{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HIFWQHW3EQK6HPF5YE3MCW2BNX","short_pith_number":"pith:HIFWQHW3","canonical_record":{"source":{"id":"1503.00312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-01T17:10:23Z","cross_cats_sorted":[],"title_canon_sha256":"15ba729ba7602e0297077dd30be6d8976af5bae726c03dd24a21a4e33fd55ede","abstract_canon_sha256":"dddfa1b61171e6e00a269005f895849bbe3a44d2a10be01c5cd87c669804865c"},"schema_version":"1.0"},"canonical_sha256":"3a0b681edb2415e3bcbdc136c15b416dec5fef0f7733bbde0080e0e837d4364d","source":{"kind":"arxiv","id":"1503.00312","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00312","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00312v1","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00312","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"HIFWQHW3EQK6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HIFWQHW3EQK6HPF5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HIFWQHW3","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HIFWQHW3EQK6HPF5YE3MCW2BNX","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-01T17:10:23Z","cross_cats_sorted":[],"title_canon_sha256":"15ba729ba7602e0297077dd30be6d8976af5bae726c03dd24a21a4e33fd55ede","abstract_canon_sha256":"dddfa1b61171e6e00a269005f895849bbe3a44d2a10be01c5cd87c669804865c"},"schema_version":"1.0"},"canonical_sha256":"3a0b681edb2415e3bcbdc136c15b416dec5fef0f7733bbde0080e0e837d4364d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:47.613649Z","signature_b64":"8iX2aSsgEnDxPxQObvBNJNEo/CeKREZKZt10udD9LH/6CAlCvDfHKgzn7+YjZ952V08jXmLy3gWlR+lZazjyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a0b681edb2415e3bcbdc136c15b416dec5fef0f7733bbde0080e0e837d4364d","last_reissued_at":"2026-05-18T01:41:47.613139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:47.613139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00312","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":"2026-05-18T01:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rt4Pzb0bk2hf7U+bUkIRavygj2aSvUx+UwWaKDgCmXtcYPOJkAACc0Wsj1k17Qf8m/icBFo5mN2azfbynAK7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:23:07.787032Z"},"content_sha256":"c73962befd1dbde18458c04d9fdd9198b4019ddc88b7d07de022f1d5049f486a","schema_version":"1.0","event_id":"sha256:c73962befd1dbde18458c04d9fdd9198b4019ddc88b7d07de022f1d5049f486a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HIFWQHW3EQK6HPF5YE3MCW2BNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Lie groups as 3-dimensional almost contact B-metric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hristo Manev","submitted_at":"2015-03-01T17:10:23Z","abstract_excerpt":"The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the studied manifolds and the explicit matrix representation of Lie groups. Some known Lie groups are equiped with almost contact B-metric structure of different types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00312","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":"2026-05-18T01:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"beVTJJyzuDtjWg2ckcarxnPb+4f+Q4zyQoEpq11UqSHQNuiI/mpbyDjGPk/VzPsmiLeJ0rJm7rpdpmUucusyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:23:07.787393Z"},"content_sha256":"e5b0667d103d1c3d845198d2919847b9caf15f88917e880fc292de91030e5bcb","schema_version":"1.0","event_id":"sha256:e5b0667d103d1c3d845198d2919847b9caf15f88917e880fc292de91030e5bcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX/bundle.json","state_url":"https://pith.science/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX/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":"2026-06-23T21:23:07Z","links":{"resolver":"https://pith.science/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX","bundle":"https://pith.science/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX/bundle.json","state":"https://pith.science/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIFWQHW3EQK6HPF5YE3MCW2BNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HIFWQHW3EQK6HPF5YE3MCW2BNX","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":"dddfa1b61171e6e00a269005f895849bbe3a44d2a10be01c5cd87c669804865c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-01T17:10:23Z","title_canon_sha256":"15ba729ba7602e0297077dd30be6d8976af5bae726c03dd24a21a4e33fd55ede"},"schema_version":"1.0","source":{"id":"1503.00312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00312","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00312v1","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00312","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"HIFWQHW3EQK6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HIFWQHW3EQK6HPF5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HIFWQHW3","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:e5b0667d103d1c3d845198d2919847b9caf15f88917e880fc292de91030e5bcb","target":"graph","created_at":"2026-05-18T01:41:47Z","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 object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the studied manifolds and the explicit matrix representation of Lie groups. Some known Lie groups are equiped with almost contact B-metric structure of different types.","authors_text":"Hristo Manev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-01T17:10:23Z","title":"Matrix Lie groups as 3-dimensional almost contact B-metric manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00312","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:c73962befd1dbde18458c04d9fdd9198b4019ddc88b7d07de022f1d5049f486a","target":"record","created_at":"2026-05-18T01:41:47Z","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":"dddfa1b61171e6e00a269005f895849bbe3a44d2a10be01c5cd87c669804865c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-01T17:10:23Z","title_canon_sha256":"15ba729ba7602e0297077dd30be6d8976af5bae726c03dd24a21a4e33fd55ede"},"schema_version":"1.0","source":{"id":"1503.00312","kind":"arxiv","version":1}},"canonical_sha256":"3a0b681edb2415e3bcbdc136c15b416dec5fef0f7733bbde0080e0e837d4364d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a0b681edb2415e3bcbdc136c15b416dec5fef0f7733bbde0080e0e837d4364d","first_computed_at":"2026-05-18T01:41:47.613139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:47.613139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8iX2aSsgEnDxPxQObvBNJNEo/CeKREZKZt10udD9LH/6CAlCvDfHKgzn7+YjZ952V08jXmLy3gWlR+lZazjyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:47.613649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c73962befd1dbde18458c04d9fdd9198b4019ddc88b7d07de022f1d5049f486a","sha256:e5b0667d103d1c3d845198d2919847b9caf15f88917e880fc292de91030e5bcb"],"state_sha256":"d2eb715a2427c90ce8e83d2e8de6b106916c1ee6bc0ed0924559cb2998d5371d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wYCh4IC7GxIZ9Inyknqh5NDBvgUBaMgD0AfZS4JeW2++6QH7n7sqNjt5Q9t3fdMgQkhgMmdlkYN9LGMuSJ8cCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:23:07.789291Z","bundle_sha256":"c798c0c886c340f85038672d18fa16380438a7475fb4a11929891f0ffc1670fa"}}