{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:57344Z2CV46KJLWMGGMZBBP6JU","short_pith_number":"pith:57344Z2C","canonical_record":{"source":{"id":"2411.16271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-25T10:47:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"47b9155a98376cf151ace0f10253c0496c2d1d5dfcccd7e78b2423c87f66528f","abstract_canon_sha256":"1d6a24f8a11b112e5f1dbdf3304b3f68d3401aa2180eeb27933ca9f56a2a89df"},"schema_version":"1.0"},"canonical_sha256":"eff7ce6742af3ca4aecc31999085fe4d2ebd2de8e5f00ef50911a84cc04d829e","source":{"kind":"arxiv","id":"2411.16271","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16271","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16271v1","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16271","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"57344Z2CV46K","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_16","alias_value":"57344Z2CV46KJLWM","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_8","alias_value":"57344Z2C","created_at":"2026-07-05T09:40:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:57344Z2CV46KJLWMGGMZBBP6JU","target":"record","payload":{"canonical_record":{"source":{"id":"2411.16271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-25T10:47:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"47b9155a98376cf151ace0f10253c0496c2d1d5dfcccd7e78b2423c87f66528f","abstract_canon_sha256":"1d6a24f8a11b112e5f1dbdf3304b3f68d3401aa2180eeb27933ca9f56a2a89df"},"schema_version":"1.0"},"canonical_sha256":"eff7ce6742af3ca4aecc31999085fe4d2ebd2de8e5f00ef50911a84cc04d829e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:06.998087Z","signature_b64":"Kf1bBj0obBNi/v0d0UwhWjtGsZ/x8Ccxl93k9Q+Q1ymqJClSkVo7dJL/yMICCGjdMnhMF2gZsmh/njD/i/1+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eff7ce6742af3ca4aecc31999085fe4d2ebd2de8e5f00ef50911a84cc04d829e","last_reissued_at":"2026-07-05T09:40:06.997522Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:06.997522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.16271","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":"2026-07-05T09:40:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjFbGc9hZN22DbxW/a2bR70f8TazHL3S6qNU+4vgEqxJGs+StkYYym684He2Taf1t1lC+0dSimBdJ1eQRKB0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T08:25:10.484441Z"},"content_sha256":"47085508ad6db8158df211714e464af2088270d04a1da56663191f4cc9236b42","schema_version":"1.0","event_id":"sha256:47085508ad6db8158df211714e464af2088270d04a1da56663191f4cc9236b42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:57344Z2CV46KJLWMGGMZBBP6JU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An exponential-free Runge--Kutta framework for developing third-order unconditionally energy stable schemes for the Cahn--Hilliard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"HaiFeng Wang, Hong Zhang, Jingwei Sun, Songhe Song, Xu Qian","submitted_at":"2024-11-25T10:47:04Z","abstract_excerpt":"In this work, we develop a class of up to third-order energy-stable schemes for the Cahn--Hilliard equation. Building on Lawson's integrating factor Runge--Kutta method, which is widely used for stiff semilinear equations, we discuss its limitations, such as the inability to preserve the equilibrium state and the oversmoothing of interfacial layers in the solution's profile because of the exponential damping effects. To overcome this drawback, we approximate the exponential term using a class of sophisticated Taylor polynomials, leading to a novel Runge--Kutta framework called exponential-free"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16271","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16271/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:40:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbceRMtGCucRs/8mM3qKfVRCLZHbzpnKzguJZWkpgmCT1/BwswfzByUQQby1i7Dbz68xNN2Zn8tvk/T78SnmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T08:25:10.484813Z"},"content_sha256":"ad3f4996472bd6765a4a36a9fe87c53ab33f2f63b4645cc82844de3f3dc55b2d","schema_version":"1.0","event_id":"sha256:ad3f4996472bd6765a4a36a9fe87c53ab33f2f63b4645cc82844de3f3dc55b2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57344Z2CV46KJLWMGGMZBBP6JU/bundle.json","state