{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CGYKKNWYSIOOEVXEVAQPIFZ5CW","short_pith_number":"pith:CGYKKNWY","canonical_record":{"source":{"id":"1103.2948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-15T16:13:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ad0c04c5b52471aea68992180f171f96238f8d645015b8cc20cdea92c2e20808","abstract_canon_sha256":"5e75142d45052a6fbbfa048524c38b81050d81e698b4758a28cf78c8a946a3ae"},"schema_version":"1.0"},"canonical_sha256":"11b0a536d8921ce256e4a820f4173d15a53f6633d1039cbe0c289fda96fd774d","source":{"kind":"arxiv","id":"1103.2948","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2948","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2948v2","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2948","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"CGYKKNWYSIOO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CGYKKNWYSIOOEVXE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CGYKKNWY","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CGYKKNWYSIOOEVXEVAQPIFZ5CW","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-15T16:13:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ad0c04c5b52471aea68992180f171f96238f8d645015b8cc20cdea92c2e20808","abstract_canon_sha256":"5e75142d45052a6fbbfa048524c38b81050d81e698b4758a28cf78c8a946a3ae"},"schema_version":"1.0"},"canonical_sha256":"11b0a536d8921ce256e4a820f4173d15a53f6633d1039cbe0c289fda96fd774d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:19.044003Z","signature_b64":"k8CWo51AaiyK+QwNqZFINILQ1yFXV2l63qnjSAcvVB+eycVfhBzl1D3cKKkOQJV55wz2Jde42LVAOCYa9DUPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11b0a536d8921ce256e4a820f4173d15a53f6633d1039cbe0c289fda96fd774d","last_reissued_at":"2026-05-18T02:22:19.043409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:19.043409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2948","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":"2026-05-18T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8jMPftYYtsYca8cKy9r62OPuT3cMdmHyoU5+DUgpOGgwFMwe0HYK0UOl62sg9QlCI6Vwvy2eKnXpb8JzTHxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:56.931774Z"},"content_sha256":"c8ed698b6c993b6587fda76f216b368cdee77b5f0a16ffe6deb2ef95388731e2","schema_version":"1.0","event_id":"sha256:c8ed698b6c993b6587fda76f216b368cdee77b5f0a16ffe6deb2ef95388731e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CGYKKNWYSIOOEVXEVAQPIFZ5CW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"N. Kopteva, S. Franz","submitted_at":"2011-03-15T16:13:19Z","abstract_excerpt":"A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem.\n  The present article is a more detailed version of our recent paper [7]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2948","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":"2026-05-18T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tp8N1Ox/fc8Mp5mQVmKnRbv72DFcAzzFcyXKLLHcoDIWN2rmbsbpTzsnNDoYZQFf5bsrU3rG7IfmVsD9OdNUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:56.932127Z"},"content_sha256":"61434510b1037c325468bf93f1bfe149540c1398bb0c5206aff2f0a2a39b2dbb","schema_version":"1.0","event_id":"sha256:61434510b1037c325468bf93f1bfe149540c1398bb0c5206aff2f0a2a39b2dbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW/bundle.json","state_url":"https://pith.science/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW/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":"2026-05-31T02:50:56Z","links":{"resolver":"https://pith.science/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW","bundle":"https://pith.science/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW/bundle.json","state":"https://pith.science/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGYKKNWYSIOOEVXEVAQPIFZ5CW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CGYKKNWYSIOOEVXEVAQPIFZ5CW","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":"5e75142d45052a6fbbfa048524c38b81050d81e698b4758a28cf78c8a946a3ae","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-15T16:13:19Z","title_canon_sha256":"ad0c04c5b52471aea68992180f171f96238f8d645015b8cc20cdea92c2e20808"},"schema_version":"1.0","source":{"id":"1103.2948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2948","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2948v2","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2948","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"CGYKKNWYSIOO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CGYKKNWYSIOOEVXE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CGYKKNWY","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:61434510b1037c325468bf93f1bfe149540c1398bb0c5206aff2f0a2a39b2dbb","target":"graph","created_at":"2026-05-18T02:22:19Z","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":"A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem.\n  The present article is a more detailed version of our recent paper [7].","authors_text":"N. Kopteva, S. Franz","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-15T16:13:19Z","title":"Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2948","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:c8ed698b6c993b6587fda76f216b368cdee77b5f0a16ffe6deb2ef95388731e2","target":"record","created_at":"2026-05-18T02:22:19Z","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":"5e75142d45052a6fbbfa048524c38b81050d81e698b4758a28cf78c8a946a3ae","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-15T16:13:19Z","title_canon_sha256":"ad0c04c5b52471aea68992180f171f96238f8d645015b8cc20cdea92c2e20808"},"schema_version":"1.0","source":{"id":"1103.2948","kind":"arxiv","version":2}},"canonical_sha256":"11b0a536d8921ce256e4a820f4173d15a53f6633d1039cbe0c289fda96fd774d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11b0a536d8921ce256e4a820f4173d15a53f6633d1039cbe0c289fda96fd774d","first_computed_at":"2026-05-18T02:22:19.043409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:19.043409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k8CWo51AaiyK+QwNqZFINILQ1yFXV2l63qnjSAcvVB+eycVfhBzl1D3cKKkOQJV55wz2Jde42LVAOCYa9DUPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:19.044003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8ed698b6c993b6587fda76f216b368cdee77b5f0a16ffe6deb2ef95388731e2","sha256:61434510b1037c325468bf93f1bfe149540c1398bb0c5206aff2f0a2a39b2dbb"],"state_sha256":"051484c8433541d73954b812c67bbc8675119291ab0cfb007baf11866d8375cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fON2mVN0vRexteyqOJXhGo1H9p6q3vA25LZycldGs8vQje6lvHZYUxNdAkVD9se2RVvlmUXnALbF2qw6DMhuDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:50:56.934521Z","bundle_sha256":"d260989484657e6c26421d36d846ca0e62dfd026ab40ef9ef40ba4ec88e5c4c2"}}