{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZHTENZMJGPN7HVZ3VTO6JAM37A","short_pith_number":"pith:ZHTENZMJ","canonical_record":{"source":{"id":"1208.2643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T21:37:52Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"d963b3215e244bdb6b5fd10f533e2595eb1ba9a1e482826c6cfb7f97105b861c","abstract_canon_sha256":"859d3876a0e277cf9e50011f3d0243484816b96dc6eec29d2a3ef25aaeb90e5c"},"schema_version":"1.0"},"canonical_sha256":"c9e646e58933dbf3d73bacdde4819bf8252dc661a9d6d72d47b1d71c496455e7","source":{"kind":"arxiv","id":"1208.2643","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2643","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2643v1","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2643","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZHTENZMJGPN7","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZHTENZMJGPN7HVZ3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZHTENZMJ","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZHTENZMJGPN7HVZ3VTO6JAM37A","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T21:37:52Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"d963b3215e244bdb6b5fd10f533e2595eb1ba9a1e482826c6cfb7f97105b861c","abstract_canon_sha256":"859d3876a0e277cf9e50011f3d0243484816b96dc6eec29d2a3ef25aaeb90e5c"},"schema_version":"1.0"},"canonical_sha256":"c9e646e58933dbf3d73bacdde4819bf8252dc661a9d6d72d47b1d71c496455e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:16.358342Z","signature_b64":"Ngt250cyHofWRxJ5B/vJM5/GzKA8425/5LbwKMLZVajAeYPUcuORcfrjX6dWYF8hpCZ3z+YnCssOeGYeRjeADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9e646e58933dbf3d73bacdde4819bf8252dc661a9d6d72d47b1d71c496455e7","last_reissued_at":"2026-05-18T01:55:16.357961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:16.357961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2643","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":"2026-05-18T01:55:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WHLTqSqQYiCBF24ByJcBDJsDA0TxxZFJd696OM/nFvpSAFiXPSu6lAoKTBIVRGG+8jhpO/GPrg4n6abbCcX+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:12:21.047722Z"},"content_sha256":"2d4a9b79eda453638d629a99749266685791fab4e816f5b01b2606ffac28d654","schema_version":"1.0","event_id":"sha256:2d4a9b79eda453638d629a99749266685791fab4e816f5b01b2606ffac28d654"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZHTENZMJGPN7HVZ3VTO6JAM37A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"math.NA","authors_text":"Arvind Baskaran, Cheng Wang, John S. Lowengrub, Peng Zhou, Steven M. Wise, Zhengzheng Hu","submitted_at":"2012-08-08T21:37:52Z","abstract_excerpt":"In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2643","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":"2026-05-18T01:55:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0T4SSXo4pB87FnUP+kISmMbRvM7TVCrMpXt7nGbQDs2WFZRPfQlJFNhMhuyyRU7WbzjHP/P3FWiivZB5QgEfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:12:21.048374Z"},"content_sha256":"e9248c86893407a8f1760b71141ef7c6a0f0435e653f1e923163c6fbea77ef98","schema_version":"1.0","event_id":"sha256:e9248c86893407a8f1760b71141ef7c6a0f0435e653f1e923163c6fbea77ef98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A/bundle.json","state_url":"https://pith.science/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A/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":"2026-05-27T02:12:21Z","links":{"resolver":"https://pith.science/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A","bundle":"https://pith.science/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A/bundle.json","state":"https://pith.science/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHTENZMJGPN7HVZ3VTO6JAM37A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZHTENZMJGPN7HVZ3VTO6JAM37A","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":"859d3876a0e277cf9e50011f3d0243484816b96dc6eec29d2a3ef25aaeb90e5c","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T21:37:52Z","title_canon_sha256":"d963b3215e244bdb6b5fd10f533e2595eb1ba9a1e482826c6cfb7f97105b861c"},"schema_version":"1.0","source":{"id":"1208.2643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2643","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2643v1","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2643","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZHTENZMJGPN7","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZHTENZMJGPN7HVZ3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZHTENZMJ","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:e9248c86893407a8f1760b71141ef7c6a0f0435e653f1e923163c6fbea77ef98","target":"graph","created_at":"2026-05-18T01:55:16Z","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 present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulat","authors_text":"Arvind Baskaran, Cheng Wang, John S. Lowengrub, Peng Zhou, Steven M. Wise, Zhengzheng Hu","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T21:37:52Z","title":"Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2643","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":"sha256:2d4a9b79eda453638d629a99749266685791fab4e816f5b01b2606ffac28d654","target":"record","created_at":"2026-05-18T01:55:16Z","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":"859d3876a0e277cf9e50011f3d0243484816b96dc6eec29d2a3ef25aaeb90e5c","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T21:37:52Z","title_canon_sha256":"d963b3215e244bdb6b5fd10f533e2595eb1ba9a1e482826c6cfb7f97105b861c"},"schema_version":"1.0","source":{"id":"1208.2643","kind":"arxiv","version":1}},"canonical_sha256":"c9e646e58933dbf3d73bacdde4819bf8252dc661a9d6d72d47b1d71c496455e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9e646e58933dbf3d73bacdde4819bf8252dc661a9d6d72d47b1d71c496455e7","first_computed_at":"2026-05-18T01:55:16.357961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:16.357961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ngt250cyHofWRxJ5B/vJM5/GzKA8425/5LbwKMLZVajAeYPUcuORcfrjX6dWYF8hpCZ3z+YnCssOeGYeRjeADg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:16.358342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d4a9b79eda453638d629a99749266685791fab4e816f5b01b2606ffac28d654","sha256:e9248c86893407a8f1760b71141ef7c6a0f0435e653f1e923163c6fbea77ef98"],"state_sha256":"c9da2aad25148ab177f04d75efcab7b7005ef1f66dc33b439699af9bada52e14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tvZ3X8/XtoYS5ODp7vj51obOCOqbijCs718FIu76hP6+WcoxxriH8suacvZ3ajqZoDkYOF4JBltp99rT5Wz3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:12:21.051758Z","bundle_sha256":"f5d61e9d85ed2b478d200d2ff8fd1b9db4516272950bfc2424cd215e622bc025"}}