{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:MWF5HOY4DJ6VCJH2FVZQCB7IOO","short_pith_number":"pith:MWF5HOY4","schema_version":"1.0","canonical_sha256":"658bd3bb1c1a7d5124fa2d730107e873ac9a0616ffc9a84a48bb3e0c32c9e06e","source":{"kind":"arxiv","id":"1911.09619","version":2},"attestation_state":"computed","paper":{"title":"The r-Hunter-Saxton equation, smooth and singular solutions and their approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AP","authors_text":"Colin Cotter, Jacob Deasy, Tristan Pryer","submitted_at":"2019-11-21T17:28:19Z","abstract_excerpt":"In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter-Saxton equation."},"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":"1911.09619","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-21T17:28:19Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"5f691422854b0b16e208e7b3f30e0149578e31ac1f74bc9af4bd0eeb684d4c55","abstract_canon_sha256":"e247835bfa39ab7fde186e9e5b832e426000f1f853aabef1446c7f58b9c85ce0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:55:44.163613Z","signature_b64":"YagsJPtNV60IQLaV8AenkLDS9UjQ2GwMN0WBtkEqrIiKNJqSyUm9MX3sOwhD3wnB+aIKuzpOlBanrf47zD3YCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"658bd3bb1c1a7d5124fa2d730107e873ac9a0616ffc9a84a48bb3e0c32c9e06e","last_reissued_at":"2026-07-05T01:55:44.163269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:55:44.163269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The r-Hunter-Saxton equation, smooth and singular solutions and their approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AP","authors_text":"Colin Cotter, Jacob Deasy, Tristan Pryer","submitted_at":"2019-11-21T17:28:19Z","abstract_excerpt":"In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter-Saxton equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09619","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.09619/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1911.09619","created_at":"2026-07-05T01:55:44.163324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.09619v2","created_at":"2026-07-05T01:55:44.163324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09619","created_at":"2026-07-05T01:55:44.163324+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWF5HOY4DJ6V","created_at":"2026-07-05T01:55:44.163324+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWF5HOY4DJ6VCJH2","created_at":"2026-07-05T01:55:44.163324+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWF5HOY4","created_at":"2026-07-05T01:55:44.163324+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/MWF5HOY4DJ6VCJH2FVZQCB7IOO","json":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO.json","graph_json":"https://pith.science/api/pith-number/MWF5HOY4DJ6VCJH2FVZQCB7IOO/graph.json","events_json":"https://pith.science/api/pith-number/MWF5HOY4DJ6VCJH2FVZQCB7IOO/events.json","paper":"https://pith.science/paper/MWF5HOY4"},"agent_actions":{"view_html":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO","download_json":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO.json","view_paper":"https://pith.science/paper/MWF5HOY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.09619&json=true","fetch_graph":"https://pith.science/api/pith-number/MWF5HOY4DJ6VCJH2FVZQCB7IOO/graph.json","fetch_events":"https://pith.science/api/pith-number/MWF5HOY4DJ6VCJH2FVZQCB7IOO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO/action/storage_attestation","attest_author":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO/action/author_attestation","sign_citation":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO/action/citation_signature","submit_replication":"https://pith.science/pith/MWF5HOY4DJ6VCJH2FVZQCB7IOO/action/replication_record"}},"created_at":"2026-07-05T01:55:44.163324+00:00","updated_at":"2026-07-05T01:55:44.163324+00:00"}