{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ROAXSBP6TGRNNUEWCD54ISD7RS","short_pith_number":"pith:ROAXSBP6","canonical_record":{"source":{"id":"2110.12867","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-10-20T03:38:00Z","cross_cats_sorted":[],"title_canon_sha256":"83d31231011dcc1ff776719f725ce95b8f9809edd5767f005b5a3ea84644e444","abstract_canon_sha256":"718ee03c5aa090ddc6f0c52221b73e4d9f1d9989595a046d4861a2cd9154635f"},"schema_version":"1.0"},"canonical_sha256":"8b817905fe99a2d6d09610fbc4487f8c82bd903d5f93d553c3d45dbd8abf9bef","source":{"kind":"arxiv","id":"2110.12867","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.12867","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"2110.12867v5","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.12867","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"ROAXSBP6TGRN","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"pith_short_16","alias_value":"ROAXSBP6TGRNNUEW","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"pith_short_8","alias_value":"ROAXSBP6","created_at":"2026-07-05T05:49:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ROAXSBP6TGRNNUEWCD54ISD7RS","target":"record","payload":{"canonical_record":{"source":{"id":"2110.12867","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-10-20T03:38:00Z","cross_cats_sorted":[],"title_canon_sha256":"83d31231011dcc1ff776719f725ce95b8f9809edd5767f005b5a3ea84644e444","abstract_canon_sha256":"718ee03c5aa090ddc6f0c52221b73e4d9f1d9989595a046d4861a2cd9154635f"},"schema_version":"1.0"},"canonical_sha256":"8b817905fe99a2d6d09610fbc4487f8c82bd903d5f93d553c3d45dbd8abf9bef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:49:52.674940Z","signature_b64":"AWTMBx+lPGRPAYbXcnj1KZAAZhPstxvCImVi0C3qOUx43mzZqxmBpwjwdUUFGMZUo2ig3r8c53Wpa7/wnCFoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b817905fe99a2d6d09610fbc4487f8c82bd903d5f93d553c3d45dbd8abf9bef","last_reissued_at":"2026-07-05T05:49:52.674505Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:49:52.674505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.12867","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:49:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GuVVSsS3DC20cdlEaIx6Nf94LTxDy0ufIMsfgHvlEMQTj0cCNN3ZPJSlWdCgH6vagWw77VrC7ucV5HzLtxb1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T10:24:57.789915Z"},"content_sha256":"c3077391b25803e8bd4473a5c35444da460a83bb1bc2c5803b925d1a406315a3","schema_version":"1.0","event_id":"sha256:c3077391b25803e8bd4473a5c35444da460a83bb1bc2c5803b925d1a406315a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ROAXSBP6TGRNNUEWCD54ISD7RS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost Ricci-Yamabe soliton on Almost Kenmotsu Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"J. P. Singh, M. Khatri","submitted_at":"2021-10-20T03:38:00Z","abstract_excerpt":"This manuscript examines almost Kenmotsu manifolds (briefly, AKMs) endowed with the almost Ricci-Yamabe solitons (ARYSs) and gradient ARYSs. The condition for an AKM with ARYS to be $\\eta$-Einstein is established. We also show that an ARYS on Kenmotsu manifold becomes Ricci-Yamabe soliton under certain restrictions. In this series, it is proven that a $(2n+1)$-dimensional $(\\kappa, \\mu)'$-AKM equipped with a gradient ARYS is either locally isometric to $\\mathbb{H}^{n+1}(-4)\\times\\mathbb{R}^n$ or the Reeb vector field and the soliton vector field are codirectional. The properties of $3$-dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12867","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.12867/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:49:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lVscBDBMrvedt/MaV8mHsXrd+776aJnpb8r823QN96Jv4BHjZa0NJYTR6NMfeW21xH52Q2RyonytSqZSBEIyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T10:24:57.790469Z"},"content_sha256":"2f9b56ffa683b3a71aa936d4baade9b1d5ff169cd1ece7c9defc304c5eb9e0ba","schema_version":"1.0","event_id":"sha256:2f9b56ffa683b3a71aa936d4baade9b1d5ff169cd1ece7c9defc304c5eb9e0ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ROAXSBP6TGRNNUEWCD54ISD7RS/bundle.json","state_url":"https://pith.science/pith/ROAXSBP6TGRNNUEWCD54ISD7RS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ROAXSBP6TGRNNUEWCD54ISD7RS/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":"2026-08-22T10:24:57Z","links":{"resolver":"https://pith.science/pith/ROAXSBP6TGRNNUEWCD54ISD7RS","bundle":"https://pith.science/pith/ROAXSBP6TGRNNUEWCD54ISD7RS/bundle.json","state":"https://pith.science/pith/ROAXSBP6TGRNNUEWCD54ISD7RS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ROAXSBP6TGRNNUEWCD54ISD7RS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ROAXSBP6TGRNNUEWCD54ISD7RS","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":"718ee03c5aa090ddc6f0c52221b73e4d9f1d9989595a046d4861a2cd9154635f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-10-20T03:38:00Z","title_canon_sha256":"83d31231011dcc1ff776719f725ce95b8f9809edd5767f005b5a3ea84644e444"},"schema_version":"1.0","source":{"id":"2110.12867","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.12867","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"2110.12867v5","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.12867","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"ROAXSBP6TGRN","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"pith_short_16","alias_value":"ROAXSBP6TGRNNUEW","created_at":"2026-07-05T05:49:52Z"},{"alias_kind":"pith_short_8","alias_value":"ROAXSBP6","created_at":"2026-07-05T05:49:52Z"}],"graph_snapshots":[{"event_id":"sha256:2f9b56ffa683b3a71aa936d4baade9b1d5ff169cd1ece7c9defc304c5eb9e0ba","target":"graph","created_at":"2026-07-05T05:49:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.12867/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This manuscript examines almost Kenmotsu manifolds (briefly, AKMs) endowed with the almost Ricci-Yamabe solitons (ARYSs) and gradient ARYSs. The condition for an AKM with ARYS to be $\\eta$-Einstein is established. We also show that an ARYS on Kenmotsu manifold becomes Ricci-Yamabe soliton under certain restrictions. In this series, it is proven that a $(2n+1)$-dimensional $(\\kappa, \\mu)'$-AKM equipped with a gradient ARYS is either locally isometric to $\\mathbb{H}^{n+1}(-4)\\times\\mathbb{R}^n$ or the Reeb vector field and the soliton vector field are codirectional. The properties of $3$-dimensi","authors_text":"J. P. Singh, M. Khatri","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-10-20T03:38:00Z","title":"Almost Ricci-Yamabe soliton on Almost Kenmotsu Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12867","kind":"arxiv","version":5},"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:c3077391b25803e8bd4473a5c35444da460a83bb1bc2c5803b925d1a406315a3","target":"record","created_at":"2026-07-05T05:49:52Z","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":"718ee03c5aa090ddc6f0c52221b73e4d9f1d9989595a046d4861a2cd9154635f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-10-20T03:38:00Z","title_canon_sha256":"83d31231011dcc1ff776719f725ce95b8f9809edd5767f005b5a3ea84644e444"},"schema_version":"1.0","source":{"id":"2110.12867","kind":"arxiv","version":5}},"canonical_sha256":"8b817905fe99a2d6d09610fbc4487f8c82bd903d5f93d553c3d45dbd8abf9bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b817905fe99a2d6d09610fbc4487f8c82bd903d5f93d553c3d45dbd8abf9bef","first_computed_at":"2026-07-05T05:49:52.674505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:49:52.674505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AWTMBx+lPGRPAYbXcnj1KZAAZhPstxvCImVi0C3qOUx43mzZqxmBpwjwdUUFGMZUo2ig3r8c53Wpa7/wnCFoAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:49:52.674940Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.12867","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3077391b25803e8bd4473a5c35444da460a83bb1bc2c5803b925d1a406315a3","sha256:2f9b56ffa683b3a71aa936d4baade9b1d5ff169cd1ece7c9defc304c5eb9e0ba"],"state_sha256":"117987c4fee5656ef5295529fe5cbb042cfde7cc1e17a2a312fef434bb786078"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UaPeenEzGb3AuJ35bO5vrBLUariqublCQfyuWAla56o0yGpmA6z1tCczvkh1B3m919DitHB33Fa9n2u02BQbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T10:24:57.796637Z","bundle_sha256":"07899e281dba320c5e95c48e45e2ec563994b1de08cab0e48b2a7c780a5a97da"}}