{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TC7WDRQ3ZB4CN25VN4V75EHAYP","short_pith_number":"pith:TC7WDRQ3","canonical_record":{"source":{"id":"1705.10179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T13:38:47Z","cross_cats_sorted":[],"title_canon_sha256":"37ab4833338911e3f1d4fb0badf45d0aa1c8b5e7623e2e40d26250b2f256886f","abstract_canon_sha256":"90bbbd2f3d9f1c5a0ab9f286ee70ec46caded97824cb378ba265a3ce00606846"},"schema_version":"1.0"},"canonical_sha256":"98bf61c61bc87826ebb56f2bfe90e0c3c9c4387dbb02edf867f29592e3564de8","source":{"kind":"arxiv","id":"1705.10179","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10179","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10179v2","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10179","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"TC7WDRQ3ZB4C","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TC7WDRQ3ZB4CN25V","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TC7WDRQ3","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TC7WDRQ3ZB4CN25VN4V75EHAYP","target":"record","payload":{"canonical_record":{"source":{"id":"1705.10179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T13:38:47Z","cross_cats_sorted":[],"title_canon_sha256":"37ab4833338911e3f1d4fb0badf45d0aa1c8b5e7623e2e40d26250b2f256886f","abstract_canon_sha256":"90bbbd2f3d9f1c5a0ab9f286ee70ec46caded97824cb378ba265a3ce00606846"},"schema_version":"1.0"},"canonical_sha256":"98bf61c61bc87826ebb56f2bfe90e0c3c9c4387dbb02edf867f29592e3564de8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:06.547655Z","signature_b64":"IEfOPQgtSWJQ/4pE5OPnBlipNEpnURoEB3wQ6ynurze7ZD37uTEi5WROEsKKwml7pVfwFepNnVQajd4UQlurBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98bf61c61bc87826ebb56f2bfe90e0c3c9c4387dbb02edf867f29592e3564de8","last_reissued_at":"2026-05-18T00:33:06.546594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:06.546594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.10179","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":"2026-05-18T00:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLCgj17vZuHOcDsEkPljoA9oy0yFDQpFJKB2D/uNJG3pKH651E34QQSbsNw1z2YvrBtxIvfqNHocg63743noCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:08:23.462477Z"},"content_sha256":"e55db804857d93068d5de9746600f5d7e268e45a8f2c6141262b4de9a3ef1fe3","schema_version":"1.0","event_id":"sha256:e55db804857d93068d5de9746600f5d7e268e45a8f2c6141262b4de9a3ef1fe3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TC7WDRQ3ZB4CN25VN4V75EHAYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The decomposition of almost paracontact metric manifolds in eleven classes revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Galia Nakova, Simeon Zamkovoy","submitted_at":"2017-05-29T13:38:47Z","abstract_excerpt":"This paper is a continuation of our previous work, where eleven basic classes of almost paracontact metric manifolds with respect to the covariant derivative of the structure tensor field were obtained. First we decompose one of the eleven classes into two classes and the basic classes of the considered manifolds become twelve. Also, we determine the classes of $\\alpha$-para-Sasakian, $\\alpha$-para-Kenmotsu, normal, paracontact metric, para-Sasakian, K-paracontact and quasi-para-Sasakian manifolds. Moreover, we study 3-dimensional almost paracontact metric manifolds and show that they belong t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10179","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":"2026-05-18T00:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shtm3tSB6ro8ZnKMia0cTQDFMLKFeuUgfBs9cYnnD8hLq6Cm8rfqwIt+A50C81o/xQzW8SSYFN9/Fs7Lu2cJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:08:23.462829Z"},"content_sha256":"3a1ba69794314d7c0a2d4b1c14e34270b325f54c331ae1fc921425fb721aad50","schema_version":"1.0","event_id":"sha256:3a1ba69794314d7c0a2d4b1c14e34270b325f54c331ae1fc921425fb721aad50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP/bundle.json","state_url":"https://pith.science/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP/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":"2026-06-23T22:08:23Z","links":{"resolver":"https://pith.science/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP","bundle":"https://pith.science/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP/bundle.json","state":"https://pith.science/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TC7WDRQ3ZB4CN25VN4V75EHAYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TC7WDRQ3ZB4CN25VN4V75EHAYP","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":"90bbbd2f3d9f1c5a0ab9f286ee70ec46caded97824cb378ba265a3ce00606846","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T13:38:47Z","title_canon_sha256":"37ab4833338911e3f1d4fb0badf45d0aa1c8b5e7623e2e40d26250b2f256886f"},"schema_version":"1.0","source":{"id":"1705.10179","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10179","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10179v2","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10179","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"TC7WDRQ3ZB4C","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TC7WDRQ3ZB4CN25V","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TC7WDRQ3","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:3a1ba69794314d7c0a2d4b1c14e34270b325f54c331ae1fc921425fb721aad50","target":"graph","created_at":"2026-05-18T00:33:06Z","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":"This paper is a continuation of our previous work, where eleven basic classes of almost paracontact metric manifolds with respect to the covariant derivative of the structure tensor field were obtained. First we decompose one of the eleven classes into two classes and the basic classes of the considered manifolds become twelve. Also, we determine the classes of $\\alpha$-para-Sasakian, $\\alpha$-para-Kenmotsu, normal, paracontact metric, para-Sasakian, K-paracontact and quasi-para-Sasakian manifolds. Moreover, we study 3-dimensional almost paracontact metric manifolds and show that they belong t","authors_text":"Galia Nakova, Simeon Zamkovoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T13:38:47Z","title":"The decomposition of almost paracontact metric manifolds in eleven classes revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10179","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:e55db804857d93068d5de9746600f5d7e268e45a8f2c6141262b4de9a3ef1fe3","target":"record","created_at":"2026-05-18T00:33:06Z","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":"90bbbd2f3d9f1c5a0ab9f286ee70ec46caded97824cb378ba265a3ce00606846","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T13:38:47Z","title_canon_sha256":"37ab4833338911e3f1d4fb0badf45d0aa1c8b5e7623e2e40d26250b2f256886f"},"schema_version":"1.0","source":{"id":"1705.10179","kind":"arxiv","version":2}},"canonical_sha256":"98bf61c61bc87826ebb56f2bfe90e0c3c9c4387dbb02edf867f29592e3564de8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98bf61c61bc87826ebb56f2bfe90e0c3c9c4387dbb02edf867f29592e3564de8","first_computed_at":"2026-05-18T00:33:06.546594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:06.546594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IEfOPQgtSWJQ/4pE5OPnBlipNEpnURoEB3wQ6ynurze7ZD37uTEi5WROEsKKwml7pVfwFepNnVQajd4UQlurBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:06.547655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10179","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e55db804857d93068d5de9746600f5d7e268e45a8f2c6141262b4de9a3ef1fe3","sha256:3a1ba69794314d7c0a2d4b1c14e34270b325f54c331ae1fc921425fb721aad50"],"state_sha256":"e0210bac917cca76e2d90241cd7b41bcffcfee503ddda896886c6eb95ae6be91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKwNbGIPkU/4RQZQ0cOYCKpfsTvg+110v4YtIhvdouN3YsZ6muIgf/lGLEFNLVlmmWVC9RN7x6hdWlRpdRFlBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:08:23.464935Z","bundle_sha256":"f7de0dc094562a576b17a3fdcc0a09a509b277f6c123458d0e7d0072ba8015e7"}}