{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CLQFL2ZXFBFFSBSU4K2OGXMAZ6","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":"db6bb475bef1476af8693b9df476a3d0730efff59f67739eeb7048d32a2d55cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-23T11:01:50Z","title_canon_sha256":"93cf73b1d6cd24c58a9cc6f520ea007b9e0a22647028a4fc7a1d27ab8a310280"},"schema_version":"1.0","source":{"id":"1312.6518","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6518","created_at":"2026-05-18T02:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6518v3","created_at":"2026-05-18T02:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6518","created_at":"2026-05-18T02:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"CLQFL2ZXFBFF","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CLQFL2ZXFBFFSBSU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CLQFL2ZX","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:83c629b10b14233fc96dd5a705aec11ee0726c985aa8965cb15a9a5a69648a94","target":"graph","created_at":"2026-05-18T02:20:36Z","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":"We study non-paraSasakian paracontact metric $(\\kappa,\\mu)$-spaces with $\\kappa=-1$ (equivalent to $h^2=0$ but $h\\neq0$). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of $h$. We will also give explicit examples of every possible constant rank of $h$.","authors_text":"Ver\\'onica Mart\\'in-Molina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-23T11:01:50Z","title":"Paracontact metric manifolds without a contact metric counterpart"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6518","kind":"arxiv","version":3},"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":"sha256:7b0b5dc116255bc4c7de406f509c182062ec7e3788e02d8f4773cc99a7ccec6b","target":"record","created_at":"2026-05-18T02:20:36Z","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":"db6bb475bef1476af8693b9df476a3d0730efff59f67739eeb7048d32a2d55cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-23T11:01:50Z","title_canon_sha256":"93cf73b1d6cd24c58a9cc6f520ea007b9e0a22647028a4fc7a1d27ab8a310280"},"schema_version":"1.0","source":{"id":"1312.6518","kind":"arxiv","version":3}},"canonical_sha256":"12e055eb37284a590654e2b4e35d80cf9e070007849e45358cbdd54882296c0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12e055eb37284a590654e2b4e35d80cf9e070007849e45358cbdd54882296c0f","first_computed_at":"2026-05-18T02:20:36.999779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:36.999779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lHP26Yl6l0QyfEWYi66vlT3/3UixCH6Wggx20FBLD84dlGI6pRc7dReU8Y8LjXLxuKkQInrL4vkr8cvqzjooAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:37.000474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6518","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b0b5dc116255bc4c7de406f509c182062ec7e3788e02d8f4773cc99a7ccec6b","sha256:83c629b10b14233fc96dd5a705aec11ee0726c985aa8965cb15a9a5a69648a94"],"state_sha256":"8ab53a71b592e156850c0336299c3ab022546c896e050c32d55ac503a6737c24"}