{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VHBFIDDRCROWQ2AOO6QJBUDXZC","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":"58642a7d27777493e286d25a9b2570f7067aa9dd1b8ff68b3508e80643614ece","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-08T15:26:30Z","title_canon_sha256":"28f39013fd8d8b2d487e70b8392b18f4805a4286d0a8051068bb3c943ea24a00"},"schema_version":"1.0","source":{"id":"1202.1735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1735","created_at":"2026-05-18T04:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1735v1","created_at":"2026-05-18T04:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1735","created_at":"2026-05-18T04:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"VHBFIDDRCROW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VHBFIDDRCROWQ2AO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VHBFIDDR","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:e2562588af8c3aeb835423cd518875b3896cc8a300e3ba2874e51cadf95238d7","target":"graph","created_at":"2026-05-18T04:02:51Z","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":"We consider the Cahn-Hilliard equation in one space dimension with scaling a small parameter \\epsilon and a non-convex potential W. In the limit \\espilon \\to 0, under the assumption that the initial data are energetically well-prepared, we show the convergence to a Stefan problem. The proof is based on variational methods and exploits the gradient flow structure of the Cahn-Hilliard equation.","authors_text":"Giovanni Bellettini, Lorenzo Bertini, Matteo Novaga, Mauro Mariani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-08T15:26:30Z","title":"Convergence of the one-dimensional Cahn-Hilliard equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1735","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":"sha256:3b198b80a41d7541e3b459c2df40ebd332daa7da79ab535075b4584ddd660ac0","target":"record","created_at":"2026-05-18T04:02:51Z","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":"58642a7d27777493e286d25a9b2570f7067aa9dd1b8ff68b3508e80643614ece","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-08T15:26:30Z","title_canon_sha256":"28f39013fd8d8b2d487e70b8392b18f4805a4286d0a8051068bb3c943ea24a00"},"schema_version":"1.0","source":{"id":"1202.1735","kind":"arxiv","version":1}},"canonical_sha256":"a9c2540c71145d68680e77a090d077c896e89b9fa62a78f4000d41a53b724337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9c2540c71145d68680e77a090d077c896e89b9fa62a78f4000d41a53b724337","first_computed_at":"2026-05-18T04:02:51.210375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:51.210375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OPmEOQlQXCluSzkDlM4lV2ERPowdbWL+Y58U22HEWw95mvt7ArfiXsONM5MjeCx6slbPDOWrdm5/Eg1alKcDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:51.211252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b198b80a41d7541e3b459c2df40ebd332daa7da79ab535075b4584ddd660ac0","sha256:e2562588af8c3aeb835423cd518875b3896cc8a300e3ba2874e51cadf95238d7"],"state_sha256":"4bd54d5992195f81502e2b02c31b23ef28119c388e1a91bfe99bfc21b6b521a1"}