{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6OOEHTBOGPUOPZ627TOMOVVFEV","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":"e267b9ea0b2571c995203f6c3b9c3e75547c32553263be78112989919ae76302","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-17T18:25:07Z","title_canon_sha256":"eb1e3c9c739a7ed2b4a6cb22a7d1ef94e002e9b620d5448d26a9116f25d4a4e4"},"schema_version":"1.0","source":{"id":"1308.3800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3800","created_at":"2026-05-18T01:48:14Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3800v1","created_at":"2026-05-18T01:48:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3800","created_at":"2026-05-18T01:48:14Z"},{"alias_kind":"pith_short_12","alias_value":"6OOEHTBOGPUO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6OOEHTBOGPUOPZ62","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6OOEHTBO","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:03ee7031754f06f0d5f2e2f37c7944349179bb019d9f69dcbfdf6cf453e0a663","target":"graph","created_at":"2026-05-18T01:48:14Z","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 present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamilton's principles and Hamiltonians for these systems and analyzes the linear stability of their equilibrium solutions in the examples of $\\mathfrak{so}(3)$ and $\\mathfrak{sl}(2,\\mathbb{R})$.","authors_text":"Darryl D. Holm, Fran\\c{c}ois Gay-Balmaz, Tudor S. Ratiu","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-17T18:25:07Z","title":"Integrable G-Strands on semisimple Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3800","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":"sha256:596305b724882c7f83298109a3edf5226517aceb1d7e36af03656a28fef489cb","target":"record","created_at":"2026-05-18T01:48:14Z","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":"e267b9ea0b2571c995203f6c3b9c3e75547c32553263be78112989919ae76302","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-17T18:25:07Z","title_canon_sha256":"eb1e3c9c739a7ed2b4a6cb22a7d1ef94e002e9b620d5448d26a9116f25d4a4e4"},"schema_version":"1.0","source":{"id":"1308.3800","kind":"arxiv","version":1}},"canonical_sha256":"f39c43cc2e33e8e7e7dafcdcc756a5256f6c453f348a197b46faa79da0c2cd1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f39c43cc2e33e8e7e7dafcdcc756a5256f6c453f348a197b46faa79da0c2cd1e","first_computed_at":"2026-05-18T01:48:14.360911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:14.360911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fjTqNFjcE9su7TbrSFFSU8ivCDaKfdmaSUkXJ2Uy5RNQ+T7ftSo4Ug/JDwNZt3YQRZY4W1ArHLvzGYGMCaMXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:14.361546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:596305b724882c7f83298109a3edf5226517aceb1d7e36af03656a28fef489cb","sha256:03ee7031754f06f0d5f2e2f37c7944349179bb019d9f69dcbfdf6cf453e0a663"],"state_sha256":"65bae010eb0b43c75cf83e76d7ebfd590b4c61b60629f2980243d20ef8830be7"}