{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:N747HYW3LCH7VHAE3QSL64WXVI","short_pith_number":"pith:N747HYW3","canonical_record":{"source":{"id":"2204.11188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-24T04:23:31Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"fc2c286f731fbd7c49587e9abf6e550310fe82676b24279b15bcc78dbb0abdfa","abstract_canon_sha256":"929d75439856a56bdc0d4d0a72d0f785f71a96899a6a4ed7fba8dc19264bfab2"},"schema_version":"1.0"},"canonical_sha256":"6ff9f3e2db588ffa9c04dc24bf72d7aa15be263fe8a6a527c611da70f0f2648c","source":{"kind":"arxiv","id":"2204.11188","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.11188","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2204.11188v1","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.11188","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"N747HYW3LCH7","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"N747HYW3LCH7VHAE","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"N747HYW3","created_at":"2026-07-05T04:17:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:N747HYW3LCH7VHAE3QSL64WXVI","target":"record","payload":{"canonical_record":{"source":{"id":"2204.11188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-24T04:23:31Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"fc2c286f731fbd7c49587e9abf6e550310fe82676b24279b15bcc78dbb0abdfa","abstract_canon_sha256":"929d75439856a56bdc0d4d0a72d0f785f71a96899a6a4ed7fba8dc19264bfab2"},"schema_version":"1.0"},"canonical_sha256":"6ff9f3e2db588ffa9c04dc24bf72d7aa15be263fe8a6a527c611da70f0f2648c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:17:41.083275Z","signature_b64":"YNtTQZOg/E2HgkDjTI007wKVTCZwfJesmVvtkwXWMfYH6XO+KBqbmocc0qAJfiOAcp3ae5RUAqjJcCVwPncHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff9f3e2db588ffa9c04dc24bf72d7aa15be263fe8a6a527c611da70f0f2648c","last_reissued_at":"2026-07-05T04:17:41.082843Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:17:41.082843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.11188","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":"2026-07-05T04:17:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9GQaKLPGHIrbV4JzvPDRyyi/ryva+vHV88/agrLLIm7xfrATppkB7Z0BtbhvB+pmLN67icGEJLB/2/T9o8sCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T09:08:31.280665Z"},"content_sha256":"e302b73424c151c6e56f17394d591dca597c59c7a7deff1648b23cf9bb2bea72","schema_version":"1.0","event_id":"sha256:e302b73424c151c6e56f17394d591dca597c59c7a7deff1648b23cf9bb2bea72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:N747HYW3LCH7VHAE3QSL64WXVI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"M2N: Mesh Movement Networks for PDE Solvers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Fanglei Sun, Joseph G. Wallwork, Junpeng Gao, Junqing Chen, Jun Wang, Matthew D. Piggott, Mingrui Zhang, Wenbin Song, Xiang Chen, Zheng Tian, Zuoqiang Shi","submitted_at":"2022-04-24T04:23:31Z","abstract_excerpt":"Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the solution is not well-resolved, whilst reducing unnecessary resolution elsewhere. However, mesh movement methods, such as the Monge-Ampere method, require the solution of auxiliary equations, which can be extremely expensive especially when the mesh is adapted frequently. In this paper, we propose to our best knowledge the first learning-based end-to-end mesh mov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.11188","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/2204.11188/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":"2026-07-05T04:17:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"toqc5YB9d7wSegprZYSBQ29bAyfgtyDw92dUj69kB6a1mwQHyZSjlUesZFLk+gy31R/pZDpbu8zQ94oiGY3kCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T09:08:31.281075Z"},"content_sha256":"dfe02ddcb93652b51a2579c0fcefb28a47f775168fb9e0f63f69309a06fba5b2","schema_version":"1.0","event_id":"sha256:dfe02ddcb93652b51a2579c0fcefb28a47f775168fb9e0f63f69309a06fba5b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N747HYW3LCH7VHAE3QSL64WXVI/bundle.json","state