{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:P7JPSP5VSDW6DPGKEYGFPXKNSO","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":"b6b0c21ed31a76c79d077cef60020fbb37d39c7da9d71d62be2295ffc47cc8ec","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-21T12:45:23Z","title_canon_sha256":"b60cdfb979d86038b7a4d5e76ff4de2b7f933070f52a0d80ed2736d35fc51886"},"schema_version":"1.0","source":{"id":"1010.4454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4454","created_at":"2026-05-18T02:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4454v1","created_at":"2026-05-18T02:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4454","created_at":"2026-05-18T02:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"P7JPSP5VSDW6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P7JPSP5VSDW6DPGK","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P7JPSP5V","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:163966777d913c2c5ad47ff1760065f511081f0afd51a1b4f989eb19187a3559","target":"graph","created_at":"2026-05-18T02:05:00Z","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 propose a two-component generalization of the generalized Hunter-Saxton equation obtained in \\cite{BLG2008}. We will show that this equation is a bihamiltonian Euler equation, and also can be viewed as a bi-variational equation.","authors_text":"Dafeng Zuo","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-21T12:45:23Z","title":"A 2-component $\\mu$-Hunter-Saxton equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4454","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":"sha256:1be1ab1998f088301cf2dcfbbeca9b618a80e2d096c7acba1a775baa6a700db9","target":"record","created_at":"2026-05-18T02:05:00Z","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":"b6b0c21ed31a76c79d077cef60020fbb37d39c7da9d71d62be2295ffc47cc8ec","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-21T12:45:23Z","title_canon_sha256":"b60cdfb979d86038b7a4d5e76ff4de2b7f933070f52a0d80ed2736d35fc51886"},"schema_version":"1.0","source":{"id":"1010.4454","kind":"arxiv","version":1}},"canonical_sha256":"7fd2f93fb590ede1bcca260c57dd4d93a6527f5657ed16dd89980797a978fd94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fd2f93fb590ede1bcca260c57dd4d93a6527f5657ed16dd89980797a978fd94","first_computed_at":"2026-05-18T02:05:00.028749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:00.028749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jiJVPQ3H45cilDLhUrqZQZJ56J3+URU9qyZsSov5THFAWutUxrPiLg1IwB2t5M+P3Nddctn0/5dR9L9eszzlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:00.029203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be1ab1998f088301cf2dcfbbeca9b618a80e2d096c7acba1a775baa6a700db9","sha256:163966777d913c2c5ad47ff1760065f511081f0afd51a1b4f989eb19187a3559"],"state_sha256":"ff10b0e545490fc50654b47c34acc2725f18e615bbca4df53462cb9852184fd8"}