{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NIWGSD2RN6RGN3NXRP22T7NW6I","short_pith_number":"pith:NIWGSD2R","canonical_record":{"source":{"id":"1301.5275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-22T19:04:55Z","cross_cats_sorted":[],"title_canon_sha256":"9ff4e494d0d6308af5587ee7e8fbd71cfa4037c466f7525819de5f76c7bfcec7","abstract_canon_sha256":"6db1367c93da6e57da6273eb8efcff87aeed78c8dd77f0c7e8fd8e8ef0018fce"},"schema_version":"1.0"},"canonical_sha256":"6a2c690f516fa266edb78bf5a9fdb6f219e8134936810eef41188638f0a56fa9","source":{"kind":"arxiv","id":"1301.5275","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5275","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5275v1","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5275","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"NIWGSD2RN6RG","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NIWGSD2RN6RGN3NX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NIWGSD2R","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NIWGSD2RN6RGN3NXRP22T7NW6I","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-22T19:04:55Z","cross_cats_sorted":[],"title_canon_sha256":"9ff4e494d0d6308af5587ee7e8fbd71cfa4037c466f7525819de5f76c7bfcec7","abstract_canon_sha256":"6db1367c93da6e57da6273eb8efcff87aeed78c8dd77f0c7e8fd8e8ef0018fce"},"schema_version":"1.0"},"canonical_sha256":"6a2c690f516fa266edb78bf5a9fdb6f219e8134936810eef41188638f0a56fa9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:52.366437Z","signature_b64":"H2Aj7d6ENhf+09NrxNoruHVTFy+Hr/V0oZYTj5WMHcZJiiHqNoLtzwuGAzaMRB5BaTIZvP87R0zaVgSibHF9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a2c690f516fa266edb78bf5a9fdb6f219e8134936810eef41188638f0a56fa9","last_reissued_at":"2026-05-18T03:35:52.365022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:52.365022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5275","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kDOoaO8p82l3vdqK+CX4tuQ5Jyews11mzcvzd3k7B2PaBNJaKjkp8ciVdg3gGUrwdMexSrLvqMmbPRCUtq/rCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:21:42.414704Z"},"content_sha256":"b450fe8f61c72e564d5e11944216d72bbafac8b579adc9787e23178e0ec7b210","schema_version":"1.0","event_id":"sha256:b450fe8f61c72e564d5e11944216d72bbafac8b579adc9787e23178e0ec7b210"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NIWGSD2RN6RGN3NXRP22T7NW6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adapted basic connections to a certain subfoliation on the tangent manifold of a Finsler space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adelina Manea, Cristian Ida","submitted_at":"2013-01-22T19:04:55Z","abstract_excerpt":"On the slit tangent manifold $TM^0$ of a Finsler space $(M,F)$ there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle, Rep. Math. Physics 58, No. 1 (2006), 131-146]. In this paper we consider a $(n,2n-1)$-codimensional subfoliation $(\\mathcal{F}_V,\\mathcal{F}_{\\Gamma})$ on $TM^0$ given by vertical foliation $\\mathcal{F}_V$ and the line foliation spanned by vertical Liouville vector field $\\Gamm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5275","kind":"arxiv","version":1},"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":"2026-05-18T03:35:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7xgD3Q3ojjEthw1KundxR6s8T//Nfz5b2kLNHQ11eZafYwhu6H7WA+LLVIZ0iUtWmKKLQujT0pWg0cM8qmJzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:21:42.415054Z"},"content_sha256":"afb5387f21224ccaf85317aa7266c5c287aac4e067ea72dec9effffd375a67fc","schema_version":"1.0","event_id":"sha256:afb5387f21224ccaf85317aa7266c5c287aac4e067ea72dec9effffd375a67fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIWGSD2RN6RGN3NXRP22T7NW6I/bundle.json","state_url":"https://pith.science/pith/NIWGSD2RN6RGN3NXRP22T7NW6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIWGSD2RN6RGN3NXRP22T7NW6I/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":"2026-06-03T15:21:42Z","links":{"resolver":"https://pith.science/pith/NIWGSD2RN6RGN3NXRP22T7NW6I","bundle":"https://pith.science/pith/NIWGSD2RN6RGN3NXRP22T7NW6I/bundle.json","state":"https://pith.science/pith/NIWGSD2RN6RGN3NXRP22T7NW6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIWGSD2RN6RGN3NXRP22T7NW6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NIWGSD2RN6RGN3NXRP22T7NW6I","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":"6db1367c93da6e57da6273eb8efcff87aeed78c8dd77f0c7e8fd8e8ef0018fce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-22T19:04:55Z","title_canon_sha256":"9ff4e494d0d6308af5587ee7e8fbd71cfa4037c466f7525819de5f76c7bfcec7"},"schema_version":"1.0","source":{"id":"1301.5275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5275","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5275v1","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5275","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"NIWGSD2RN6RG","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NIWGSD2RN6RGN3NX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NIWGSD2R","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:afb5387f21224ccaf85317aa7266c5c287aac4e067ea72dec9effffd375a67fc","target":"graph","created_at":"2026-05-18T03:35:52Z","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"},"paper":{"abstract_excerpt":"On the slit tangent manifold $TM^0$ of a Finsler space $(M,F)$ there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle, Rep. Math. Physics 58, No. 1 (2006), 131-146]. In this paper we consider a $(n,2n-1)$-codimensional subfoliation $(\\mathcal{F}_V,\\mathcal{F}_{\\Gamma})$ on $TM^0$ given by vertical foliation $\\mathcal{F}_V$ and the line foliation spanned by vertical Liouville vector field $\\Gamm","authors_text":"Adelina Manea, Cristian Ida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-22T19:04:55Z","title":"Adapted basic connections to a certain subfoliation on the tangent manifold of a Finsler space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5275","kind":"arxiv","version":1},"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:b450fe8f61c72e564d5e11944216d72bbafac8b579adc9787e23178e0ec7b210","target":"record","created_at":"2026-05-18T03:35:52Z","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":"6db1367c93da6e57da6273eb8efcff87aeed78c8dd77f0c7e8fd8e8ef0018fce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-22T19:04:55Z","title_canon_sha256":"9ff4e494d0d6308af5587ee7e8fbd71cfa4037c466f7525819de5f76c7bfcec7"},"schema_version":"1.0","source":{"id":"1301.5275","kind":"arxiv","version":1}},"canonical_sha256":"6a2c690f516fa266edb78bf5a9fdb6f219e8134936810eef41188638f0a56fa9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a2c690f516fa266edb78bf5a9fdb6f219e8134936810eef41188638f0a56fa9","first_computed_at":"2026-05-18T03:35:52.365022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:52.365022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H2Aj7d6ENhf+09NrxNoruHVTFy+Hr/V0oZYTj5WMHcZJiiHqNoLtzwuGAzaMRB5BaTIZvP87R0zaVgSibHF9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:52.366437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b450fe8f61c72e564d5e11944216d72bbafac8b579adc9787e23178e0ec7b210","sha256:afb5387f21224ccaf85317aa7266c5c287aac4e067ea72dec9effffd375a67fc"],"state_sha256":"9e6dc01684620ad5466531ed85e27d5a0b7074eacc0acb7d7b8a07280bc72585"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkmI4Ut2KvbJ5kKmtTCvuVVZsc13Oh3n7wzAzpRvyda2Z1k4CB7VW2kPDsbvqNc97Za/QD9lD0AabbQPYTcTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:21:42.417060Z","bundle_sha256":"38dbd4ee5c6ab3bd753950fb93287fa0ec8b237788f0728cbc1ef80d6a6f06a2"}}