{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TNKXRNCZCH3S2VP2FINDRBFKFL","short_pith_number":"pith:TNKXRNCZ","canonical_record":{"source":{"id":"1504.04180","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-16T11:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"47df0e4293087ae56f90eb66effa0f5ea9b5333ddf5507f579a8dc18037c904c","abstract_canon_sha256":"6ed4af8f97a1b44344fd08b4ba1de01da27e2516cf07366adf7cfe42d3d64e51"},"schema_version":"1.0"},"canonical_sha256":"9b5578b45911f72d55fa2a1a3884aa2ae92a72450f588f1883ebfbb9de2fea1d","source":{"kind":"arxiv","id":"1504.04180","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04180","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04180v3","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04180","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"TNKXRNCZCH3S","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNKXRNCZCH3S2VP2","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNKXRNCZ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TNKXRNCZCH3S2VP2FINDRBFKFL","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04180","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-16T11:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"47df0e4293087ae56f90eb66effa0f5ea9b5333ddf5507f579a8dc18037c904c","abstract_canon_sha256":"6ed4af8f97a1b44344fd08b4ba1de01da27e2516cf07366adf7cfe42d3d64e51"},"schema_version":"1.0"},"canonical_sha256":"9b5578b45911f72d55fa2a1a3884aa2ae92a72450f588f1883ebfbb9de2fea1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:33.688921Z","signature_b64":"9mt/Dar+1+GOzfYVXt+AzJ/12uvTijL4rcfMda53/eZPAVL20oeTRjZw50GrqCi97e42nUm751/SIrrW5MvdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b5578b45911f72d55fa2a1a3884aa2ae92a72450f588f1883ebfbb9de2fea1d","last_reissued_at":"2026-05-18T01:33:33.688168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:33.688168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04180","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wvdBRT9NXZTQIu+7F5xV+G1m6qWld4/dYiGxkzbuD9X+FM7u0GX+4Ouuy/awSQfGsiXnFp7oa40TVvSWIJCTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:36:31.668458Z"},"content_sha256":"676ae96df43275b8a346e9b2ebde8440487dc7cbda9f16b0c0234eb2b2bc949b","schema_version":"1.0","event_id":"sha256:676ae96df43275b8a346e9b2ebde8440487dc7cbda9f16b0c0234eb2b2bc949b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TNKXRNCZCH3S2VP2FINDRBFKFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"A. Beri, C. Murathan, I. K\\\"upeli Erken","submitted_at":"2015-04-16T11:02:26Z","abstract_excerpt":"The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic vector field {\\xi} is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04180","kind":"arxiv","version":3},"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":"2026-05-18T01:33:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nvf01SDWUw1LRzl4cvXtRYPDq+1G05jKSA8esnQufcnYxritxv4It+8sMkADVJkt/W4gPxCvLDWWB2RSyzvTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:36:31.668804Z"},"content_sha256":"f26d8705248a19bf6eea4145cb3016f30f9ee70eaeef14f66db156d530e947a1","schema_version":"1.0","event_id":"sha256:f26d8705248a19bf6eea4145cb3016f30f9ee70eaeef14f66db156d530e947a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNKXRNCZCH3S2VP2FINDRBFKFL/bundle.json","state_url":"https://pith.science/pith/TNKXRNCZCH3S2VP2FINDRBFKFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNKXRNCZCH3S2VP2FINDRBFKFL/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":"2026-05-31T03:36:31Z","links":{"resolver":"https://pith.science/pith/TNKXRNCZCH3S2VP2FINDRBFKFL","bundle":"https://pith.science/pith/TNKXRNCZCH3S2VP2FINDRBFKFL/bundle.json","state":"https://pith.science/pith/TNKXRNCZCH3S2VP2FINDRBFKFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNKXRNCZCH3S2VP2FINDRBFKFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TNKXRNCZCH3S2VP2FINDRBFKFL","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":"6ed4af8f97a1b44344fd08b4ba1de01da27e2516cf07366adf7cfe42d3d64e51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-16T11:02:26Z","title_canon_sha256":"47df0e4293087ae56f90eb66effa0f5ea9b5333ddf5507f579a8dc18037c904c"},"schema_version":"1.0","source":{"id":"1504.04180","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04180","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04180v3","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04180","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"TNKXRNCZCH3S","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNKXRNCZCH3S2VP2","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNKXRNCZ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:f26d8705248a19bf6eea4145cb3016f30f9ee70eaeef14f66db156d530e947a1","target":"graph","created_at":"2026-05-18T01:33:33Z","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 purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic vector field {\\xi} is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermo","authors_text":"A. Beri, C. Murathan, I. K\\\"upeli Erken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-16T11:02:26Z","title":"Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04180","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":"sha256:676ae96df43275b8a346e9b2ebde8440487dc7cbda9f16b0c0234eb2b2bc949b","target":"record","created_at":"2026-05-18T01:33:33Z","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":"6ed4af8f97a1b44344fd08b4ba1de01da27e2516cf07366adf7cfe42d3d64e51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-16T11:02:26Z","title_canon_sha256":"47df0e4293087ae56f90eb66effa0f5ea9b5333ddf5507f579a8dc18037c904c"},"schema_version":"1.0","source":{"id":"1504.04180","kind":"arxiv","version":3}},"canonical_sha256":"9b5578b45911f72d55fa2a1a3884aa2ae92a72450f588f1883ebfbb9de2fea1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b5578b45911f72d55fa2a1a3884aa2ae92a72450f588f1883ebfbb9de2fea1d","first_computed_at":"2026-05-18T01:33:33.688168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:33.688168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mt/Dar+1+GOzfYVXt+AzJ/12uvTijL4rcfMda53/eZPAVL20oeTRjZw50GrqCi97e42nUm751/SIrrW5MvdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:33.688921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04180","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:676ae96df43275b8a346e9b2ebde8440487dc7cbda9f16b0c0234eb2b2bc949b","sha256:f26d8705248a19bf6eea4145cb3016f30f9ee70eaeef14f66db156d530e947a1"],"state_sha256":"c856e8f9a6d27ce03d5fa77a7d5d465e4f3b839aeba35158f125fe131f5fb8c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WZ16cv6UnmFQAFwOWN2IEsvq0ZVG6zcwLnFYRTyhfTeR71o54fstVEYyy3KLNPMMCKr/flZQgKi0MnOzBdYsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:36:31.670725Z","bundle_sha256":"1dbc4f4288a9e2c5b7e9f2886534ca7e2fca7db785f64e33e9427cc0b83563da"}}