{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JYOLKNC3HBAM5SVFTMVBPYGRUN","short_pith_number":"pith:JYOLKNC3","schema_version":"1.0","canonical_sha256":"4e1cb5345b3840cecaa59b2a17e0d1a34ffb225c521c943169fd89389a549918","source":{"kind":"arxiv","id":"1307.4504","version":2},"attestation_state":"computed","paper":{"title":"Global estimates and blow-up criteria for the generalized Hunter-Saxton system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Sarria","submitted_at":"2013-07-17T05:05:27Z","abstract_excerpt":"The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation formula for periodic solutions to the system, which is valid for arbitrary values of parameters $(\\lambda,\\kappa)\\in\\mathbb{R}\\times\\mathbb{R}$, is derived. This allows us to examine in great detail qualitative properties of blow-up as well as the asymptotic behaviour of solutions, including convergence to steady states in finite or infinite time."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.4504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-17T05:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"39ffc3c4072c7cedce54239a607e70d50a843380821534744ad5f636e2c08bb9","abstract_canon_sha256":"a896979cfd29ea80156b011530beda2ff25d43fb3b2341f44bfa97fe1c220a23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:52.102974Z","signature_b64":"cg94yCAqnLPw95BsMH7fVRCzoiJF9BjBmBFtvE2xqTUHf2ivrg1WL0c+jyiyayBQWzwAqCEfJrCi2QWTHQN/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e1cb5345b3840cecaa59b2a17e0d1a34ffb225c521c943169fd89389a549918","last_reissued_at":"2026-05-18T02:37:52.102299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:52.102299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global estimates and blow-up criteria for the generalized Hunter-Saxton system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Sarria","submitted_at":"2013-07-17T05:05:27Z","abstract_excerpt":"The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation formula for periodic solutions to the system, which is valid for arbitrary values of parameters $(\\lambda,\\kappa)\\in\\mathbb{R}\\times\\mathbb{R}$, is derived. This allows us to examine in great detail qualitative properties of blow-up as well as the asymptotic behaviour of solutions, including convergence to steady states in finite or infinite time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4504","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.4504","created_at":"2026-05-18T02:37:52.102397+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4504v2","created_at":"2026-05-18T02:37:52.102397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4504","created_at":"2026-05-18T02:37:52.102397+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYOLKNC3HBAM","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYOLKNC3HBAM5SVF","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYOLKNC3","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN","json":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN.json","graph_json":"https://pith.science/api/pith-number/JYOLKNC3HBAM5SVFTMVBPYGRUN/graph.json","events_json":"https://pith.science/api/pith-number/JYOLKNC3HBAM5SVFTMVBPYGRUN/events.json","paper":"https://pith.science/paper/JYOLKNC3"},"agent_actions":{"view_html":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN","download_json":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN.json","view_paper":"https://pith.science/paper/JYOLKNC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4504&json=true","fetch_graph":"https://pith.science/api/pith-number/JYOLKNC3HBAM5SVFTMVBPYGRUN/graph.json","fetch_events":"https://pith.science/api/pith-number/JYOLKNC3HBAM5SVFTMVBPYGRUN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN/action/storage_attestation","attest_author":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN/action/author_attestation","sign_citation":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN/action/citation_signature","submit_replication":"https://pith.science/pith/JYOLKNC3HBAM5SVFTMVBPYGRUN/action/replication_record"}},"created_at":"2026-05-18T02:37:52.102397+00:00","updated_at":"2026-05-18T02:37:52.102397+00:00"}