{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SMQOJB3N5FSBAO5IRHDQZNSYEB","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":"826954fa9e8ff37219ebf1959ebf863308d094280c4dca64022853699be4c719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-23T17:55:15Z","title_canon_sha256":"bbfbd3ab8e7b57ed3b968eadb085747a98fddb6a062bba34e15952dcd827fd7a"},"schema_version":"1.0","source":{"id":"1011.5179","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5179","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5179v3","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5179","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"SMQOJB3N5FSB","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SMQOJB3N5FSBAO5I","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SMQOJB3N","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:a0f872fd72e6fd51cd60dd9e6476aa9505b00160649cb01c263bc3443f6d05ca","target":"graph","created_at":"2026-05-18T04:28:07Z","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":"Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of Beale \\cite{beale_1}. In this monograph, we develop a new mathematical framework to resolve this question. If the free interface is horizontally infinite, we establish that it decays to a flat surface at an algebraic rate. On the other hand, if the free interface is periodic, we establish that it decays at an almost exponential rate, i.e. at an arbitrarily ","authors_text":"Ian Tice, Yan Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-23T17:55:15Z","title":"Decay of viscous surface waves without surface tension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5179","kind":"arxiv","version":3},"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":"sha256:9862aabbd3c92057df4d66cbcd0d791c27880ccfbca3903bd34c3c7563d6a908","target":"record","created_at":"2026-05-18T04:28:07Z","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":"826954fa9e8ff37219ebf1959ebf863308d094280c4dca64022853699be4c719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-23T17:55:15Z","title_canon_sha256":"bbfbd3ab8e7b57ed3b968eadb085747a98fddb6a062bba34e15952dcd827fd7a"},"schema_version":"1.0","source":{"id":"1011.5179","kind":"arxiv","version":3}},"canonical_sha256":"9320e4876de964103ba889c70cb65820756169a640b57123f7c8efbb9eb4c7a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9320e4876de964103ba889c70cb65820756169a640b57123f7c8efbb9eb4c7a4","first_computed_at":"2026-05-18T04:28:07.895121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:07.895121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlkaIEgKxy+MrtS/Z3pbv6Fq3I7NW9iMFBnDg7Z80Ldb22y3iVsx7tYMHTj6wLOCnzYGCi5DBrS/OEzeZqPzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:07.895911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5179","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9862aabbd3c92057df4d66cbcd0d791c27880ccfbca3903bd34c3c7563d6a908","sha256:a0f872fd72e6fd51cd60dd9e6476aa9505b00160649cb01c263bc3443f6d05ca"],"state_sha256":"6a180ed348b589fdd5774383f462e5a650865f1d8e074b186bace87976d6a22f"}