{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NJALHX42XBYGAWW7J5CT6IJ7TN","short_pith_number":"pith:NJALHX42","canonical_record":{"source":{"id":"1508.02660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-11T17:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"ee1e0fe2afb9930f185bbe9f4786a926606477caa96d4ba24cd35c880e038073","abstract_canon_sha256":"c8af41c44444616921204eed7d4737e4eb910069a5e15d479d230eef7688670f"},"schema_version":"1.0"},"canonical_sha256":"6a40b3df9ab870605adf4f453f213f9b567e584991db35725cc22997ed798934","source":{"kind":"arxiv","id":"1508.02660","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02660","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02660v1","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02660","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"NJALHX42XBYG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJALHX42XBYGAWW7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJALHX42","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NJALHX42XBYGAWW7J5CT6IJ7TN","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-11T17:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"ee1e0fe2afb9930f185bbe9f4786a926606477caa96d4ba24cd35c880e038073","abstract_canon_sha256":"c8af41c44444616921204eed7d4737e4eb910069a5e15d479d230eef7688670f"},"schema_version":"1.0"},"canonical_sha256":"6a40b3df9ab870605adf4f453f213f9b567e584991db35725cc22997ed798934","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:28.629427Z","signature_b64":"tpPHpEba17P2tUDgBi90U70ZS2HyGe4yTyxIoYf/nvX8S8X1sc7EXIywveZyPeHikYBH5DdSLFDO1PYeC4wTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a40b3df9ab870605adf4f453f213f9b567e584991db35725cc22997ed798934","last_reissued_at":"2026-05-18T01:35:28.628798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:28.628798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02660","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":"2026-05-18T01:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkidx12jMuhTaHAgU1LIpq4iTi0lUJUOcAiZUm2UAb3ycNqMBlMMPLhz/u6IVjEP/VOahZL66w375O4YDLKQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:52:38.381627Z"},"content_sha256":"6f6874859f394b247b04d1db77b428eb10ef4bcdef05304724f29edce58d1db0","schema_version":"1.0","event_id":"sha256:6f6874859f394b247b04d1db77b428eb10ef4bcdef05304724f29edce58d1db0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NJALHX42XBYGAWW7J5CT6IJ7TN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Nicola Zamponi","submitted_at":"2015-08-11T17:16:31Z","abstract_excerpt":"The existence of global weak solutions to a coupled spin drift-diffusion and Maxwell-Landau-Lifshitz system is proved. The equations are considered in a two-dimensional magnetic layer structure and are supplemented with Dirichlet-Neumann boundary conditions. The spin drift-diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial Boltzmann equation for a vanishing spin polarization constant. The Maxwell-Landau-Lifshitz system consists of the time-dependent Maxwell equations for the electric and magnetic fields and of the Landau-Lifshitz-Gilbert equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02660","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":"2026-05-18T01:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgxO63/Qnw4f1VXk+5Iuqy1kyBnuDeDR7z+sVePEXQBemCENrhl22TG1emtCvUONAIGNOPoIcLET6Gy+O7IjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:52:38.382344Z"},"content_sha256":"52a1b1b1ade74e19f42f7154fe383a9c6a1beaa895fa94cb886f48daddff0fd0","schema_version":"1.0","event_id":"sha256:52a1b1b1ade74e19f42f7154fe383a9c6a1beaa895fa94cb886f48daddff0fd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJALHX42XBYGAWW7J5CT6IJ7TN/bundle.json","state_url":"https://pith.science/pith/NJALHX42XBYGAWW7J5CT6IJ7TN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJALHX42XBYGAWW7J5CT6IJ7TN/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":"2026-06-11T19:52:38Z","links":{"resolver":"https://pith.science/pith/NJALHX42XBYGAWW7J5CT6IJ7TN","bundle":"https://pith.science/pith/NJALHX42XBYGAWW7J5CT6IJ7TN/bundle.json","state":"https://pith.science/pith/NJALHX42XBYGAWW7J5CT6IJ7TN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJALHX42XBYGAWW7J5CT6IJ7TN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NJALHX42XBYGAWW7J5CT6IJ7TN","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":"c8af41c44444616921204eed7d4737e4eb910069a5e15d479d230eef7688670f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-11T17:16:31Z","title_canon_sha256":"ee1e0fe2afb9930f185bbe9f4786a926606477caa96d4ba24cd35c880e038073"},"schema_version":"1.0","source":{"id":"1508.02660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02660","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02660v1","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02660","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"NJALHX42XBYG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJALHX42XBYGAWW7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJALHX42","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:52a1b1b1ade74e19f42f7154fe383a9c6a1beaa895fa94cb886f48daddff0fd0","target":"graph","created_at":"2026-05-18T01:35:28Z","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":"The existence of global weak solutions to a coupled spin drift-diffusion and Maxwell-Landau-Lifshitz system is proved. The equations are considered in a two-dimensional magnetic layer structure and are supplemented with Dirichlet-Neumann boundary conditions. The spin drift-diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial Boltzmann equation for a vanishing spin polarization constant. The Maxwell-Landau-Lifshitz system consists of the time-dependent Maxwell equations for the electric and magnetic fields and of the Landau-Lifshitz-Gilbert equati","authors_text":"Ansgar J\\\"ungel, Nicola Zamponi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-11T17:16:31Z","title":"Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02660","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":"sha256:6f6874859f394b247b04d1db77b428eb10ef4bcdef05304724f29edce58d1db0","target":"record","created_at":"2026-05-18T01:35:28Z","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":"c8af41c44444616921204eed7d4737e4eb910069a5e15d479d230eef7688670f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-11T17:16:31Z","title_canon_sha256":"ee1e0fe2afb9930f185bbe9f4786a926606477caa96d4ba24cd35c880e038073"},"schema_version":"1.0","source":{"id":"1508.02660","kind":"arxiv","version":1}},"canonical_sha256":"6a40b3df9ab870605adf4f453f213f9b567e584991db35725cc22997ed798934","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a40b3df9ab870605adf4f453f213f9b567e584991db35725cc22997ed798934","first_computed_at":"2026-05-18T01:35:28.628798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:28.628798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tpPHpEba17P2tUDgBi90U70ZS2HyGe4yTyxIoYf/nvX8S8X1sc7EXIywveZyPeHikYBH5DdSLFDO1PYeC4wTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:28.629427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f6874859f394b247b04d1db77b428eb10ef4bcdef05304724f29edce58d1db0","sha256:52a1b1b1ade74e19f42f7154fe383a9c6a1beaa895fa94cb886f48daddff0fd0"],"state_sha256":"e38fea4488d05a17beddccbff39c8c73363fc229f15a15dedd78a8b98c937161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9N/CXqRbqA42tn/0yI9wDHY+8sQbC1hSv5DrJ25o6h6Fh004wkGJRdOMqwb/izF9ww1TVHDnvLttuFG7hzuCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T19:52:38.386276Z","bundle_sha256":"7d54e90839c6dac7a63fd0f28e978d5ee8a07c2f250510e3a9d1f23c0d3571a5"}}