{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BFNGHQ2Y5W4QL2PI7GYUAPRH7N","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":"1001ab95ae270de6dcead8f50e27d7412e1196737c24e9a44841ad8e9ee00d00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-07T05:49:06Z","title_canon_sha256":"e51014eaa861ae4d2780e6bc595cfe765d303543d5de19a642ab090afa1c2979"},"schema_version":"1.0","source":{"id":"1806.02519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02519","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02519v2","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02519","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"BFNGHQ2Y5W4Q","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BFNGHQ2Y5W4QL2PI","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BFNGHQ2Y","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7dfa7242a6d4a6a391cb7807b8dba40ac52fb70dd15928518dba2ef643093d96","target":"graph","created_at":"2026-05-17T23:41:01Z","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 derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance---in terms of either a first moment or the excess mass---to a kink profile and capture the decay rate of the energy and the perturbation. Our tools include Nash-type inequalities, duality arguments, and Schauder estimates.","authors_text":"Felix Otto, Maria G. Westdickenberg, Sebastian Scholtes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-07T05:49:06Z","title":"Optimal $L^1$-type relaxation rates for the Cahn-Hilliard equation on the line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02519","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":"sha256:1eac106dcfe2c873ea6dcef6c40f0d0ec605bbfa322f1df5304e2a6afa9deaae","target":"record","created_at":"2026-05-17T23:41:01Z","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":"1001ab95ae270de6dcead8f50e27d7412e1196737c24e9a44841ad8e9ee00d00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-07T05:49:06Z","title_canon_sha256":"e51014eaa861ae4d2780e6bc595cfe765d303543d5de19a642ab090afa1c2979"},"schema_version":"1.0","source":{"id":"1806.02519","kind":"arxiv","version":2}},"canonical_sha256":"095a63c358edb905e9e8f9b1403e27fb503429ec0263a5fa0a7ea91a1ebf9db0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"095a63c358edb905e9e8f9b1403e27fb503429ec0263a5fa0a7ea91a1ebf9db0","first_computed_at":"2026-05-17T23:41:01.279581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:01.279581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e8rKfzsoi5JCLD3hdt/Llr+YAKiKgm0uiq20kdE5c8ZszzGxIevOLoW8MNivJAEsJT3QwtjuGS87EA76voM3DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:01.280097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eac106dcfe2c873ea6dcef6c40f0d0ec605bbfa322f1df5304e2a6afa9deaae","sha256:7dfa7242a6d4a6a391cb7807b8dba40ac52fb70dd15928518dba2ef643093d96"],"state_sha256":"66115772c4a297135491e7e1579fb3a81e76ea756b9f2be6ba8d26f52520c6c0"}