{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3FHCZAIELIEMT4RKBQP7VTFKMY","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":"73193e9089a093dacde6064107f5801445421d3bc2bde4df780b4e856b4178cd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-24T19:51:46Z","title_canon_sha256":"b6457fb055f61b447866c4c04ede9d85b2d3f6c79ce6651967f50435c305133d"},"schema_version":"1.0","source":{"id":"0903.4134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4134","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4134v1","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4134","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"3FHCZAIELIEM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3FHCZAIELIEMT4RK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3FHCZAIE","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a708d8a35bc8aea13ae68a8d9991d035b916d772a034edb276db354c4d456f90","target":"graph","created_at":"2026-05-18T01:09:24Z","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":"We study a family of equations defined on the space of tensor densities of weight $\\lambda$ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been identified in any form before. We present their Lax pair formulations and describe their bihamiltonian structures. We prove local wellposedness of the corresponding Cauchy problem and include results on blow-up as well as global existence of solutions. Moreover, we construct \"peakon\" and \"multi-peakon\" solutions for all $\\lambda \\neq 0,1$, and","authors_text":"Feride Ti\\u{g}lay, Gerard Misio{\\l}ek, Jonatan Lenells","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-24T19:51:46Z","title":"Integrable evolution equations on spaces of tensor densities and their peakon solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4134","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:decfca9ddc7e6f6810b88f700d4bc921255cebefd455d2d1a23d27b2d25ef647","target":"record","created_at":"2026-05-18T01:09:24Z","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":"73193e9089a093dacde6064107f5801445421d3bc2bde4df780b4e856b4178cd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-24T19:51:46Z","title_canon_sha256":"b6457fb055f61b447866c4c04ede9d85b2d3f6c79ce6651967f50435c305133d"},"schema_version":"1.0","source":{"id":"0903.4134","kind":"arxiv","version":1}},"canonical_sha256":"d94e2c81045a08c9f22a0c1ffaccaa661fc73ba813cbd24ea7afb211f976eeda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d94e2c81045a08c9f22a0c1ffaccaa661fc73ba813cbd24ea7afb211f976eeda","first_computed_at":"2026-05-18T01:09:24.302280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:24.302280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ZIUg3v4L7VL0Xm2IByKVpcc79vPCiEHEuPRLKGeoacJWUKIUlpXTxbVEQJNXgHj6U6XGaS0QTNY/9Ykc43sBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:24.302811Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:decfca9ddc7e6f6810b88f700d4bc921255cebefd455d2d1a23d27b2d25ef647","sha256:a708d8a35bc8aea13ae68a8d9991d035b916d772a034edb276db354c4d456f90"],"state_sha256":"4dd6364f27409d7c0f84a184f144cbdce2553b333b571b150dba064f0a1be22b"}