{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UFO3C5JEQ25J66EUVH73OED5DO","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":"1569d4b6262801c101456048cc7854d1fcdb6d9d47a3c9482dea3ec443dde472","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-22T14:31:22Z","title_canon_sha256":"877c6a3874f4cf09b79980ab094dc45d6f23d0c9b7dabd4f4dd098d68cbcef83"},"schema_version":"1.0","source":{"id":"1102.4520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4520","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4520v2","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4520","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"pith_short_12","alias_value":"UFO3C5JEQ25J","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UFO3C5JEQ25J66EU","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UFO3C5JE","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:9257dae78f23aa4d5f3ddde8758f6a30637e64fc39fa5c19634faeb97f14bde8","target":"graph","created_at":"2026-05-18T03:19:46Z","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":"Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its derivatives in the $L_1$ norm. For this, in this paper we establish the corresponding lower bounds. Both upper and lower bounds explicitly show any dependence on the singular perturbation parameter.","authors_text":"Natalia Kopteva, Sebastian Franz","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-22T14:31:22Z","title":"On the sharpness of Green's function estimates for a convection-diffusion problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4520","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":"sha256:958520469408f82d6f390552f27adce6fca05092df41bba421d35319c2c85cf1","target":"record","created_at":"2026-05-18T03:19:46Z","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":"1569d4b6262801c101456048cc7854d1fcdb6d9d47a3c9482dea3ec443dde472","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-22T14:31:22Z","title_canon_sha256":"877c6a3874f4cf09b79980ab094dc45d6f23d0c9b7dabd4f4dd098d68cbcef83"},"schema_version":"1.0","source":{"id":"1102.4520","kind":"arxiv","version":2}},"canonical_sha256":"a15db1752486ba9f7894a9ffb7107d1b99efc994c9b0c1c108125db142f0e86a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a15db1752486ba9f7894a9ffb7107d1b99efc994c9b0c1c108125db142f0e86a","first_computed_at":"2026-05-18T03:19:46.400473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:46.400473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kGYVqcPXtoUrQ1X+O7nbU0/Gwe1ePQZsBabOxl2GRgNyc/f9WdbspNEY8hzqtMdUWpo5Go0/m0pfhdlKDqzfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:46.401089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:958520469408f82d6f390552f27adce6fca05092df41bba421d35319c2c85cf1","sha256:9257dae78f23aa4d5f3ddde8758f6a30637e64fc39fa5c19634faeb97f14bde8"],"state_sha256":"5936f4ae21261b37120d3cfeeb22e52d26b66782f5dffb8a9544aa97e143f974"}