{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HYOTLOFHGIZJFV7QSUGAHR5EWT","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":"19bbbbd0242167a7719fdca9b085977114291ee58bffda78b7af838c02c35e81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-04T11:58:00Z","title_canon_sha256":"ac815304510ec1d753148dc77577ff78fb9120177bc808a23df6d8a0a213a9b4"},"schema_version":"1.0","source":{"id":"1810.02161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02161","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02161v1","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02161","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"HYOTLOFHGIZJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HYOTLOFHGIZJFV7Q","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HYOTLOFH","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:f37664c11e5c172ae62ee00e88b896a8f5bbf5067f70b9e63b590042b94267fd","target":"graph","created_at":"2026-05-18T00:04:06Z","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":"In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.","authors_text":"Georgy Kitavtsev, Roman M. Taranets","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-04T11:58:00Z","title":"Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02161","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:b7f34c98fd56f51b8f2e3cb771d67732e2645d6c2f4e8ea68f0ff62ad787436b","target":"record","created_at":"2026-05-18T00:04:06Z","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":"19bbbbd0242167a7719fdca9b085977114291ee58bffda78b7af838c02c35e81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-04T11:58:00Z","title_canon_sha256":"ac815304510ec1d753148dc77577ff78fb9120177bc808a23df6d8a0a213a9b4"},"schema_version":"1.0","source":{"id":"1810.02161","kind":"arxiv","version":1}},"canonical_sha256":"3e1d35b8a7323292d7f0950c03c7a4b4c01789d59608aef809b334e317ade4a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e1d35b8a7323292d7f0950c03c7a4b4c01789d59608aef809b334e317ade4a4","first_computed_at":"2026-05-18T00:04:06.062128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:06.062128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tLwPlJMKNlUfFlXIVr0ynoMrNfxyCWh+7M1qUXMyIhyx6eIalsTtROr4XqbJ4VdzWLP2IYCRgUtKrOCgoAyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:06.062812Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7f34c98fd56f51b8f2e3cb771d67732e2645d6c2f4e8ea68f0ff62ad787436b","sha256:f37664c11e5c172ae62ee00e88b896a8f5bbf5067f70b9e63b590042b94267fd"],"state_sha256":"2b6e632416d038e59483bdbcac0da3541c532dfb281d578523f18fe285a966bc"}