{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:L5SVDBODKLWF6HK3KQKV4XI7SI","short_pith_number":"pith:L5SVDBOD","canonical_record":{"source":{"id":"0805.2599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-05-16T18:43:05Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"f5e0fbfa5ab2edce6d700de9d3b227ff9774c2935df6bc27501bf1968ad21adc","abstract_canon_sha256":"372da97894b34cde1fc1ec44d6a65f56004c58319f8ee5afeb5651fa705f4423"},"schema_version":"1.0"},"canonical_sha256":"5f655185c352ec5f1d5b54155e5d1f92323530366b505f900e77bac98c6b524e","source":{"kind":"arxiv","id":"0805.2599","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2599","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2599v3","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2599","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"pith_short_12","alias_value":"L5SVDBODKLWF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"L5SVDBODKLWF6HK3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"L5SVDBOD","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:L5SVDBODKLWF6HK3KQKV4XI7SI","target":"record","payload":{"canonical_record":{"source":{"id":"0805.2599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-05-16T18:43:05Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"f5e0fbfa5ab2edce6d700de9d3b227ff9774c2935df6bc27501bf1968ad21adc","abstract_canon_sha256":"372da97894b34cde1fc1ec44d6a65f56004c58319f8ee5afeb5651fa705f4423"},"schema_version":"1.0"},"canonical_sha256":"5f655185c352ec5f1d5b54155e5d1f92323530366b505f900e77bac98c6b524e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:34.500602Z","signature_b64":"DupnL7fIegUUhz/HDh4y0KWVKk1YcUo4Yn86TbubC/bj+aCX0825dD4ZPsDZKPqxlr4SDnCJQ0KQRlushzgHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f655185c352ec5f1d5b54155e5d1f92323530366b505f900e77bac98c6b524e","last_reissued_at":"2026-05-18T04:37:34.500139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:34.500139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.2599","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":"2026-05-18T04:37:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WFXOcOoJYV53uaEte1GbZFgK0/n6DmQwoVMkd659r+5GG+0+pC6bQEQSirLpwE/tc2clzD3ZuL+Yt66TYl4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:13:37.398086Z"},"content_sha256":"65a278546f8c59a720e0d8f95ee96f0da0194bc111d8a9587699cffbb9fb45a7","schema_version":"1.0","event_id":"sha256:65a278546f8c59a720e0d8f95ee96f0da0194bc111d8a9587699cffbb9fb45a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:L5SVDBODKLWF6HK3KQKV4XI7SI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concurrent $\\pi$-vector fields and energy beta-change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"A. Soleiman, Nabil L. Youssef, S. H. Abed","submitted_at":"2008-05-16T18:43:05Z","abstract_excerpt":"The present paper deals with an \\emph{intrinsic} investigation of the notion of a concurrent $\\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\\beta$-change, namely the energy $\\beta$-change ($\\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \\ B:=g(\\bar{\\zeta},\\bar{\\eta})$; $\\bar{\\zeta} $ being a concurrent $\\pi$-vector field), is established. The relation between the two Barthel connections $\\Gamma$ and $\\widet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2599","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":"2026-05-18T04:37:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wztVc6bC7hsmMMqH+tlEE6okHYEtLeEBt9WwYKxppT2jd2/duxehaZY0XVSF+cQEiwxQIG5j9mQNFcyR4MTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:13:37.398447Z"},"content_sha256":"1ebc7e6f969c9772f7152259d2239d773a9dc6883da8f3ab9590aa56c4f4a528","schema_version":"1.0","event_id":"sha256:1ebc7e6f969c9772f7152259d2239d773a9dc6883da8f3ab9590aa56c4f4a528"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5SVDBODKLWF6HK3KQKV4XI7SI/bundle.json","state_url":"https://pith.science/pith/L5SVDBODKLWF6HK3KQKV4XI7SI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5SVDBODKLWF6HK3KQKV4XI7SI/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":"2026-06-25T19:13:37Z","links":{"resolver":"https://pith.science/pith/L5SVDBODKLWF6HK3KQKV4XI7SI","bundle":"https://pith.science/pith/L5SVDBODKLWF6HK3KQKV4XI7SI/bundle.json","state":"https://pith.science/pith/L5SVDBODKLWF6HK3KQKV4XI7SI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5SVDBODKLWF6HK3KQKV4XI7SI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:L5SVDBODKLWF6HK3KQKV4XI7SI","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":"372da97894b34cde1fc1ec44d6a65f56004c58319f8ee5afeb5651fa705f4423","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-05-16T18:43:05Z","title_canon_sha256":"f5e0fbfa5ab2edce6d700de9d3b227ff9774c2935df6bc27501bf1968ad21adc"},"schema_version":"1.0","source":{"id":"0805.2599","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2599","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2599v3","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2599","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"pith_short_12","alias_value":"L5SVDBODKLWF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"L5SVDBODKLWF6HK3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"L5SVDBOD","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1ebc7e6f969c9772f7152259d2239d773a9dc6883da8f3ab9590aa56c4f4a528","target":"graph","created_at":"2026-05-18T04:37:34Z","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 present paper deals with an \\emph{intrinsic} investigation of the notion of a concurrent $\\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\\beta$-change, namely the energy $\\beta$-change ($\\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \\ B:=g(\\bar{\\zeta},\\bar{\\eta})$; $\\bar{\\zeta} $ being a concurrent $\\pi$-vector field), is established. The relation between the two Barthel connections $\\Gamma$ and $\\widet","authors_text":"A. Soleiman, Nabil L. Youssef, S. H. Abed","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-05-16T18:43:05Z","title":"Concurrent $\\pi$-vector fields and energy beta-change"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2599","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":"sha256:65a278546f8c59a720e0d8f95ee96f0da0194bc111d8a9587699cffbb9fb45a7","target":"record","created_at":"2026-05-18T04:37:34Z","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":"372da97894b34cde1fc1ec44d6a65f56004c58319f8ee5afeb5651fa705f4423","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-05-16T18:43:05Z","title_canon_sha256":"f5e0fbfa5ab2edce6d700de9d3b227ff9774c2935df6bc27501bf1968ad21adc"},"schema_version":"1.0","source":{"id":"0805.2599","kind":"arxiv","version":3}},"canonical_sha256":"5f655185c352ec5f1d5b54155e5d1f92323530366b505f900e77bac98c6b524e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f655185c352ec5f1d5b54155e5d1f92323530366b505f900e77bac98c6b524e","first_computed_at":"2026-05-18T04:37:34.500139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:34.500139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DupnL7fIegUUhz/HDh4y0KWVKk1YcUo4Yn86TbubC/bj+aCX0825dD4ZPsDZKPqxlr4SDnCJQ0KQRlushzgHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:34.500602Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.2599","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65a278546f8c59a720e0d8f95ee96f0da0194bc111d8a9587699cffbb9fb45a7","sha256:1ebc7e6f969c9772f7152259d2239d773a9dc6883da8f3ab9590aa56c4f4a528"],"state_sha256":"3be37108ec5b1d0695debe162fc7beab7d2f5f312679870e3efd5fac8e7b5dd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYvtYWdsjGRhqzQLcd9jmW0TE0OcIFwr13xCS27iCL0c3ewe+We00CtOtEi1kh/H7q6ff1Hv5qosVIH+vRFeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:13:37.400456Z","bundle_sha256":"7a7b2e77db6f5f729b58847a906a3f550c1f49007528d417940bf603c13e94d5"}}