{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:A5NMNK56NGOXFXQC5UEAW6FA3A","short_pith_number":"pith:A5NMNK56","canonical_record":{"source":{"id":"1704.06126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-20T13:13:50Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"55c1293c481846e8fcb0c383381ed2c44846c0861f5cbb35909f86f13edd3a56","abstract_canon_sha256":"3f07153c65345eaee491912a9423f35330a3e5230c3d28bc139d201e971521d3"},"schema_version":"1.0"},"canonical_sha256":"075ac6abbe699d72de02ed080b78a0d81abb9e45ec8c3b92699e9916b1af1faf","source":{"kind":"arxiv","id":"1704.06126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06126","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06126v1","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06126","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"A5NMNK56NGOX","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A5NMNK56NGOXFXQC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A5NMNK56","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:A5NMNK56NGOXFXQC5UEAW6FA3A","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-20T13:13:50Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"55c1293c481846e8fcb0c383381ed2c44846c0861f5cbb35909f86f13edd3a56","abstract_canon_sha256":"3f07153c65345eaee491912a9423f35330a3e5230c3d28bc139d201e971521d3"},"schema_version":"1.0"},"canonical_sha256":"075ac6abbe699d72de02ed080b78a0d81abb9e45ec8c3b92699e9916b1af1faf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:03.227902Z","signature_b64":"AT7ycpc30KoZT9Ivt0sCGwAD2PTUood5HNf1Ud29ILLkM9rlnksSNpJJaJ5H0kHSsJGGxMcFlXM3DPde1OMdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"075ac6abbe699d72de02ed080b78a0d81abb9e45ec8c3b92699e9916b1af1faf","last_reissued_at":"2026-05-18T00:46:03.227374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:03.227374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06126","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":"2026-05-18T00:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fYokMh1tnMW/6aXOuJdqWtvZxKg4U4teNWjc9mh5hvyEIWsUEs7ya2Cjfc1wpd4xvEBnERPEHS5hVPFlrudgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:33:57.274123Z"},"content_sha256":"f06aae18437d0d00deb35784eca4df4b167f6b3e84de106a5637331dcb092b36","schema_version":"1.0","event_id":"sha256:f06aae18437d0d00deb35784eca4df4b167f6b3e84de106a5637331dcb092b36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:A5NMNK56NGOXFXQC5UEAW6FA3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral representation for fractional Laplace-Beltrami operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CA","authors_text":"Angel D. Martinez, Antonio Cordoba, Diego Alonso-Oran","submitted_at":"2017-04-20T13:13:50Z","abstract_excerpt":"In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of essentially the same result. One of them deals with compact manifolds with or without boundary, while the other approach treats the case of riemannian manifolds without boundary whose Ricci curvature is uniformly bounded below."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06126","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":"2026-05-18T00:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sn/HgfCpy5ouKrFU4aJ+8zeUwDrm19xDkxZgTLuVHGJ2evrwn9WZVks+bxtYGTl47QIDGiVDD8iebes5R0pMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:33:57.274500Z"},"content_sha256":"7c6a71221ab334e40fff49ae3b656c8ed1ab58bc4e4d34643914bcf32278ccab","schema_version":"1.0","event_id":"sha256:7c6a71221ab334e40fff49ae3b656c8ed1ab58bc4e4d34643914bcf32278ccab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5NMNK56NGOXFXQC5UEAW6FA3A/bundle.json","state_url":"https://pith.science/pith/A5NMNK56NGOXFXQC5UEAW6FA3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5NMNK56NGOXFXQC5UEAW6FA3A/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":"2026-06-27T12:33:57Z","links":{"resolver":"https://pith.science/pith/A5NMNK56NGOXFXQC5UEAW6FA3A","bundle":"https://pith.science/pith/A5NMNK56NGOXFXQC5UEAW6FA3A/bundle.json","state":"https://pith.science/pith/A5NMNK56NGOXFXQC5UEAW6FA3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5NMNK56NGOXFXQC5UEAW6FA3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A5NMNK56NGOXFXQC5UEAW6FA3A","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":"3f07153c65345eaee491912a9423f35330a3e5230c3d28bc139d201e971521d3","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-20T13:13:50Z","title_canon_sha256":"55c1293c481846e8fcb0c383381ed2c44846c0861f5cbb35909f86f13edd3a56"},"schema_version":"1.0","source":{"id":"1704.06126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06126","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06126v1","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06126","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"A5NMNK56NGOX","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A5NMNK56NGOXFXQC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A5NMNK56","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:7c6a71221ab334e40fff49ae3b656c8ed1ab58bc4e4d34643914bcf32278ccab","target":"graph","created_at":"2026-05-18T00:46:03Z","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":"In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of essentially the same result. One of them deals with compact manifolds with or without boundary, while the other approach treats the case of riemannian manifolds without boundary whose Ricci curvature is uniformly bounded below.","authors_text":"Angel D. Martinez, Antonio Cordoba, Diego Alonso-Oran","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-20T13:13:50Z","title":"Integral representation for fractional Laplace-Beltrami operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06126","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:f06aae18437d0d00deb35784eca4df4b167f6b3e84de106a5637331dcb092b36","target":"record","created_at":"2026-05-18T00:46:03Z","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":"3f07153c65345eaee491912a9423f35330a3e5230c3d28bc139d201e971521d3","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-20T13:13:50Z","title_canon_sha256":"55c1293c481846e8fcb0c383381ed2c44846c0861f5cbb35909f86f13edd3a56"},"schema_version":"1.0","source":{"id":"1704.06126","kind":"arxiv","version":1}},"canonical_sha256":"075ac6abbe699d72de02ed080b78a0d81abb9e45ec8c3b92699e9916b1af1faf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"075ac6abbe699d72de02ed080b78a0d81abb9e45ec8c3b92699e9916b1af1faf","first_computed_at":"2026-05-18T00:46:03.227374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:03.227374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AT7ycpc30KoZT9Ivt0sCGwAD2PTUood5HNf1Ud29ILLkM9rlnksSNpJJaJ5H0kHSsJGGxMcFlXM3DPde1OMdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:03.227902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f06aae18437d0d00deb35784eca4df4b167f6b3e84de106a5637331dcb092b36","sha256:7c6a71221ab334e40fff49ae3b656c8ed1ab58bc4e4d34643914bcf32278ccab"],"state_sha256":"96f64def9bd69e030975edd9b1d153932a71d391fda37a9363f3ffd09188161c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0irVcn9XnwkQ0eE/bn2pd7tomlsD+9BNV4Kh217jrbpPUT4beDD4nrEAchycYTzScih2Y+ov2D6rzHymaJmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:33:57.276325Z","bundle_sha256":"3c3c3595887ba9c90b1bbc75e81408728eb9b52d625350867eacdf42fca53e66"}}