{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IBNMJ7THJGVPWQMWDYACJSF4M3","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":"031ae117226a1437edd1fda57214fbe808f784dfd561822c0349cb6d4fb93b0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-16T12:14:59Z","title_canon_sha256":"6a8ab4e4d03f8cffecddc503a29fe66ced49dbde22fbd95c6de8f12256e1fad2"},"schema_version":"1.0","source":{"id":"1305.3776","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3776","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3776v1","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3776","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"IBNMJ7THJGVP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IBNMJ7THJGVPWQMW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IBNMJ7TH","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:476b93378a87c286ffa6bcf7791e7275c73fc78693a645cd076939d87ad6c952","target":"graph","created_at":"2026-05-18T01:25:40Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping f:GR_N → G K-bar_N with respect to the four kinds of covariant derivatives."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The almost complex structure F is covariantly constant with respect to the first kind of covariant derivative in the generalized Kählerian space of the first kind."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Necessary and sufficient conditions are found for geodesic mappings onto generalized Kählerian spaces of the first kind with respect to four covariant derivatives."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Necessary and sufficient conditions for geodesic mappings from generalized Riemannian spaces onto generalized Kählerian spaces of the first kind are derived using a non-symmetric metric tensor."}],"snapshot_sha256":"ea443556deee3266b56a31effe1c4f6406bff4d7e9694864dc6f04b29d9d3aab"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the present paper a generalized K\\\"ahlerian space $\\mathbb{G}\\underset 1 {\\mathbb{K}}{}_N$ of the first kind is considered, as a generalized Riemannian space $\\mathbb{GR}_N$ with almost complex structure $F^h_i$, that is covariantly constant with respect to the first kind of covariant derivative.\n  Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping $f:\\mathbb{GR}_N\\to \\mathbb{G}\\underset 1 {\\mathbb{\\bar{K}}}{}_N$ with respect to the four kinds of covariant derivatives.","authors_text":"Irena Hinterleitner, Marija Najdanovi\\'c, Milan Zlatanovi\\'c","cross_cats":[],"headline":"Necessary and sufficient conditions for geodesic mappings from generalized Riemannian spaces onto generalized Kählerian spaces of the first kind are derived using a non-symmetric metric tensor.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-16T12:14:59Z","title":"Geodesic mapping onto K\\\"ahlerian space of the first kind"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3776","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T22:21:40.736756Z","id":"3c184c7b-ae72-4454-9e8f-abd8954c8bb6","model_set":{"reader":"grok-4.3"},"one_line_summary":"Necessary and sufficient conditions are found for geodesic mappings onto generalized Kählerian spaces of the first kind with respect to four covariant derivatives.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Necessary and sufficient conditions for geodesic mappings from generalized Riemannian spaces onto generalized Kählerian spaces of the first kind are derived using a non-symmetric metric tensor.","strongest_claim":"Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping f:GR_N → G K-bar_N with respect to the four kinds of covariant derivatives.","weakest_assumption":"The almost complex structure F is covariantly constant with respect to the first kind of covariant derivative in the generalized Kählerian space of the first kind."}},"verdict_id":"3c184c7b-ae72-4454-9e8f-abd8954c8bb6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:71d6b60cee71ca6e7f5b7d1f0e3345c5b405b1654da893219fb0fddec90d769d","target":"record","created_at":"2026-05-18T01:25:40Z","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":"031ae117226a1437edd1fda57214fbe808f784dfd561822c0349cb6d4fb93b0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-16T12:14:59Z","title_canon_sha256":"6a8ab4e4d03f8cffecddc503a29fe66ced49dbde22fbd95c6de8f12256e1fad2"},"schema_version":"1.0","source":{"id":"1305.3776","kind":"arxiv","version":1}},"canonical_sha256":"405ac4fe6749aafb41961e0024c8bc66d5f2cf84d060f8e84333435b670e96fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"405ac4fe6749aafb41961e0024c8bc66d5f2cf84d060f8e84333435b670e96fa","first_computed_at":"2026-05-18T01:25:40.003845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:40.003845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X0a36GNzhrhV/V1P7G1BFn1rS/XGqZezF1ht4idMevcODyJwqxkkdZ0jIlCBjJ1O0ZasD4vEuxDacJlLbQmyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:40.004514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3776","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71d6b60cee71ca6e7f5b7d1f0e3345c5b405b1654da893219fb0fddec90d769d","sha256:476b93378a87c286ffa6bcf7791e7275c73fc78693a645cd076939d87ad6c952"],"state_sha256":"fa1645eca80c08e340e2c7ac1bc3504b45317215cdbec87996c3e95d20dfca54"}