{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NAIRX3RI6DGBX6TR7RW7KYHIUH","short_pith_number":"pith:NAIRX3RI","canonical_record":{"source":{"id":"1803.06047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-16T01:06:52Z","cross_cats_sorted":["math.NA","physics.comp-ph"],"title_canon_sha256":"d49db2a3bce8fe3003411835f089007dfc188da61cc4225c44e5cd9aa18a3248","abstract_canon_sha256":"fa9c38cc36fdf3672c6316f77fc55f1b192a8a34c78eb620161abaad33bf126d"},"schema_version":"1.0"},"canonical_sha256":"68111bee28f0cc1bfa71fc6df560e8a1e006a3190d21bbdf9afc9a9e51eb2b62","source":{"kind":"arxiv","id":"1803.06047","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06047","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06047v1","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06047","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"NAIRX3RI6DGB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NAIRX3RI6DGBX6TR","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NAIRX3RI","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NAIRX3RI6DGBX6TR7RW7KYHIUH","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-16T01:06:52Z","cross_cats_sorted":["math.NA","physics.comp-ph"],"title_canon_sha256":"d49db2a3bce8fe3003411835f089007dfc188da61cc4225c44e5cd9aa18a3248","abstract_canon_sha256":"fa9c38cc36fdf3672c6316f77fc55f1b192a8a34c78eb620161abaad33bf126d"},"schema_version":"1.0"},"canonical_sha256":"68111bee28f0cc1bfa71fc6df560e8a1e006a3190d21bbdf9afc9a9e51eb2b62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:50.887071Z","signature_b64":"S5oMSQQRqlDRD/3WdnXGU1ZIIek7Jhjku1L2OWVKXTA1V8249OnkofBtLDweqItXcCj//UQidhPW839d88kKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68111bee28f0cc1bfa71fc6df560e8a1e006a3190d21bbdf9afc9a9e51eb2b62","last_reissued_at":"2026-05-18T00:20:50.886424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:50.886424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06047","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ZLgDYU2HIKFDSvQjKnqA4cy42OByW7CgmQ2sp0XURe0EZKStyEODVKnx6PDH4UgDWznYeaLI19oNK2CVscnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:14:38.569005Z"},"content_sha256":"16bc32922d57ffad588b8b2c6a3c4982f744d0789cf87ca7505825c6f2641187","schema_version":"1.0","event_id":"sha256:16bc32922d57ffad588b8b2c6a3c4982f744d0789cf87ca7505825c6f2641187"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NAIRX3RI6DGBX6TR7RW7KYHIUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Family of Second-Order Energy-Stable Schemes for Cahn-Hilliard Type Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.comp-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Lianlei Lin, Suchuan Dong, Zhiguo Yang","submitted_at":"2018-03-16T01:06:52Z","abstract_excerpt":"We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary variable, we approximate the system at the time step $(n+\\theta)$ ($n$ denoting the time step index and $\\theta$ is a real-valued parameter), and devise a family of corresponding approximations that are second-order accurate and unconditionally energy stable. This family of approximations contains the often-used Crank-Nicolson scheme and the second-order backw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06047","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/azlzyAaBp+5qnEq1XZzR2+iJJmKUFqa5kPBmGpPJvgnlE0Xrd5zYdSs0XphebaKr7rMN/g++Ue+kA6LeDQ0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:14:38.569368Z"},"content_sha256":"2bbe4279996ae49ec18458738f2f2f0673785c382abf9d0f46e1e1325e52ca39","schema_version":"1.0","event_id":"sha256:2bbe4279996ae49ec18458738f2f2f0673785c382abf9d0f46e1e1325e52ca39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH/bundle.json","state_url":"https://pith.science/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T07:14:38Z","links":{"resolver":"https://pith.science/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH","bundle":"https://pith.science/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH/bundle.json","state":"https://pith.science/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NAIRX3RI6DGBX6TR7RW7KYHIUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NAIRX3RI6DGBX6TR7RW7KYHIUH","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":"fa9c38cc36fdf3672c6316f77fc55f1b192a8a34c78eb620161abaad33bf126d","cross_cats_sorted":["math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-16T01:06:52Z","title_canon_sha256":"d49db2a3bce8fe3003411835f089007dfc188da61cc4225c44e5cd9aa18a3248"},"schema_version":"1.0","source":{"id":"1803.06047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06047","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06047v1","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06047","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"NAIRX3RI6DGB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NAIRX3RI6DGBX6TR","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NAIRX3RI","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:2bbe4279996ae49ec18458738f2f2f0673785c382abf9d0f46e1e1325e52ca39","target":"graph","created_at":"2026-05-18T00:20:50Z","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 focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary variable, we approximate the system at the time step $(n+\\theta)$ ($n$ denoting the time step index and $\\theta$ is a real-valued parameter), and devise a family of corresponding approximations that are second-order accurate and unconditionally energy stable. This family of approximations contains the often-used Crank-Nicolson scheme and the second-order backw","authors_text":"Lianlei Lin, Suchuan Dong, Zhiguo Yang","cross_cats":["math.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-16T01:06:52Z","title":"A Family of Second-Order Energy-Stable Schemes for Cahn-Hilliard Type Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06047","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":"sha256:16bc32922d57ffad588b8b2c6a3c4982f744d0789cf87ca7505825c6f2641187","target":"record","created_at":"2026-05-18T00:20:50Z","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":"fa9c38cc36fdf3672c6316f77fc55f1b192a8a34c78eb620161abaad33bf126d","cross_cats_sorted":["math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-16T01:06:52Z","title_canon_sha256":"d49db2a3bce8fe3003411835f089007dfc188da61cc4225c44e5cd9aa18a3248"},"schema_version":"1.0","source":{"id":"1803.06047","kind":"arxiv","version":1}},"canonical_sha256":"68111bee28f0cc1bfa71fc6df560e8a1e006a3190d21bbdf9afc9a9e51eb2b62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68111bee28f0cc1bfa71fc6df560e8a1e006a3190d21bbdf9afc9a9e51eb2b62","first_computed_at":"2026-05-18T00:20:50.886424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:50.886424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S5oMSQQRqlDRD/3WdnXGU1ZIIek7Jhjku1L2OWVKXTA1V8249OnkofBtLDweqItXcCj//UQidhPW839d88kKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:50.887071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16bc32922d57ffad588b8b2c6a3c4982f744d0789cf87ca7505825c6f2641187","sha256:2bbe4279996ae49ec18458738f2f2f0673785c382abf9d0f46e1e1325e52ca39"],"state_sha256":"0d43db1c89ba5e59df67fd4fb439dbf9fb196c9622f0711daeb168784fc231e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/WLCJWJ0zybRnunN9RQGMjUVPtedxqE5tXWI9nW0mjPosnjyHeGfDz8NQr8BMNAceHtCgLACp+o6xX0XTad5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T07:14:38.571414Z","bundle_sha256":"93cd7ea45244b309a3bb8eb89787d5334434ea016df883729c2d62f9ff6dc35c"}}