{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MWF5HOY4DJ6VCJH2FVZQCB7IOO","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":"e247835bfa39ab7fde186e9e5b832e426000f1f853aabef1446c7f58b9c85ce0","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-21T17:28:19Z","title_canon_sha256":"5f691422854b0b16e208e7b3f30e0149578e31ac1f74bc9af4bd0eeb684d4c55"},"schema_version":"1.0","source":{"id":"1911.09619","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.09619","created_at":"2026-07-05T01:55:44Z"},{"alias_kind":"arxiv_version","alias_value":"1911.09619v2","created_at":"2026-07-05T01:55:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09619","created_at":"2026-07-05T01:55:44Z"},{"alias_kind":"pith_short_12","alias_value":"MWF5HOY4DJ6V","created_at":"2026-07-05T01:55:44Z"},{"alias_kind":"pith_short_16","alias_value":"MWF5HOY4DJ6VCJH2","created_at":"2026-07-05T01:55:44Z"},{"alias_kind":"pith_short_8","alias_value":"MWF5HOY4","created_at":"2026-07-05T01:55:44Z"}],"graph_snapshots":[{"event_id":"sha256:a8c698205e327599f4d1e1107e804c6d983d4097fee866cef0d8a1cd1f622575","target":"graph","created_at":"2026-07-05T01:55:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.09619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Colin Cotter, Jacob Deasy, Tristan Pryer","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-21T17:28:19Z","title":"The r-Hunter-Saxton equation, smooth and singular solutions and their approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09619","kind":"arxiv","version":2},"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:d7b96e3aa252dce80fc888f1202956fe0a5f2be7f76e88eeaac069376473294f","target":"record","created_at":"2026-07-05T01:55:44Z","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":"e247835bfa39ab7fde186e9e5b832e426000f1f853aabef1446c7f58b9c85ce0","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-21T17:28:19Z","title_canon_sha256":"5f691422854b0b16e208e7b3f30e0149578e31ac1f74bc9af4bd0eeb684d4c55"},"schema_version":"1.0","source":{"id":"1911.09619","kind":"arxiv","version":2}},"canonical_sha256":"658bd3bb1c1a7d5124fa2d730107e873ac9a0616ffc9a84a48bb3e0c32c9e06e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"658bd3bb1c1a7d5124fa2d730107e873ac9a0616ffc9a84a48bb3e0c32c9e06e","first_computed_at":"2026-07-05T01:55:44.163269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:55:44.163269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YagsJPtNV60IQLaV8AenkLDS9UjQ2GwMN0WBtkEqrIiKNJqSyUm9MX3sOwhD3wnB+aIKuzpOlBanrf47zD3YCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:55:44.163613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.09619","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7b96e3aa252dce80fc888f1202956fe0a5f2be7f76e88eeaac069376473294f","sha256:a8c698205e327599f4d1e1107e804c6d983d4097fee866cef0d8a1cd1f622575"],"state_sha256":"4771eb0ac11c555d8e686c64e0692c2e596a191fe133da309224ef0adfc85c1f"}