{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OOP7TE35NO3EEOX5WFMYD7PN4W","short_pith_number":"pith:OOP7TE35","canonical_record":{"source":{"id":"2411.10758","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-16T09:27:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6217589c3d9087a1f24abb81b171edaea893d3d8c79d014ddc35a97bc4c2f202","abstract_canon_sha256":"9e974ff66a7c13aa6df102d430190ef7b300fc31eeb1397c3cc240c8398c314b"},"schema_version":"1.0"},"canonical_sha256":"739ff9937d6bb6423afdb15981fdede5944f4868d76af10e4cf52d7a78fd0d84","source":{"kind":"arxiv","id":"2411.10758","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.10758","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"2411.10758v2","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.10758","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"OOP7TE35NO3E","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"pith_short_16","alias_value":"OOP7TE35NO3EEOX5","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"pith_short_8","alias_value":"OOP7TE35","created_at":"2026-07-05T11:33:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OOP7TE35NO3EEOX5WFMYD7PN4W","target":"record","payload":{"canonical_record":{"source":{"id":"2411.10758","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-16T09:27:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6217589c3d9087a1f24abb81b171edaea893d3d8c79d014ddc35a97bc4c2f202","abstract_canon_sha256":"9e974ff66a7c13aa6df102d430190ef7b300fc31eeb1397c3cc240c8398c314b"},"schema_version":"1.0"},"canonical_sha256":"739ff9937d6bb6423afdb15981fdede5944f4868d76af10e4cf52d7a78fd0d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:17.531482Z","signature_b64":"mhmbh0hkVvqDGpJklNh7Hf59ABzlSCZLiBUeTbJ7oLNxl3+VfmHDTahFxQbiJhl8n5SJE4bwFZdEC1rlRI8JCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"739ff9937d6bb6423afdb15981fdede5944f4868d76af10e4cf52d7a78fd0d84","last_reissued_at":"2026-07-05T11:33:17.530986Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:17.530986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.10758","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:33:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xXZCIsoN5TvROHCGCWCV1FE+a75wanMyvh0n9qGM1jNRWOT/lq+H6JUzsN+W1iw0juq4nirB/5HeShK/mkt/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:59:24.349399Z"},"content_sha256":"8eb0333d011d86445a5af78d9912457fe12323be95d72f2d9020bfff228f4aa8","schema_version":"1.0","event_id":"sha256:8eb0333d011d86445a5af78d9912457fe12323be95d72f2d9020bfff228f4aa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OOP7TE35NO3EEOX5WFMYD7PN4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Liqun Cao, Shu Xu","submitted_at":"2024-11-16T09:27:45Z","abstract_excerpt":"We present a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model, which is the most popular model for lithium-ion batteries. Central to our approach is a novel projection operator designed for the pseudo-($N$+1)-dimensional equation, offering a powerful tool for multiscale equation analysis. Our results bridge a gap in the analysis for dimensions $2 \\le N \\le 3$ and achieve optimal convergence rates of $h+(\\Delta r)^2$. Additionally, we perform a detailed numerical verification, marking the first such validation in this context. By avoiding the change of variables, ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10758","kind":"arxiv","version":2},"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/2411.10758/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":"2026-07-05T11:33:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8h+r1POiXZXb6HMIJ0ta+m0/4TP0jI4R5V6ujZI4pZG8sK6F2gmPilR8610xZV+FKgcYc2UKocoehF1k+GSWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:59:24.349909Z"},"content_sha256":"51ca054e1ae3ae7e53b2e12075c54f1b669e31f5b02743de6f1d8e6a34fe552e","schema_version":"1.0","event_id":"sha256:51ca054e1ae3ae7e53b2e12075c54f1b669e31f5b02743de6f1d8e6a34fe552e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOP7TE35NO3EEOX5WFMYD7PN4W/bundle.json","state_url":"https://pith