{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OGLKMY5B6BJLFAABOY7UUEQSSS","short_pith_number":"pith:OGLKMY5B","canonical_record":{"source":{"id":"2604.16627","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2026-04-17T18:28:17Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"85b584bd799d7b7f4da992894ba7f4f8ee1ebcb35ddc293167a02f664107d287","abstract_canon_sha256":"58ad15b0a5026ae7deb13bdc2eca268575cd6dda6b4f7ec98b92a70b614d1bd2"},"schema_version":"1.0"},"canonical_sha256":"7196a663a1f052b28001763f4a1212949cec0740d72a7232e3649fc5a0368401","source":{"kind":"arxiv","id":"2604.16627","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.16627","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"2604.16627v2","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.16627","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"OGLKMY5B6BJL","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"pith_short_16","alias_value":"OGLKMY5B6BJLFAAB","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"pith_short_8","alias_value":"OGLKMY5B","created_at":"2026-07-02T01:18:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OGLKMY5B6BJLFAABOY7UUEQSSS","target":"record","payload":{"canonical_record":{"source":{"id":"2604.16627","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2026-04-17T18:28:17Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"85b584bd799d7b7f4da992894ba7f4f8ee1ebcb35ddc293167a02f664107d287","abstract_canon_sha256":"58ad15b0a5026ae7deb13bdc2eca268575cd6dda6b4f7ec98b92a70b614d1bd2"},"schema_version":"1.0"},"canonical_sha256":"7196a663a1f052b28001763f4a1212949cec0740d72a7232e3649fc5a0368401","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:08.213400Z","signature_b64":"MSWLtOk8fypXJ4a33l9jV8dKoo3/iGPPtemrP33E88E98oRoEm1DzNNj3WsdGDiIvZIWP1giipc9lCQZvPi1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7196a663a1f052b28001763f4a1212949cec0740d72a7232e3649fc5a0368401","last_reissued_at":"2026-07-02T01:18:08.213005Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:08.213005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.16627","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":"2026-07-02T01:18:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slCDUosjMb+yEACMBwVi23koQTTcQa9cw0SFcV3I30D/095Yh5km+hC2WoXB9KaAtxCPN6e1Kz9rhtg5sJAcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T01:35:00.172687Z"},"content_sha256":"13828bbcc2665b8991951a8a281c56bf5e8933175a413dbccfbc4cbfbf3b14d2","schema_version":"1.0","event_id":"sha256:13828bbcc2665b8991951a8a281c56bf5e8933175a413dbccfbc4cbfbf3b14d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OGLKMY5B6BJLFAABOY7UUEQSSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling and Analytical Approximation of Porous Electrode Theory for Reaction-limited Batteries","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Martin Z. Bazant, Shakul Pathak","submitted_at":"2026-04-17T18:28:17Z","abstract_excerpt":"Porous electrode theory (PET) provides essential insights into electrochemical states, but its computational complexity hinders real-time control and obscures scaling relations. To bridge the gap between high-fidelity simulations and reduced-order models, we present a framework of scaling analysis and analytical approximations. By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified \"lean model\" governed by four dimensionless numbers: (i) a traditional Damk\\\"ohler number, $Da$, scaling the characteristic reaction rate to the diffusion r"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified 'lean model' governed by four dimensionless numbers... For batteries, we derive analytical solutions for standard protocols... our formulae show excellent agreement at negligible computational cost.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that high-performance electrodes minimize transport limitations and overpotentials, which is invoked to justify collapsing the full porous electrode theory into the lean model (stated in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Scaling analysis produces a lean porous electrode model with four Damkohler numbers (Da, Da_p, Da_w, Da_c) and closed-form solutions for battery protocols that match full simulations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8c920002715590aeae11677f12b4c6c2de8caafcd9b18e4d8ec7a657e49afec6"},"source":{"id":"2604.16627","kind":"arxiv","version":2},"verdict":{"id":"b9b78683-b65e-41f2-b9b8-7f423c056462","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T07:20:25.554597Z","strongest_claim":"By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified 'lean model' governed by four dimensionless numbers... For batteries, we derive analytical solutions for standard protocols... our formulae show excellent agreement at negligible computational cost.","one_line_summary":"Scaling analysis produces a lean porous electrode model with four Damkohler numbers (Da, Da_p, Da_w, Da_c) and closed-form solutions for battery protocols that match full simulations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that high-performance electrodes minimize transport limitations and overpotentials, which is invoked to justify collapsing the full porous electrode theory into the lean model (stated in the