{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5SQOAKYDEU5VMXC2EO4XFJRHY2","short_pith_number":"pith:5SQOAKYD","canonical_record":{"source":{"id":"1508.06418","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-26T09:23:53Z","cross_cats_sorted":[],"title_canon_sha256":"391b26b97427a00ab66ba28935582e26b3a3fb0dcac06036ea0cd373eaf054c1","abstract_canon_sha256":"6034710623b841f2d279ddf07569c6b17670e58f460916271e7499cb1db494ad"},"schema_version":"1.0"},"canonical_sha256":"eca0e02b03253b565c5a23b972a627c6bf4d543683f6e2ac550500d2995eac9d","source":{"kind":"arxiv","id":"1508.06418","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06418","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06418v3","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06418","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"5SQOAKYDEU5V","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5SQOAKYDEU5VMXC2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5SQOAKYD","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5SQOAKYDEU5VMXC2EO4XFJRHY2","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06418","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-26T09:23:53Z","cross_cats_sorted":[],"title_canon_sha256":"391b26b97427a00ab66ba28935582e26b3a3fb0dcac06036ea0cd373eaf054c1","abstract_canon_sha256":"6034710623b841f2d279ddf07569c6b17670e58f460916271e7499cb1db494ad"},"schema_version":"1.0"},"canonical_sha256":"eca0e02b03253b565c5a23b972a627c6bf4d543683f6e2ac550500d2995eac9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:30.664103Z","signature_b64":"OOIMuqDcRhoMIVgrvE2o2MojmpDv1OF11Es9yzQy/SgtB7gfpw3ehWAvVW5EpM1L18yJfz3whNI6Jl7KT51cCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eca0e02b03253b565c5a23b972a627c6bf4d543683f6e2ac550500d2995eac9d","last_reissued_at":"2026-05-18T01:12:30.663730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:30.663730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06418","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":"2026-05-18T01:12:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3pT+baZjCjhJB8UkoQrnGla+tyxaUfLVPpRCkLJGcQy3M64En4txiJWJab9XOAUngpDkG/Q/h6B1Ak75+e7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:55:24.609128Z"},"content_sha256":"752e6cf0662c786c6baaf59f6b0f65158cb542ad4beb736e91dc89f8223ab862","schema_version":"1.0","event_id":"sha256:752e6cf0662c786c6baaf59f6b0f65158cb542ad4beb736e91dc89f8223ab862"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5SQOAKYDEU5VMXC2EO4XFJRHY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic Mappings into non-negatively curved Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Irina Tsyganok, Sergey Stepanov","submitted_at":"2015-08-26T09:23:53Z","abstract_excerpt":"Fifty years ago, Eells and Sampson have proved a famous theorem in which they argued that any harmonic mapping $f:(M,g) \\rightarrow (\\bar{M},\\bar{g})$ is totally geodesic if $(M, g)$ is a compact manifold with the nonnegative Ricci tensor and the section curvature of $(\\bar{M},\\bar{g})$ is nonpositive. Moreover, other main results of the theory of harmonic mappings \"in the large\" are the results on harmonic maps into nonpositively curved Riemannian manifolds.\n  In our paper we develop a theory of harmonic mappings into Riemannian manifolds with nonnegative sectional curvature. In particular, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06418","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":"2026-05-18T01:12:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zsG8E4DCMRYqqT7J3r58Y+sf7z2u2hZGzgrB0O31/WIZiCTkPvoUAuZcQEnMNOGFwnEywYq7BNUkF3e4dY1cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:55:24.609910Z"},"content_sha256":"5b45104e9cb8c6a41c39d55f1cf7aaa142a6b526d1f1fac537dd077320dda47f","schema_version":"1.0","event_id":"sha256:5b45104e9cb8c6a41c39d55f1cf7aaa142a6b526d1f1fac537dd077320dda47f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2/bundle.json","state_url":"https://pith.science/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2/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":"2026-05-31T06:55:24Z","links":{"resolver":"https://pith.science/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2","bundle":"https://pith.science/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2/bundle.json","state":"https://pith.science/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SQOAKYDEU5VMXC2EO4XFJRHY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5SQOAKYDEU5VMXC2EO4XFJRHY2","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":"6034710623b841f2d279ddf07569c6b17670e58f460916271e7499cb1db494ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-26T09:23:53Z","title_canon_sha256":"391b26b97427a00ab66ba28935582e26b3a3fb0dcac06036ea0cd373eaf054c1"},"schema_version":"1.0","source":{"id":"1508.06418","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06418","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06418v3","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06418","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"5SQOAKYDEU5V","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5SQOAKYDEU5VMXC2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5SQOAKYD","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:5b45104e9cb8c6a41c39d55f1cf7aaa142a6b526d1f1fac537dd077320dda47f","target":"graph","created_at":"2026-05-18T01:12:30Z","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":"Fifty years ago, Eells and Sampson have proved a famous theorem in which they argued that any harmonic mapping $f:(M,g) \\rightarrow (\\bar{M},\\bar{g})$ is totally geodesic if $(M, g)$ is a compact manifold with the nonnegative Ricci tensor and the section curvature of $(\\bar{M},\\bar{g})$ is nonpositive. Moreover, other main results of the theory of harmonic mappings \"in the large\" are the results on harmonic maps into nonpositively curved Riemannian manifolds.\n  In our paper we develop a theory of harmonic mappings into Riemannian manifolds with nonnegative sectional curvature. In particular, w","authors_text":"Irina Tsyganok, Sergey Stepanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-26T09:23:53Z","title":"Harmonic Mappings into non-negatively curved Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06418","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":"sha256:752e6cf0662c786c6baaf59f6b0f65158cb542ad4beb736e91dc89f8223ab862","target":"record","created_at":"2026-05-18T01:12:30Z","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":"6034710623b841f2d279ddf07569c6b17670e58f460916271e7499cb1db494ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-26T09:23:53Z","title_canon_sha256":"391b26b97427a00ab66ba28935582e26b3a3fb0dcac06036ea0cd373eaf054c1"},"schema_version":"1.0","source":{"id":"1508.06418","kind":"arxiv","version":3}},"canonical_sha256":"eca0e02b03253b565c5a23b972a627c6bf4d543683f6e2ac550500d2995eac9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eca0e02b03253b565c5a23b972a627c6bf4d543683f6e2ac550500d2995eac9d","first_computed_at":"2026-05-18T01:12:30.663730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:30.663730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OOIMuqDcRhoMIVgrvE2o2MojmpDv1OF11Es9yzQy/SgtB7gfpw3ehWAvVW5EpM1L18yJfz3whNI6Jl7KT51cCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:30.664103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06418","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752e6cf0662c786c6baaf59f6b0f65158cb542ad4beb736e91dc89f8223ab862","sha256:5b45104e9cb8c6a41c39d55f1cf7aaa142a6b526d1f1fac537dd077320dda47f"],"state_sha256":"17742c0b536c9b20a0abf0304af5d2db57c2a19c16aea1bb7458759989cc0486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alMuH/ijbyOz3vKAqYkoZAjPEJybeWXBzGgJ4shk4NpMy1xfKYBQJnfP2/PZcRQ4phMugpRjSqAi6XlcrD4iCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:55:24.614380Z","bundle_sha256":"f1e28f57e4cd63a7c497c9a4010551372234f50100d4c755f5f39f9802e74cb0"}}