{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ODCRQ4K6GDSCPABJV23M5XG5FB","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":"beccef539653a816f64f2208e73ce5a798fc81fd4ea7e30a6ad2abcc01ff2482","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-29T02:52:37Z","title_canon_sha256":"737d403babddf6dcb3b3db20ad8ae866efe62043ffb7caa628b80b1426ebe90a"},"schema_version":"1.0","source":{"id":"2209.14522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14522","created_at":"2026-07-05T05:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14522v1","created_at":"2026-07-05T05:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14522","created_at":"2026-07-05T05:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"ODCRQ4K6GDSC","created_at":"2026-07-05T05:01:53Z"},{"alias_kind":"pith_short_16","alias_value":"ODCRQ4K6GDSCPABJ","created_at":"2026-07-05T05:01:53Z"},{"alias_kind":"pith_short_8","alias_value":"ODCRQ4K6","created_at":"2026-07-05T05:01:53Z"}],"graph_snapshots":[{"event_id":"sha256:e1c3c6881c625ae3e2e2d8e5a323306f1bed765f6d16ca559d7cdc85768bbf14","target":"graph","created_at":"2026-07-05T05:01:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.14522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the generalized parabolic Cahn-Hilliard equation $$ u_t=-\\Delta\\left[\\Delta u -W'(u)\\right]+W''(u)\\left[\\Delta u -W'(u)\\right] \\qquad \\forall\\, (t, x)\\in \\widetilde{{\\mathbb R}}\\times{\\mathbb R}^n, $$ where $n=2$ or $n\\geq 4$, $W(\\cdot)$ is the typical double-well potential function and $\\widetilde{\\mathbb R}$ is given by $$ \\widetilde{\\mathbb R}=\\left\\{\n  \\begin{array}{rl}\n  (0, \\infty), &\\quad \\mbox{if } n=2,\n  (-\\infty, 0), & \\quad\\mbox{if } n\\geq 4.\n  \\end{array}\n  \\right. $$ We construct a radial solution $u(t, x)$ possessing an interface. At main order this solution consists ","authors_text":"Chao Liu, Jun Yang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-29T02:52:37Z","title":"Solutions with single radial interface of the generalized Cahn-Hilliard flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14522","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":"sha256:3774bee7f9e712dc36a790bf3ec7139adc2106d46c7e533683e00348fdde1121","target":"record","created_at":"2026-07-05T05:01:53Z","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":"beccef539653a816f64f2208e73ce5a798fc81fd4ea7e30a6ad2abcc01ff2482","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-29T02:52:37Z","title_canon_sha256":"737d403babddf6dcb3b3db20ad8ae866efe62043ffb7caa628b80b1426ebe90a"},"schema_version":"1.0","source":{"id":"2209.14522","kind":"arxiv","version":1}},"canonical_sha256":"70c518715e30e4278029aeb6cedcdd286cc8803475d4fa3311d49347e3d93411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70c518715e30e4278029aeb6cedcdd286cc8803475d4fa3311d49347e3d93411","first_computed_at":"2026-07-05T05:01:53.830831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:01:53.830831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qxU0hWAWtj6lCWXQw5AX//V6xIIO4HHAY0Sl5BZ26Dk499Rw4bQ+AwDASHQPKRk1Nnl4YcPHnJIZdqtQYzA+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:01:53.831204Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.14522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3774bee7f9e712dc36a790bf3ec7139adc2106d46c7e533683e00348fdde1121","sha256:e1c3c6881c625ae3e2e2d8e5a323306f1bed765f6d16ca559d7cdc85768bbf14"],"state_sha256":"2427cfe4feb437dad863f5a1073ddd5dd7b5ac593c822d2ce0479c0b022bf64e"}