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Ghostpeakons and characteristic curves for theCamassa–Holm, Degasperis–ProcesiandNovikovequations.Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 15:","work_id":"78b6f0fb-ea77-4361-a344-df072a1204fe","year":null},{"cited_arxiv_id":"","doi":"10.3842/sigma.2019.017","is_internal_anchor":false,"ref_index":4,"title":"doi: 10.3842/SIGMA.2019.017","work_id":"588d82b3-7502-475f-a1ef-7f7435dd7e27","year":2019},{"cited_arxiv_id":"","doi":"10.1016/0167-2789(81)90004-x","is_internal_anchor":false,"ref_index":5,"title":"B. Fuchssteiner and A. S. Fokas. Symplectic structures, their Bäcklund transformations and hereditary symmetries.Physica D: Nonlinear Phe- nomena, 4(1):47–66, 1981/1982. doi: 10.1016/0167-2789(81)9000","work_id":"4472cbd9-e56e-49ca-a5d9-e175b97ee46a","year":1981}],"snapshot_sha256":"b0ae474739ec3c27e312837260112be67e0152d9d33983571dd7795c2560a3e8"},"source":{"id":"2604.17348","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-19T18:23:02.433181Z","id":"7673ef98-0102-430a-9f92-1d0b1a7ef96a","model_set":{"reader":"grok-4.3"},"one_line_summary":"The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Asymptotic expansions construct soliton- and peakon-like solutions to arbitrary accuracy for the variable-coefficient Camassa-Holm equation with small dispersion.","strongest_claim":"Theorems on the asymptotic accuracy of the constructed asymptotic solutions have been proved; in the one-phase case the solvability of higher-order singular corrections is established in suitable functional spaces, enabling construction of asymptotic solutions to arbitrary accuracy in a small parameter.","weakest_assumption":"The precise definition of the main singular term (the leading peakon or soliton profile) is chosen so that the resulting correction equations remain solvable at every order; this choice is stated to play a central role but is not derived from first principles within the paper."}},"verdict_id":"7673ef98-0102-430a-9f92-1d0b1a7ef96a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8b1060244379a0320604dac175e27152ea21a5dc4a0b58018d4345065f94163a","target":"record","created_at":"2026-05-20T00:01:41Z","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":"63dab6ed94c02e3aa05319715d0ad41f99f3044623afba30fe42ca8c613b9877","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2026-04-19T09:44:07Z","title_canon_sha256":"b00d85074aa073040c9343ffb017890b2294579a135905e1dd3433668279f8bf"},"schema_version":"1.0","source":{"id":"2604.17348","kind":"arxiv","version":2}},"canonical_sha256":"44053781eecf1680db2a9b0b5d7ceff5cf2933d9535a71105cc142720127afbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44053781eecf1680db2a9b0b5d7ceff5cf2933d9535a71105cc142720127afbd","first_computed_at":"2026-05-20T00:01:41.420850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:41.420850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3hjau2H1XgQ/luFYyZPXYaph4tUnhvlwOThr+05Tx6SRXgkJPzf3Z/jt+gWyP3AejH2SOGZp3n4AbOhga4EPAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:41.421632Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.17348","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b1060244379a0320604dac175e27152ea21a5dc4a0b58018d4345065f94163a","sha256:5f93902cfec647b750be33234df196d9eeab477097f34e6e952e8aeda3c6e127"],"state_sha256":"01a686469364507121591b44005ab9fab03c3cb23f962b288e5175e091d63465"}