MKFIKL42","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:e5014c77393b7f55d6d29d8c9f5c161078bfe520611d809f9b634418f205f09c","target":"graph","created_at":"2026-05-18T02:54:21Z","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":"Integrable hypercomplex structures with Hermitian and Norden metrics on Lie groups of dimension 4 are considered. The corresponding five types of invariant hypercomplex structures with hyper-Hermitian metric, studied by M.L. Barberis, are constructed here. The different cases regarding the signature of the basic pseudo-Riemannian metric are considered.","authors_text":"Mancho Manev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-04T10:57:52Z","title":"Hypercomplex structures with Hermitian-Norden metrics on four-dimensional Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0975","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":"sha256:62c4ce2dbf74d1762c0a47ed3d1c4896eba64512a0ee82eaa1e8dc665bfbf41e","target":"record","created_at":"2026-05-18T02:54:21Z","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":"70cf88fd8416f44f812c497bfe48e6222615cc42c417bd086147e7db35782adf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-04T10:57:52Z","title_canon_sha256":"1de7e008a337d0d6bfabc9058b7001000201d476ed75d939e479e65154d5277b"},"schema_version":"1.0","source":{"id":"1309.0975","kind":"arxiv","version":1}},"canonical_sha256":"628a852f9a6b5a0ef22e63c2ee2b4d62faffb04a3348e0ebf01292274ea39426","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"628a852f9a6b5a0ef22e63c2ee2b4d62faffb04a3348e0ebf01292274ea39426","first_computed_at":"2026-05-18T02:54:21.310297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:21.310297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yGGvS2e3xKBUVltFmxK2Vt3C2x60un1KQ8y6MNk+5HsqNeqTya906y6OKeK1dq8TbJinylK7BzefVQUAQo/aAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:21.310729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62c4ce2dbf74d1762c0a47ed3d1c4896eba64512a0ee82eaa1e8dc665bfbf41e","sha256:e5014c77393b7f55d6d29d8c9f5c161078bfe520611d809f9b634418f205f09c"],"state_sha256":"2b6ca84bd81eece0d52031160906d669d7afb2f4975c2de20cb015eedf97bb89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEUlPqZudjgK//55vCtxbaKapP6W8IlGbxj+hHOIcUwkBTdzzDRld3SILb3gu0cCveh+gUdjhe62gl5Pl4XxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T15:51:03.862464Z","bundle_sha256":"e52883b9535bef8baab5f3d2b3d8e13997a9317407ddc701b3c260756b9f790c"}}