_url":"https://pith.science/pith/57344Z2CV46KJLWMGGMZBBP6JU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57344Z2CV46KJLWMGGMZBBP6JU/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":"2026-07-20T08:25:10Z","links":{"resolver":"https://pith.science/pith/57344Z2CV46KJLWMGGMZBBP6JU","bundle":"https://pith.science/pith/57344Z2CV46KJLWMGGMZBBP6JU/bundle.json","state":"https://pith.science/pith/57344Z2CV46KJLWMGGMZBBP6JU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57344Z2CV46KJLWMGGMZBBP6JU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:57344Z2CV46KJLWMGGMZBBP6JU","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":"1d6a24f8a11b112e5f1dbdf3304b3f68d3401aa2180eeb27933ca9f56a2a89df","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-25T10:47:04Z","title_canon_sha256":"47b9155a98376cf151ace0f10253c0496c2d1d5dfcccd7e78b2423c87f66528f"},"schema_version":"1.0","source":{"id":"2411.16271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16271","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16271v1","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16271","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"57344Z2CV46K","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_16","alias_value":"57344Z2CV46KJLWM","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_8","alias_value":"57344Z2C","created_at":"2026-07-05T09:40:06Z"}],"graph_snapshots":[{"event_id":"sha256:ad3f4996472bd6765a4a36a9fe87c53ab33f2f63b4645cc82844de3f3dc55b2d","target":"graph","created_at":"2026-07-05T09:40:06Z","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/2411.16271/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we develop a class of up to third-order energy-stable schemes for the Cahn--Hilliard equation. Building on Lawson's integrating factor Runge--Kutta method, which is widely used for stiff semilinear equations, we discuss its limitations, such as the inability to preserve the equilibrium state and the oversmoothing of interfacial layers in the solution's profile because of the exponential damping effects. To overcome this drawback, we approximate the exponential term using a class of sophisticated Taylor polynomials, leading to a novel Runge--Kutta framework called exponential-free","authors_text":"HaiFeng Wang, Hong Zhang, Jingwei Sun, Songhe Song, Xu Qian","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-25T10:47:04Z","title":"An exponential-free Runge--Kutta framework for developing third-order unconditionally energy stable schemes for the Cahn--Hilliard equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16271","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":"sha256:47085508ad6db8158df211714e464af2088270d04a1da56663191f4cc9236b42","target":"record","created_at":"2026-07-05T09:40:06Z","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":"1d6a24f8a11b112e5f1dbdf3304b3f68d3401aa2180eeb27933ca9f56a2a89df","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-25T10:47:04Z","title_canon_sha256":"47b9155a98376cf151ace0f10253c0496c2d1d5dfcccd7e78b2423c87f66528f"},"schema_version":"1.0","source":{"id":"2411.16271","kind":"arxiv","version":1}},"canonical_sha256":"eff7ce6742af3ca4aecc31999085fe4d2ebd2de8e5f00ef50911a84cc04d829e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eff7ce6742af3ca4aecc31999085fe4d2ebd2de8e5f00ef50911a84cc04d829e","first_computed_at":"2026-07-05T09:40:06.997522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:06.997522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kf1bBj0obBNi/v0d0UwhWjtGsZ/x8Ccxl93k9Q+Q1ymqJClSkVo7dJL/yMICCGjdMnhMF2gZsmh/njD/i/1+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:06.998087Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47085508ad6db8158df211714e464af2088270d04a1da56663191f4cc9236b42","sha256:ad3f4996472bd6765a4a36a9fe87c53ab33f2f63b4645cc82844de3f3dc55b2d"],"state_sha256":"87e70e4bd19ea6a07137800019fdb8fa0bcc4f4340012029a21dd7785826ff5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YokJhJYdy3gAR5GZCr/mpQ/RHAvU6w9OpIKHswUImJSzOLvb37SSvGb6fUr4kCNtz7FsBuPEKODeIXg6+c0oDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-20T08:25:10.487384Z","bundle_sha256":"a4f16e59130a40b9623c63747d5601d14ed1f6a642172895b915a11bf4790c9c"}}