{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SRWRZ5LHDWBITBUDRMUMGRBYVN","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":"8adafa05351232fc49d0fd164b566a7440cf1fbe9490b6c6fadc18d45ac60d9a","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-12T12:17:36Z","title_canon_sha256":"59245d0046e7a49bb393d9b0506f636af4569626e37d443f761a0288bc52bc92"},"schema_version":"1.0","source":{"id":"2107.05349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.05349","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"2107.05349v1","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05349","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"SRWRZ5LHDWBI","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_16","alias_value":"SRWRZ5LHDWBITBUD","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_8","alias_value":"SRWRZ5LH","created_at":"2026-07-05T02:57:01Z"}],"graph_snapshots":[{"event_id":"sha256:17af10e5cd68de188de07345516c7f65b02cb875245ec14418eca93c9cf468b3","target":"graph","created_at":"2026-07-05T02:57:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.05349/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher Sobolev norms. This is the first strong stability result for second order operator-splitting methods for the Cahn-Hilliard equation. In particular we settle several long-standing open issues in the work of Cheng, Kurganov, Qu and Tang \\cite{Tang15}.","authors_text":"Chaoyu Quan, Dong Li","cross_cats":["cs.NA","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-12T12:17:36Z","title":"On the energy stability of Strang-splitting for Cahn-Hilliard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05349","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":"sha256:3eee32ab8eceb9a61f2c2711c4aa2664f1d95b41e1619b2b7170ee99a73361d7","target":"record","created_at":"2026-07-05T02:57:01Z","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":"8adafa05351232fc49d0fd164b566a7440cf1fbe9490b6c6fadc18d45ac60d9a","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-12T12:17:36Z","title_canon_sha256":"59245d0046e7a49bb393d9b0506f636af4569626e37d443f761a0288bc52bc92"},"schema_version":"1.0","source":{"id":"2107.05349","kind":"arxiv","version":1}},"canonical_sha256":"946d1cf5671d828986838b28c34438ab557ad74f9608fe9ff630718dc2568172","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"946d1cf5671d828986838b28c34438ab557ad74f9608fe9ff630718dc2568172","first_computed_at":"2026-07-05T02:57:01.901795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:57:01.901795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QIhJ7GAGQKLoQCB33XWhepOVssIOLuSDyMiR36jVNKTcBYvVsBhYKnI3964oR0rbm1JyUuQKPOtI11ga0Zx+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:57:01.902182Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.05349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eee32ab8eceb9a61f2c2711c4aa2664f1d95b41e1619b2b7170ee99a73361d7","sha256:17af10e5cd68de188de07345516c7f65b02cb875245ec14418eca93c9cf468b3"],"state_sha256":"d3c5b8fccc55a4d7fca2821cd3239fadec7d5b558c3225db4210e43269d43955"}