abstract).","pith_extraction_headline":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16627/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":"b9b78683-b65e-41f2-b9b8-7f423c056462"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-02T01:18:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bzjtBYPds/44AfdKUnw0X/Ah0rXxIgyGAd+SjF7Jt9k2XYoBUjfWGzcIck0cch3RQJjXbWDQDY8XC1piW/KAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T01:35:00.173149Z"},"content_sha256":"257a5e3779ac8cdd0644409c203a6014c15230dd0abbc2e0ac4f5f3f52b1a730","schema_version":"1.0","event_id":"sha256:257a5e3779ac8cdd0644409c203a6014c15230dd0abbc2e0ac4f5f3f52b1a730"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGLKMY5B6BJLFAABOY7UUEQSSS/bundle.json","state_url":"https://pith.science/pith/OGLKMY5B6BJLFAABOY7UUEQSSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGLKMY5B6BJLFAABOY7UUEQSSS/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":"2026-07-04T01:35:00Z","links":{"resolver":"https://pith.science/pith/OGLKMY5B6BJLFAABOY7UUEQSSS","bundle":"https://pith.science/pith/OGLKMY5B6BJLFAABOY7UUEQSSS/bundle.json","state":"https://pith.science/pith/OGLKMY5B6BJLFAABOY7UUEQSSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGLKMY5B6BJLFAABOY7UUEQSSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OGLKMY5B6BJLFAABOY7UUEQSSS","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":"58ad15b0a5026ae7deb13bdc2eca268575cd6dda6b4f7ec98b92a70b614d1bd2","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2026-04-17T18:28:17Z","title_canon_sha256":"85b584bd799d7b7f4da992894ba7f4f8ee1ebcb35ddc293167a02f664107d287"},"schema_version":"1.0","source":{"id":"2604.16627","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.16627","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"2604.16627v2","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.16627","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"OGLKMY5B6BJL","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"pith_short_16","alias_value":"OGLKMY5B6BJLFAAB","created_at":"2026-07-02T01:18:08Z"},{"alias_kind":"pith_short_8","alias_value":"OGLKMY5B","created_at":"2026-07-02T01:18:08Z"}],"graph_snapshots":[{"event_id":"sha256:257a5e3779ac8cdd0644409c203a6014c15230dd0abbc2e0ac4f5f3f52b1a730","target":"graph","created_at":"2026-07-02T01:18:08Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified 'lean model' governed by four dimensionless numbers... For batteries, we derive analytical solutions for standard protocols... our formulae show excellent agreement at negligible computational cost."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that high-performance electrodes minimize transport limitations and overpotentials, which is invoked to justify collapsing the full porous electrode theory into the lean model (stated in the abstract)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Scaling analysis produces a lean porous electrode model with four Damkohler numbers (Da, Da_p, Da_w, Da_c) and closed-form solutions for battery protocols that match full simulations."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries."}],"snapshot_sha256":"8c920002715590aeae11677f12b4c6c2de8caafcd9b18e4d8ec7a657e49afec6"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.16627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Porous electrode theory (PET) provides essential insights into electrochemical states, but its computational complexity hinders real-time control and obscures scaling relations. To bridge the gap between high-fidelity simulations and reduced-order models, we present a framework of scaling analysis and analytical approximations. By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified \"lean model\" governed by four dimensionless numbers: (i) a traditional Damk\\\"ohler number, $Da$, scaling the characteristic reaction rate to the diffusion r","authors_text":"Martin Z. Bazant, Shakul Pathak","cross_cats":["cs.SY"],"headline":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2026-04-17T18:28:17Z","title":"Scaling and Analytical Approximation of Porous Electrode Theory for Reaction-limited Batteries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.16627","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T07:20:25.554597Z","id":"b9b78683-b65e-41f2-b9b8-7f423c056462","model_set":{"reader":"grok-4.3"},"one_line_summary":"Scaling analysis produces a lean porous electrode model with four Damkohler numbers (Da, Da_p, Da_w, Da_c) and closed-form solutions for battery protocols that match full simulations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.","strongest_claim":"By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified 'lean model' governed by four dimensionless numbers... For batteries, we derive analytical solutions for standard protocols... our formulae show excellent agreement at negligible computational cost.","weakest_assumption":"The assumption that high-performance electrodes minimize transport limitations and overpotentials, which is invoked to justify collapsing the full porous electrode theory into the lean model (stated in the abstract)."}},"verdict_id":"b9b78683-b65e-41f2-b9b8-7f423c056462"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:13828bbcc2665b8991951a8a281c56bf5e8933175a413dbccfbc4cbfbf3b14d2","target":"record","created_at":"2026-07-02T01:18:08Z","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":"58ad15b0a5026ae7deb13bdc2eca268575cd6dda6b4f7ec98b92a70b614d1bd2","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2026-04-17T18:28:17Z","title_canon_sha256":"85b584bd799d7b7f4da992894ba7f4f8ee1ebcb35ddc293167a02f664107d287"},"schema_version":"1.0","source":{"id":"2604.16627","kind":"arxiv","version":2}},"canonical_sha256":"7196a663a1f052b28001763f4a1212949cec0740d72a7232e3649fc5a0368401","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7196a663a1f052b28001763f4a1212949cec0740d72a7232e3649fc5a0368401","first_computed_at":"2026-07-02T01:18:08.213005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:08.213005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MSWLtOk8fypXJ4a33l9jV8dKoo3/iGPPtemrP33E88E98oRoEm1DzNNj3WsdGDiIvZIWP1giipc9lCQZvPi1DA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:08.213400Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.16627","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13828bbcc2665b8991951a8a281c56bf5e8933175a413dbccfbc4cbfbf3b14d2","sha256:257a5e3779ac8cdd0644409c203a6014c15230dd0abbc2e0ac4f5f3f52b1a730"],"state_sha256":"084dead16cc50641be02464740739ee2e24bd59d68d1af2024514423d6a01825"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRrMREHViidfg/7YN6BXASM8V5060Gm1cgovhnnChH0+nwlbovEwgKnpPng9cuQIKg5EfRHFyABgDA8KH7ZxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T01:35:00.175766Z","bundle_sha256":"dc0a015575a3ef0e9be1f4d209a49c1163ac5ffbe7a41964e51d678f983abcef"}}