{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RHRFCHHJVA4ITZYR62KE2YRTQ2","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":"553d5a208db049c1280d837d24bdbd1024c6f2be285d0c573d4cee70213ecef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-15T10:00:40Z","title_canon_sha256":"b52c0a87e8c18205b22a90c7cfd52d01c598695f7a38496258083fdf244e9952"},"schema_version":"1.0","source":{"id":"1104.3002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3002","created_at":"2026-05-18T02:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3002v1","created_at":"2026-05-18T02:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3002","created_at":"2026-05-18T02:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"RHRFCHHJVA4I","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHRFCHHJVA4ITZYR","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHRFCHHJ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:c0b54563f98c69dabf61978cddd1f53d9bdd299008d6c206088dc7230cd20582","target":"graph","created_at":"2026-05-18T02:02:28Z","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":"A Lagrangian is introduced which includes the coupling between magnetic moments $\\mathbf{m}$ and the degrees of freedom $\\boldsymbol{\\sigma}$ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments $\\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying Noeth","authors_text":"Steffen Trimper, Thomas Bose","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-15T10:00:40Z","title":"Lagrangian approach and dissipative magnetic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3002","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":"sha256:2516cfa741167724f9c7eeb0b896f99a274553cc3e3b3af3da8f1b7e61490b47","target":"record","created_at":"2026-05-18T02:02:28Z","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":"553d5a208db049c1280d837d24bdbd1024c6f2be285d0c573d4cee70213ecef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-15T10:00:40Z","title_canon_sha256":"b52c0a87e8c18205b22a90c7cfd52d01c598695f7a38496258083fdf244e9952"},"schema_version":"1.0","source":{"id":"1104.3002","kind":"arxiv","version":1}},"canonical_sha256":"89e2511ce9a83889e711f6944d6233868525d45368ed208223a43272c14d39e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89e2511ce9a83889e711f6944d6233868525d45368ed208223a43272c14d39e3","first_computed_at":"2026-05-18T02:02:28.247870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:28.247870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MJECNUWP2DicC5FFA5D5WYCPTL8PFWtHGH9se8w0vJQpGmNOA2xpLWZxOe+qAzIepBBdtcuDE2xZ4XVhw4c4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:28.248547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2516cfa741167724f9c7eeb0b896f99a274553cc3e3b3af3da8f1b7e61490b47","sha256:c0b54563f98c69dabf61978cddd1f53d9bdd299008d6c206088dc7230cd20582"],"state_sha256":"a5a42df978d2849f780da31afd4a1546e97ceeb4f42be8c3d79cd931439396c4"}