.science/pith/OOP7TE35NO3EEOX5WFMYD7PN4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOP7TE35NO3EEOX5WFMYD7PN4W/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":"2026-08-13T05:59:24Z","links":{"resolver":"https://pith.science/pith/OOP7TE35NO3EEOX5WFMYD7PN4W","bundle":"https://pith.science/pith/OOP7TE35NO3EEOX5WFMYD7PN4W/bundle.json","state":"https://pith.science/pith/OOP7TE35NO3EEOX5WFMYD7PN4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOP7TE35NO3EEOX5WFMYD7PN4W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OOP7TE35NO3EEOX5WFMYD7PN4W","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":"9e974ff66a7c13aa6df102d430190ef7b300fc31eeb1397c3cc240c8398c314b","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-16T09:27:45Z","title_canon_sha256":"6217589c3d9087a1f24abb81b171edaea893d3d8c79d014ddc35a97bc4c2f202"},"schema_version":"1.0","source":{"id":"2411.10758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.10758","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"2411.10758v2","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.10758","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"OOP7TE35NO3E","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"pith_short_16","alias_value":"OOP7TE35NO3EEOX5","created_at":"2026-07-05T11:33:17Z"},{"alias_kind":"pith_short_8","alias_value":"OOP7TE35","created_at":"2026-07-05T11:33:17Z"}],"graph_snapshots":[{"event_id":"sha256:51ca054e1ae3ae7e53b2e12075c54f1b669e31f5b02743de6f1d8e6a34fe552e","target":"graph","created_at":"2026-07-05T11:33:17Z","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/2411.10758/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model, which is the most popular model for lithium-ion batteries. Central to our approach is a novel projection operator designed for the pseudo-($N$+1)-dimensional equation, offering a powerful tool for multiscale equation analysis. Our results bridge a gap in the analysis for dimensions $2 \\le N \\le 3$ and achieve optimal convergence rates of $h+(\\Delta r)^2$. Additionally, we perform a detailed numerical verification, marking the first such validation in this context. By avoiding the change of variables, ou","authors_text":"Liqun Cao, Shu Xu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-16T09:27:45Z","title":"Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10758","kind":"arxiv","version":2},"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":"sha256:8eb0333d011d86445a5af78d9912457fe12323be95d72f2d9020bfff228f4aa8","target":"record","created_at":"2026-07-05T11:33:17Z","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":"9e974ff66a7c13aa6df102d430190ef7b300fc31eeb1397c3cc240c8398c314b","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-16T09:27:45Z","title_canon_sha256":"6217589c3d9087a1f24abb81b171edaea893d3d8c79d014ddc35a97bc4c2f202"},"schema_version":"1.0","source":{"id":"2411.10758","kind":"arxiv","version":2}},"canonical_sha256":"739ff9937d6bb6423afdb15981fdede5944f4868d76af10e4cf52d7a78fd0d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"739ff9937d6bb6423afdb15981fdede5944f4868d76af10e4cf52d7a78fd0d84","first_computed_at":"2026-07-05T11:33:17.530986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:17.530986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mhmbh0hkVvqDGpJklNh7Hf59ABzlSCZLiBUeTbJ7oLNxl3+VfmHDTahFxQbiJhl8n5SJE4bwFZdEC1rlRI8JCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:17.531482Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.10758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eb0333d011d86445a5af78d9912457fe12323be95d72f2d9020bfff228f4aa8","sha256:51ca054e1ae3ae7e53b2e12075c54f1b669e31f5b02743de6f1d8e6a34fe552e"],"state_sha256":"ea605466a6f7d0b0db5fef116fc8e6202bc8fbb87f8fe892fbb86f00963bcf83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uU35cJhB8zYvNR/wiUcRD0/6KLth/OUOiln/QkdQ4cLcUWsahlM5mYpVvyfB37nr2/TdNIVIOsWT75GJx3CpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:59:24.354516Z","bundle_sha256":"56a8b856d908f1263e3293ead38b6224ef264e3b1e68e11c95ff6c624a0b3a2e"}}