{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5J6YSEGT4RA4HPVK3JEJLLEVLI","short_pith_number":"pith:5J6YSEGT","canonical_record":{"source":{"id":"1610.00798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-03T23:48:18Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a61a656d5c4fcb1c61a4a757946d20723225d77ed81e6fd31a291b667258893e","abstract_canon_sha256":"2dbc4177347c4e38a815f33be5b7be7ce83b85f8035266493ae3c7611a514595"},"schema_version":"1.0"},"canonical_sha256":"ea7d8910d3e441c3beaada4895ac955a13bac5492ee828d1159ac097ea692508","source":{"kind":"arxiv","id":"1610.00798","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00798","created_at":"2026-05-18T00:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00798v2","created_at":"2026-05-18T00:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00798","created_at":"2026-05-18T00:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"5J6YSEGT4RA4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5J6YSEGT4RA4HPVK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5J6YSEGT","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5J6YSEGT4RA4HPVK3JEJLLEVLI","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-03T23:48:18Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a61a656d5c4fcb1c61a4a757946d20723225d77ed81e6fd31a291b667258893e","abstract_canon_sha256":"2dbc4177347c4e38a815f33be5b7be7ce83b85f8035266493ae3c7611a514595"},"schema_version":"1.0"},"canonical_sha256":"ea7d8910d3e441c3beaada4895ac955a13bac5492ee828d1159ac097ea692508","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:21.014595Z","signature_b64":"DlrDYoIB1PpkoL+v9QLLQ2QCGTqLEjrrsP896jLhqYWnWx2aI0XsvlFDcgB3oYXY2EffE5c5oxWs9iG/wLOWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea7d8910d3e441c3beaada4895ac955a13bac5492ee828d1159ac097ea692508","last_reissued_at":"2026-05-18T00:41:21.013898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:21.013898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00798","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":"2026-05-18T00:41:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdnpVOtM+lwqOY4bfqnV/XZA3wsa7AhCPlCCKwslAPSF77l7V/XWpNSDBI/VK4+Cb6sp02TcnKkuErXsVWfsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:57:33.861172Z"},"content_sha256":"d896bd34937d9b599db26790c2b30625efb2da1dcf8d034f04d3a379d4af9ace","schema_version":"1.0","event_id":"sha256:d896bd34937d9b599db26790c2b30625efb2da1dcf8d034f04d3a379d4af9ace"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5J6YSEGT4RA4HPVK3JEJLLEVLI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anisotropic finite elements for elliptic problems with singular data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Ignacio Ojea","submitted_at":"2016-10-03T23:48:18Z","abstract_excerpt":"We study the problem $-\\Delta u = \\gamma$, where $\\gamma$ is a singular measure, with support on a curve or a point. We prove that optimal rates of convergence for the finite element method can be obtained using properly graded meshes. In particular, we consider isotropic graded meshes when $\\gamma$ is a point Dirac delta, and anisotropic graded meshes when $\\gamma$ is a measure supported on a segment. Numerical experiments are shown that verify our results, and lead to interesting observations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00798","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":"2026-05-18T00:41:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJM4dTAZdOxSlCgi4iSWfRPx1QbWGUHAZ2PdLsF2Ty1HNfowVktBAbVC0To/+K6LPrM6bHc1VY/Jn62GXCjnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:57:33.861520Z"},"content_sha256":"fec1cbb62794b0b5971fffe8c97b321022a10938c58a5272160bfa83911d766f","schema_version":"1.0","event_id":"sha256:fec1cbb62794b0b5971fffe8c97b321022a10938c58a5272160bfa83911d766f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI/bundle.json","state_url":"https://pith.science/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI/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":"2026-06-26T16:57:33Z","links":{"resolver":"https://pith.science/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI","bundle":"https://pith.science/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI/bundle.json","state":"https://pith.science/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5J6YSEGT4RA4HPVK3JEJLLEVLI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5J6YSEGT4RA4HPVK3JEJLLEVLI","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":"2dbc4177347c4e38a815f33be5b7be7ce83b85f8035266493ae3c7611a514595","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-03T23:48:18Z","title_canon_sha256":"a61a656d5c4fcb1c61a4a757946d20723225d77ed81e6fd31a291b667258893e"},"schema_version":"1.0","source":{"id":"1610.00798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00798","created_at":"2026-05-18T00:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00798v2","created_at":"2026-05-18T00:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00798","created_at":"2026-05-18T00:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"5J6YSEGT4RA4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5J6YSEGT4RA4HPVK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5J6YSEGT","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:fec1cbb62794b0b5971fffe8c97b321022a10938c58a5272160bfa83911d766f","target":"graph","created_at":"2026-05-18T00:41:21Z","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 study the problem $-\\Delta u = \\gamma$, where $\\gamma$ is a singular measure, with support on a curve or a point. We prove that optimal rates of convergence for the finite element method can be obtained using properly graded meshes. In particular, we consider isotropic graded meshes when $\\gamma$ is a point Dirac delta, and anisotropic graded meshes when $\\gamma$ is a measure supported on a segment. Numerical experiments are shown that verify our results, and lead to interesting observations.","authors_text":"Ignacio Ojea","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-03T23:48:18Z","title":"Anisotropic finite elements for elliptic problems with singular data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00798","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:d896bd34937d9b599db26790c2b30625efb2da1dcf8d034f04d3a379d4af9ace","target":"record","created_at":"2026-05-18T00:41:21Z","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":"2dbc4177347c4e38a815f33be5b7be7ce83b85f8035266493ae3c7611a514595","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-03T23:48:18Z","title_canon_sha256":"a61a656d5c4fcb1c61a4a757946d20723225d77ed81e6fd31a291b667258893e"},"schema_version":"1.0","source":{"id":"1610.00798","kind":"arxiv","version":2}},"canonical_sha256":"ea7d8910d3e441c3beaada4895ac955a13bac5492ee828d1159ac097ea692508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea7d8910d3e441c3beaada4895ac955a13bac5492ee828d1159ac097ea692508","first_computed_at":"2026-05-18T00:41:21.013898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:21.013898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DlrDYoIB1PpkoL+v9QLLQ2QCGTqLEjrrsP896jLhqYWnWx2aI0XsvlFDcgB3oYXY2EffE5c5oxWs9iG/wLOWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:21.014595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d896bd34937d9b599db26790c2b30625efb2da1dcf8d034f04d3a379d4af9ace","sha256:fec1cbb62794b0b5971fffe8c97b321022a10938c58a5272160bfa83911d766f"],"state_sha256":"8d3fe88a52c938fcdebeeeedede8c2cd0b20a8cf246882b6698e96cfdd8f3d45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dstQtgTJgIEBDRUAUHjLFfJoaiW8UJ5w1hIvlxzi1qw2jtccs1vb04t1DyLVgIVdceBaPgZeAM+LbgKMZbMPCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:57:33.863368Z","bundle_sha256":"99c4c59fdb0bd86e9db1c784b9eb0c87dc887801b5bf998e779e15adceaa18c2"}}