{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CL5SNWJDNEMRVUW7ZQ3L5UPRFR","short_pith_number":"pith:CL5SNWJD","canonical_record":{"source":{"id":"1604.00190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-01T10:18:33Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"0b699d9c72b3c0d18d91b2570227a0ff41d883429f0c3fec91c0250c45363a44","abstract_canon_sha256":"40f21ba83c2ae001e063267211cb9a5e88715162da3b7a87e251a020c6c015c8"},"schema_version":"1.0"},"canonical_sha256":"12fb26d92369191ad2dfcc36bed1f12c4eb07d5aed04ea00ecf0a441de1ff7ae","source":{"kind":"arxiv","id":"1604.00190","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00190","created_at":"2026-05-18T01:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00190v1","created_at":"2026-05-18T01:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00190","created_at":"2026-05-18T01:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"CL5SNWJDNEMR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CL5SNWJDNEMRVUW7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CL5SNWJD","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CL5SNWJDNEMRVUW7ZQ3L5UPRFR","target":"record","payload":{"canonical_record":{"source":{"id":"1604.00190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-01T10:18:33Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"0b699d9c72b3c0d18d91b2570227a0ff41d883429f0c3fec91c0250c45363a44","abstract_canon_sha256":"40f21ba83c2ae001e063267211cb9a5e88715162da3b7a87e251a020c6c015c8"},"schema_version":"1.0"},"canonical_sha256":"12fb26d92369191ad2dfcc36bed1f12c4eb07d5aed04ea00ecf0a441de1ff7ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:54.349164Z","signature_b64":"GnpIpkB9jbAcXcNK851eMbwrm3mnDlWLRh7gCCNxF59lehN1/RtvGebexvjyX6UrrG4zFL2/jegiq6ptX9UeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12fb26d92369191ad2dfcc36bed1f12c4eb07d5aed04ea00ecf0a441de1ff7ae","last_reissued_at":"2026-05-18T01:17:54.348583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:54.348583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.00190","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":"2026-05-18T01:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0VJnq313EmB/m2OAeHz43WmoQF3VcVxxs0t7NpxasLHaC4uRW480tLOKjcHYXiGmgmUSC/r2reME8MmaVMHrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:05:09.808400Z"},"content_sha256":"3b2bc046bf49dd146f478bb8dcce90755c03f6f4f7066eaa83429acc1cee8289","schema_version":"1.0","event_id":"sha256:3b2bc046bf49dd146f478bb8dcce90755c03f6f4f7066eaa83429acc1cee8289"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CL5SNWJDNEMRVUW7ZQ3L5UPRFR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modeling battery cells under discharge using kinetic and stochastic battery models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Ingemar Kaj, Victorien Konan\\'e","submitted_at":"2016-04-01T10:18:33Z","abstract_excerpt":"In this paper we review several approaches to mathematical modeling of simple battery cells and develop these ideas further with emphasis on charge recovery and the response behavior of batteries to given external load. We focus on models which use few parameters and basic battery data, rather than detailed reaction and material characteristics of a specific battery cell chemistry, starting with the coupled ODE linear dynamics of the kinetic battery model. We show that a related system of PDE with Robin type boundary conditions arises in the limiting regime of a spatial kinetic battery model, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00190","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":"2026-05-18T01:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yacd1klbzSqrjVQwcQOadV33Bv2nnv122YCZPituGoouknGpSwtxyMMthH9awYD3RN4VOINY0u8ZJxhDsYPtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:05:09.809116Z"},"content_sha256":"5f64a90453323debd75252ef1356d14482867c00e53e722007ad89b63f3bb0f6","schema_version":"1.0","event_id":"sha256:5f64a90453323debd75252ef1356d14482867c00e53e722007ad89b63f3bb0f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR/bundle.json","state_url":"https://pith.science/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR/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":"2026-06-08T19:05:09Z","links":{"resolver":"https://pith.science/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR","bundle":"https://pith.science/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR/bundle.json","state":"https://pith.science/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CL5SNWJDNEMRVUW7ZQ3L5UPRFR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CL5SNWJDNEMRVUW7ZQ3L5UPRFR","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":"40f21ba83c2ae001e063267211cb9a5e88715162da3b7a87e251a020c6c015c8","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-01T10:18:33Z","title_canon_sha256":"0b699d9c72b3c0d18d91b2570227a0ff41d883429f0c3fec91c0250c45363a44"},"schema_version":"1.0","source":{"id":"1604.00190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00190","created_at":"2026-05-18T01:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00190v1","created_at":"2026-05-18T01:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00190","created_at":"2026-05-18T01:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"CL5SNWJDNEMR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CL5SNWJDNEMRVUW7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CL5SNWJD","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:5f64a90453323debd75252ef1356d14482867c00e53e722007ad89b63f3bb0f6","target":"graph","created_at":"2026-05-18T01:17:54Z","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 review several approaches to mathematical modeling of simple battery cells and develop these ideas further with emphasis on charge recovery and the response behavior of batteries to given external load. We focus on models which use few parameters and basic battery data, rather than detailed reaction and material characteristics of a specific battery cell chemistry, starting with the coupled ODE linear dynamics of the kinetic battery model. We show that a related system of PDE with Robin type boundary conditions arises in the limiting regime of a spatial kinetic battery model, ","authors_text":"Ingemar Kaj, Victorien Konan\\'e","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-01T10:18:33Z","title":"Modeling battery cells under discharge using kinetic and stochastic battery models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00190","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":"sha256:3b2bc046bf49dd146f478bb8dcce90755c03f6f4f7066eaa83429acc1cee8289","target":"record","created_at":"2026-05-18T01:17:54Z","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":"40f21ba83c2ae001e063267211cb9a5e88715162da3b7a87e251a020c6c015c8","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-01T10:18:33Z","title_canon_sha256":"0b699d9c72b3c0d18d91b2570227a0ff41d883429f0c3fec91c0250c45363a44"},"schema_version":"1.0","source":{"id":"1604.00190","kind":"arxiv","version":1}},"canonical_sha256":"12fb26d92369191ad2dfcc36bed1f12c4eb07d5aed04ea00ecf0a441de1ff7ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12fb26d92369191ad2dfcc36bed1f12c4eb07d5aed04ea00ecf0a441de1ff7ae","first_computed_at":"2026-05-18T01:17:54.348583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:54.348583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GnpIpkB9jbAcXcNK851eMbwrm3mnDlWLRh7gCCNxF59lehN1/RtvGebexvjyX6UrrG4zFL2/jegiq6ptX9UeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:54.349164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b2bc046bf49dd146f478bb8dcce90755c03f6f4f7066eaa83429acc1cee8289","sha256:5f64a90453323debd75252ef1356d14482867c00e53e722007ad89b63f3bb0f6"],"state_sha256":"75179c412300cae299f4b4f9fbbae29d8c4c48e366059b909a49267d572bc125"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TP7y/t/+SrzNDobHWUUV81CLw5rkuldvIWuAs0pwLt8xwjwyuPO/xp08thiJ5RUKMgnO6Xq/3pZYjiEKdOA0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:05:09.812987Z","bundle_sha256":"216066eb8df99831a2be9b7f1d7d256bec8fc4858d0333a793c98e8e6e158e1d"}}