{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DSF7UD6KL735AQQCU2SO45U4S6","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":"4f7a082f056829958b4a304eab616d5ad8b47283c42925621533bdbb7ba13404","cross_cats_sorted":["cond-mat.supr-con","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-09T21:49:51Z","title_canon_sha256":"7333bf5fc8c52fc10218adfab4c8efa6c1e9c95091daba9c62081f47e3d7fbab"},"schema_version":"1.0","source":{"id":"1207.2191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2191","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2191v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2191","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"DSF7UD6KL735","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DSF7UD6KL735AQQC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DSF7UD6K","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:ad77635d807f26c22fb329525ab55a110dd849b1f2f66fe14024f639ad28a4d2","target":"graph","created_at":"2026-05-18T03:51:24Z","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 boundary value problem related to a parabolic higher order operator with a small parameter is analized. When the small parameter tends to zero, the reduced operator is hyperbolic. When t tends to infinity a parabolic hyperbolic boundary layer appears. In this paper a rigorous asymptotic approximation uniformly valid for all t is established.","authors_text":"Monica De Angelis","cross_cats":["cond-mat.supr-con","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-09T21:49:51Z","title":"Parabolic - hyperbolic boundary layer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2191","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":"sha256:6e768228e7b225051ca9b64f8528785098cd29115f7066352775cad986bc6011","target":"record","created_at":"2026-05-18T03:51:24Z","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":"4f7a082f056829958b4a304eab616d5ad8b47283c42925621533bdbb7ba13404","cross_cats_sorted":["cond-mat.supr-con","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-09T21:49:51Z","title_canon_sha256":"7333bf5fc8c52fc10218adfab4c8efa6c1e9c95091daba9c62081f47e3d7fbab"},"schema_version":"1.0","source":{"id":"1207.2191","kind":"arxiv","version":1}},"canonical_sha256":"1c8bfa0fca5ff7d04202a6a4ee769c97971b4067527e5d7baa7dc6ebce7af4de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c8bfa0fca5ff7d04202a6a4ee769c97971b4067527e5d7baa7dc6ebce7af4de","first_computed_at":"2026-05-18T03:51:24.763777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:24.763777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2NI1eozfG79gnPXk0h62DsMV8OmcJId4eGyOBoTRlMej7iV6SNMZwv9SLJaNkZfKxHFQvgKrsNj19SZiHOdiDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:24.764530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e768228e7b225051ca9b64f8528785098cd29115f7066352775cad986bc6011","sha256:ad77635d807f26c22fb329525ab55a110dd849b1f2f66fe14024f639ad28a4d2"],"state_sha256":"d3ad284429422e44c53d95100be4904c3d491577bf6d34220622149e85d8eac7"}