_url":"https://pith.science/pith/N747HYW3LCH7VHAE3QSL64WXVI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N747HYW3LCH7VHAE3QSL64WXVI/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":"2026-08-21T09:08:31Z","links":{"resolver":"https://pith.science/pith/N747HYW3LCH7VHAE3QSL64WXVI","bundle":"https://pith.science/pith/N747HYW3LCH7VHAE3QSL64WXVI/bundle.json","state":"https://pith.science/pith/N747HYW3LCH7VHAE3QSL64WXVI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N747HYW3LCH7VHAE3QSL64WXVI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:N747HYW3LCH7VHAE3QSL64WXVI","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":"929d75439856a56bdc0d4d0a72d0f785f71a96899a6a4ed7fba8dc19264bfab2","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-24T04:23:31Z","title_canon_sha256":"fc2c286f731fbd7c49587e9abf6e550310fe82676b24279b15bcc78dbb0abdfa"},"schema_version":"1.0","source":{"id":"2204.11188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.11188","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2204.11188v1","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.11188","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"N747HYW3LCH7","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"N747HYW3LCH7VHAE","created_at":"2026-07-05T04:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"N747HYW3","created_at":"2026-07-05T04:17:41Z"}],"graph_snapshots":[{"event_id":"sha256:dfe02ddcb93652b51a2579c0fcefb28a47f775168fb9e0f63f69309a06fba5b2","target":"graph","created_at":"2026-07-05T04:17:41Z","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/2204.11188/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the solution is not well-resolved, whilst reducing unnecessary resolution elsewhere. However, mesh movement methods, such as the Monge-Ampere method, require the solution of auxiliary equations, which can be extremely expensive especially when the mesh is adapted frequently. In this paper, we propose to our best knowledge the first learning-based end-to-end mesh mov","authors_text":"Fanglei Sun, Joseph G. Wallwork, Junpeng Gao, Junqing Chen, Jun Wang, Matthew D. Piggott, Mingrui Zhang, Wenbin Song, Xiang Chen, Zheng Tian, Zuoqiang Shi","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-24T04:23:31Z","title":"M2N: Mesh Movement Networks for PDE Solvers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.11188","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:e302b73424c151c6e56f17394d591dca597c59c7a7deff1648b23cf9bb2bea72","target":"record","created_at":"2026-07-05T04:17:41Z","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":"929d75439856a56bdc0d4d0a72d0f785f71a96899a6a4ed7fba8dc19264bfab2","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-24T04:23:31Z","title_canon_sha256":"fc2c286f731fbd7c49587e9abf6e550310fe82676b24279b15bcc78dbb0abdfa"},"schema_version":"1.0","source":{"id":"2204.11188","kind":"arxiv","version":1}},"canonical_sha256":"6ff9f3e2db588ffa9c04dc24bf72d7aa15be263fe8a6a527c611da70f0f2648c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff9f3e2db588ffa9c04dc24bf72d7aa15be263fe8a6a527c611da70f0f2648c","first_computed_at":"2026-07-05T04:17:41.082843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:17:41.082843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNtTQZOg/E2HgkDjTI007wKVTCZwfJesmVvtkwXWMfYH6XO+KBqbmocc0qAJfiOAcp3ae5RUAqjJcCVwPncHAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:17:41.083275Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.11188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e302b73424c151c6e56f17394d591dca597c59c7a7deff1648b23cf9bb2bea72","sha256:dfe02ddcb93652b51a2579c0fcefb28a47f775168fb9e0f63f69309a06fba5b2"],"state_sha256":"c81bb9b57169e582c0cef423591f6fcd9532585f4105ffb01e62fddb678ce93a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Em9IfhwScsEP2EZWDtnZoR+naPQTGrvJIvl0UH3GaUkERUwuyGNAOSsZAiP7C7XKkcE6qDWW2D+MREM/Az6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T09:08:31.300189Z","bundle_sha256":"00f0735981c46e90782f377432fb951f1bb832b1d0cba7dfc2da03bb96039d25"}}