{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TUUEHTIFF6MWX4OSLNEMB7A5C6","short_pith_number":"pith:TUUEHTIF","canonical_record":{"source":{"id":"1407.4403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-16T18:05:50Z","cross_cats_sorted":[],"title_canon_sha256":"112c34ccd2d7037be725e34ae98a5bf4dd5218babd5057237e5fd212eacf3cb0","abstract_canon_sha256":"65147e292671740a8e7c5eeef49d3afa11c0849cd2a5832ffbe52bb1edfecc40"},"schema_version":"1.0"},"canonical_sha256":"9d2843cd052f996bf1d25b48c0fc1d17867f7a826b3663bab39e3cec34cd3e1a","source":{"kind":"arxiv","id":"1407.4403","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4403","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4403v1","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4403","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"TUUEHTIFF6MW","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUUEHTIFF6MWX4OS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUUEHTIF","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TUUEHTIFF6MWX4OSLNEMB7A5C6","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-16T18:05:50Z","cross_cats_sorted":[],"title_canon_sha256":"112c34ccd2d7037be725e34ae98a5bf4dd5218babd5057237e5fd212eacf3cb0","abstract_canon_sha256":"65147e292671740a8e7c5eeef49d3afa11c0849cd2a5832ffbe52bb1edfecc40"},"schema_version":"1.0"},"canonical_sha256":"9d2843cd052f996bf1d25b48c0fc1d17867f7a826b3663bab39e3cec34cd3e1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:58.006110Z","signature_b64":"PfniKeNZ7J+gLx/e/ZCSOjH8A9NQWlJBBfDKKJFoR8LILJiVhrkt7hXW8ua2iQo9nNKTkhMVBjjx+UXPSubECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d2843cd052f996bf1d25b48c0fc1d17867f7a826b3663bab39e3cec34cd3e1a","last_reissued_at":"2026-05-18T01:41:58.005589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:58.005589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4403","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":"2026-05-18T01:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CDOYcRwRz0NTspn9guttN5JVb3LiA9gnvhl1pOst6UgzpEFATDSl4A6mVGoZeaAwBYxY3PHi1Xn5hpxD8fRBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:02:29.453561Z"},"content_sha256":"1f8bfe667a960cd3fd9481756f7772b2848c68b2dda030322258a45cbe2719fe","schema_version":"1.0","event_id":"sha256:1f8bfe667a960cd3fd9481756f7772b2848c68b2dda030322258a45cbe2719fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TUUEHTIFF6MWX4OSLNEMB7A5C6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"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":"Dimitar Mekerov, Hristo Manev","submitted_at":"2014-07-16T18:05:50Z","abstract_excerpt":"The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes. An example is given as a support of obtained results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4403","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":"2026-05-18T01:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQ0ORnAuZP3KLz5g1QBpv5IYo1/sEQgwSJQBpFdMcYxErh/T8pV7eNop2fcc1YTDFGuXvFV6PM5W0gs6tlxSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:02:29.454798Z"},"content_sha256":"17662ccdf3689785cc0ee644888a79bd889ade1aece0f3f225ad945742dcc52e","schema_version":"1.0","event_id":"sha256:17662ccdf3689785cc0ee644888a79bd889ade1aece0f3f225ad945742dcc52e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6/bundle.json","state_url":"https://pith.science/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6/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":"2026-06-11T20:02:29Z","links":{"resolver":"https://pith.science/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6","bundle":"https://pith.science/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6/bundle.json","state":"https://pith.science/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUUEHTIFF6MWX4OSLNEMB7A5C6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TUUEHTIFF6MWX4OSLNEMB7A5C6","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":"65147e292671740a8e7c5eeef49d3afa11c0849cd2a5832ffbe52bb1edfecc40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-16T18:05:50Z","title_canon_sha256":"112c34ccd2d7037be725e34ae98a5bf4dd5218babd5057237e5fd212eacf3cb0"},"schema_version":"1.0","source":{"id":"1407.4403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4403","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4403v1","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4403","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"TUUEHTIFF6MW","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUUEHTIFF6MWX4OS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUUEHTIF","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:17662ccdf3689785cc0ee644888a79bd889ade1aece0f3f225ad945742dcc52e","target":"graph","created_at":"2026-05-18T01:41:58Z","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 investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes. An example is given as a support of obtained results.","authors_text":"Dimitar Mekerov, Hristo Manev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-16T18:05:50Z","title":"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":"1407.4403","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":"sha256:1f8bfe667a960cd3fd9481756f7772b2848c68b2dda030322258a45cbe2719fe","target":"record","created_at":"2026-05-18T01:41:58Z","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":"65147e292671740a8e7c5eeef49d3afa11c0849cd2a5832ffbe52bb1edfecc40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-16T18:05:50Z","title_canon_sha256":"112c34ccd2d7037be725e34ae98a5bf4dd5218babd5057237e5fd212eacf3cb0"},"schema_version":"1.0","source":{"id":"1407.4403","kind":"arxiv","version":1}},"canonical_sha256":"9d2843cd052f996bf1d25b48c0fc1d17867f7a826b3663bab39e3cec34cd3e1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d2843cd052f996bf1d25b48c0fc1d17867f7a826b3663bab39e3cec34cd3e1a","first_computed_at":"2026-05-18T01:41:58.005589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:58.005589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfniKeNZ7J+gLx/e/ZCSOjH8A9NQWlJBBfDKKJFoR8LILJiVhrkt7hXW8ua2iQo9nNKTkhMVBjjx+UXPSubECw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:58.006110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f8bfe667a960cd3fd9481756f7772b2848c68b2dda030322258a45cbe2719fe","sha256:17662ccdf3689785cc0ee644888a79bd889ade1aece0f3f225ad945742dcc52e"],"state_sha256":"bb4749be36359b5bcd87071483c2997b129f67b4d4d3b3e82912f8eb3633749d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AkiiWDJNil/5pS/sSTSAaxhWlzqi9grtndxR/ei/wPdMdlWFN9UZGIC6Xr0wL8UCSUZnz988bwHTL2dwpqQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:02:29.458786Z","bundle_sha256":"1675f8e859d3f6523f2f805095d66631c442f689339e2c3d08cdbbd8560f1ad7"}}