{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CDPH5KDNHLNEE62KCRVJREYKQP","short_pith_number":"pith:CDPH5KDN","canonical_record":{"source":{"id":"1810.07499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-17T12:16:36Z","cross_cats_sorted":[],"title_canon_sha256":"9fa4f8e53257d3ec72992705231c1ed44b96a48135bc8a457a0f5937508f6bdc","abstract_canon_sha256":"770d11447c98a41a600ae14f84709fbb4ed970c36aff3ae649c38782adf4d016"},"schema_version":"1.0"},"canonical_sha256":"10de7ea86d3ada427b4a146a98930a83c5d20fc37cf0e3361978b5482b27b1d1","source":{"kind":"arxiv","id":"1810.07499","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07499","created_at":"2026-05-17T23:57:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07499v2","created_at":"2026-05-17T23:57:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07499","created_at":"2026-05-17T23:57:56Z"},{"alias_kind":"pith_short_12","alias_value":"CDPH5KDNHLNE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CDPH5KDNHLNEE62K","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CDPH5KDN","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CDPH5KDNHLNEE62KCRVJREYKQP","target":"record","payload":{"canonical_record":{"source":{"id":"1810.07499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-17T12:16:36Z","cross_cats_sorted":[],"title_canon_sha256":"9fa4f8e53257d3ec72992705231c1ed44b96a48135bc8a457a0f5937508f6bdc","abstract_canon_sha256":"770d11447c98a41a600ae14f84709fbb4ed970c36aff3ae649c38782adf4d016"},"schema_version":"1.0"},"canonical_sha256":"10de7ea86d3ada427b4a146a98930a83c5d20fc37cf0e3361978b5482b27b1d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:56.962487Z","signature_b64":"ZlSZLeU/Z5qka8DNeT0co2SVGUKC0+kInxrm507Rq+d4HrJjlRPdmAE2NnU7ytQyq79inlNKzqvYZmBCXBk7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10de7ea86d3ada427b4a146a98930a83c5d20fc37cf0e3361978b5482b27b1d1","last_reissued_at":"2026-05-17T23:57:56.961934Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:56.961934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.07499","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CK4sJ+9RKapRqofrSYhDkh6mLZ2ICaAZGtlhjKSj5XbdPRiWdhIz3LF5B9W1tZGiCZq7P9GeSlz//li2RRnMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:53:55.289481Z"},"content_sha256":"0a6248d47267fc05da96cc925b799aa410c4d0bd452099caf56c09755498b0f2","schema_version":"1.0","event_id":"sha256:0a6248d47267fc05da96cc925b799aa410c4d0bd452099caf56c09755498b0f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CDPH5KDNHLNEE62KCRVJREYKQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anisotropic nonlocal diffusion equations with singular forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Rodr\\'iguez, Arturo de Pablo, Fernando Quir\\'os","submitted_at":"2018-10-17T12:16:36Z","abstract_excerpt":"We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very few regularity and that the spectral measure can be singular in some directions. The proofs require having good enough estimates for the corresponding heat kernels and their derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07499","kind":"arxiv","version":2},"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":"2026-05-17T23:57:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OmSJW1GyTQWFunAOSEMUTs2Jj04UFzZ5jKlS6U46JmErHZoXHwHZSsvQP3/mRR/PWH65puBuZRh8mAnWeCoUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:53:55.289832Z"},"content_sha256":"0a78df806ed827326df78be52aff3fc4b833af8e41e84bc594fc2c6f68a5e249","schema_version":"1.0","event_id":"sha256:0a78df806ed827326df78be52aff3fc4b833af8e41e84bc594fc2c6f68a5e249"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDPH5KDNHLNEE62KCRVJREYKQP/bundle.json","state_url":"https://pith.science/pith/CDPH5KDNHLNEE62KCRVJREYKQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDPH5KDNHLNEE62KCRVJREYKQP/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":"2026-05-30T00:53:55Z","links":{"resolver":"https://pith.science/pith/CDPH5KDNHLNEE62KCRVJREYKQP","bundle":"https://pith.science/pith/CDPH5KDNHLNEE62KCRVJREYKQP/bundle.json","state":"https://pith.science/pith/CDPH5KDNHLNEE62KCRVJREYKQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDPH5KDNHLNEE62KCRVJREYKQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CDPH5KDNHLNEE62KCRVJREYKQP","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":"770d11447c98a41a600ae14f84709fbb4ed970c36aff3ae649c38782adf4d016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-17T12:16:36Z","title_canon_sha256":"9fa4f8e53257d3ec72992705231c1ed44b96a48135bc8a457a0f5937508f6bdc"},"schema_version":"1.0","source":{"id":"1810.07499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07499","created_at":"2026-05-17T23:57:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07499v2","created_at":"2026-05-17T23:57:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07499","created_at":"2026-05-17T23:57:56Z"},{"alias_kind":"pith_short_12","alias_value":"CDPH5KDNHLNE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CDPH5KDNHLNEE62K","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CDPH5KDN","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:0a78df806ed827326df78be52aff3fc4b833af8e41e84bc594fc2c6f68a5e249","target":"graph","created_at":"2026-05-17T23:57:56Z","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":"We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very few regularity and that the spectral measure can be singular in some directions. The proofs require having good enough estimates for the corresponding heat kernels and their derivatives.","authors_text":"Ana Rodr\\'iguez, Arturo de Pablo, Fernando Quir\\'os","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-17T12:16:36Z","title":"Anisotropic nonlocal diffusion equations with singular forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07499","kind":"arxiv","version":2},"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":"sha256:0a6248d47267fc05da96cc925b799aa410c4d0bd452099caf56c09755498b0f2","target":"record","created_at":"2026-05-17T23:57:56Z","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":"770d11447c98a41a600ae14f84709fbb4ed970c36aff3ae649c38782adf4d016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-17T12:16:36Z","title_canon_sha256":"9fa4f8e53257d3ec72992705231c1ed44b96a48135bc8a457a0f5937508f6bdc"},"schema_version":"1.0","source":{"id":"1810.07499","kind":"arxiv","version":2}},"canonical_sha256":"10de7ea86d3ada427b4a146a98930a83c5d20fc37cf0e3361978b5482b27b1d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10de7ea86d3ada427b4a146a98930a83c5d20fc37cf0e3361978b5482b27b1d1","first_computed_at":"2026-05-17T23:57:56.961934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:56.961934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZlSZLeU/Z5qka8DNeT0co2SVGUKC0+kInxrm507Rq+d4HrJjlRPdmAE2NnU7ytQyq79inlNKzqvYZmBCXBk7Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:56.962487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a6248d47267fc05da96cc925b799aa410c4d0bd452099caf56c09755498b0f2","sha256:0a78df806ed827326df78be52aff3fc4b833af8e41e84bc594fc2c6f68a5e249"],"state_sha256":"11e464547c9d0cd03a7400b4a6c21330294cade5e25134516e28f989d1ca186a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WLhpayahvNnry0IM7Dg1h0CQuwOklSwT4OlC1slb80RiRP5x9uBsnRSuwCiidA4PBgENqh0msWR5V2L05QlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:53:55.292002Z","bundle_sha256":"37cc15c3858882df9b790f00da2edf0560196901cefacf3677adcfe7a9d1e2d5"}}