{"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"}