{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KDUN272WGQGERI2TL52UVBFTK2","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":"666b6bc41e3c987ddf973e5e3320a6f46cf6c6899001657e63b34b28fc955052","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-25T18:11:25Z","title_canon_sha256":"36dfd10ce3e2fb58ed1529a81b81c4e6e74abe43e4aa50443620ce71d6815e14"},"schema_version":"1.0","source":{"id":"1701.07410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07410","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07410v1","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07410","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"KDUN272WGQGE","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KDUN272WGQGERI2T","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KDUN272W","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:f2e3282e2caa19809c235070d59239baecc4c7f4c548f2eb6da43c1d5f6110c3","target":"graph","created_at":"2026-05-18T00:52:04Z","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 consider the numerical approximations for the fourth order Cahn-Hilliard equation with concentration dependent mobility, and the logarithmic Flory-Huggins potential. One challenge in solving such a diffusive system numerically is how to develop proper temporal discretization for nonlinear terms in order to preserve the energy stability at the time-discrete level. We resolve this issue by developing a set of the first and second order time marching schemes based on a novel, called \"Invariant Energy Quadratization\" approach. Its novelty is that the proposed scheme is linear and","authors_text":"Jia Zhao, Xiaofeng Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-25T18:11:25Z","title":"On Linear and unconditionally energy stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07410","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":"sha256:67f694d85325d059d77633b4771536b81c38ba8ffcd57ffb051fa397307fd13f","target":"record","created_at":"2026-05-18T00:52:04Z","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":"666b6bc41e3c987ddf973e5e3320a6f46cf6c6899001657e63b34b28fc955052","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-25T18:11:25Z","title_canon_sha256":"36dfd10ce3e2fb58ed1529a81b81c4e6e74abe43e4aa50443620ce71d6815e14"},"schema_version":"1.0","source":{"id":"1701.07410","kind":"arxiv","version":1}},"canonical_sha256":"50e8dd7f56340c48a3535f754a84b356af7c8318efec3b41486c0ead72947b7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50e8dd7f56340c48a3535f754a84b356af7c8318efec3b41486c0ead72947b7c","first_computed_at":"2026-05-18T00:52:04.626284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:04.626284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHxzd1WAXQGjZsa2OF6pw3gTqX5KzFQOxMffTZYXZkB8BsjQKOjCakK+vrYFFaOnL2gOFZWeJ1NDe2GgFMDpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:04.626769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67f694d85325d059d77633b4771536b81c38ba8ffcd57ffb051fa397307fd13f","sha256:f2e3282e2caa19809c235070d59239baecc4c7f4c548f2eb6da43c1d5f6110c3"],"state_sha256":"276a6ed0d82b58b04105a0c161bc00406f03c19d84bb4af76123df4959e97cf9"}