{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XY7CGAADXNQURPVS7WRNV24XFX","short_pith_number":"pith:XY7CGAAD","canonical_record":{"source":{"id":"1807.01910","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2018-07-05T09:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"6ce9f3b4d04e3242cbc3ec88914abf7a47ae2a6094e5db8276e8601ebc651521","abstract_canon_sha256":"68234e08713050c818f19529b839b2661cc4a4a080ae32d8eb7eaf015468c11d"},"schema_version":"1.0"},"canonical_sha256":"be3e230003bb6148beb2fda2daeb972dfe5c9550597e00f56713a03915183bd2","source":{"kind":"arxiv","id":"1807.01910","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01910","created_at":"2026-05-17T23:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01910v2","created_at":"2026-05-17T23:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01910","created_at":"2026-05-17T23:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"XY7CGAADXNQU","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XY7CGAADXNQURPVS","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XY7CGAAD","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XY7CGAADXNQURPVS7WRNV24XFX","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01910","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2018-07-05T09:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"6ce9f3b4d04e3242cbc3ec88914abf7a47ae2a6094e5db8276e8601ebc651521","abstract_canon_sha256":"68234e08713050c818f19529b839b2661cc4a4a080ae32d8eb7eaf015468c11d"},"schema_version":"1.0"},"canonical_sha256":"be3e230003bb6148beb2fda2daeb972dfe5c9550597e00f56713a03915183bd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:58.971922Z","signature_b64":"u7BcZ34grAeEx+nwRm/VWMMhMy06vIxe/3LNVHBF3wMx+Xk7BYspm6h9vYoPqQrvfxQ7+qxiQAbpbBlL9UO0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be3e230003bb6148beb2fda2daeb972dfe5c9550597e00f56713a03915183bd2","last_reissued_at":"2026-05-17T23:51:58.971510Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:58.971510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01910","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mK9tAm1ceX9SCf4uU8WZwEz4KNgJt+ueQgeO8DcPJMfrkMm6wBmX0JwEbUVPLup37/+9oHG+TiY+pzz1/0yZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:55:27.298457Z"},"content_sha256":"85036e7042a5a0724bdfa711b67e9d051d45bb1632a5d4f69b98a0ee40db1bf2","schema_version":"1.0","event_id":"sha256:85036e7042a5a0724bdfa711b67e9d051d45bb1632a5d4f69b98a0ee40db1bf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XY7CGAADXNQURPVS7WRNV24XFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ghostpeakons and Characteristic Curves for the Camassa-Holm, Degasperis-Procesi and Novikov Equations","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Budor Shuaib, Hans Lundmark","submitted_at":"2018-07-05T09:20:27Z","abstract_excerpt":"We derive explicit formulas for the characteristic curves associated with the multipeakon solutions of the Camassa-Holm, Degasperis-Procesi and Novikov equations. Such a curve traces the path of a fluid particle whose instantaneous velocity equals the elevation of the wave at that point (or the square of the elevation, in the Novikov case). The peakons themselves follow characteristic curves, and the remaining characteristic curves can be viewed as paths of 'ghostpeakons' with zero amplitude; hence, they can be obtained as solutions of the ODEs governing the dynamics of multipeakon solutions. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01910","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NzmaHTNCmqfB4fZZK3YQhs+Vo0NUzX+k4D5IWU+X9wwM+NYHrCmjKIcIO44u4Ah5/Lx8IPmA/Rwscb6wcmpJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:55:27.298801Z"},"content_sha256":"90db3f3ab5bde64f6732a0a058b3db925a3f9b1c02036e4a076d27d2a70205c6","schema_version":"1.0","event_id":"sha256:90db3f3ab5bde64f6732a0a058b3db925a3f9b1c02036e4a076d27d2a70205c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XY7CGAADXNQURPVS7WRNV24XFX/bundle.json","state_url":"https://pith.science/pith/XY7CGAADXNQURPVS7WRNV24XFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XY7CGAADXNQURPVS7WRNV24XFX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T15:55:27Z","links":{"resolver":"https://pith.science/pith/XY7CGAADXNQURPVS7WRNV24XFX","bundle":"https://pith.science/pith/XY7CGAADXNQURPVS7WRNV24XFX/bundle.json","state":"https://pith.science/pith/XY7CGAADXNQURPVS7WRNV24XFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XY7CGAADXNQURPVS7WRNV24XFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XY7CGAADXNQURPVS7WRNV24XFX","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":"68234e08713050c818f19529b839b2661cc4a4a080ae32d8eb7eaf015468c11d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2018-07-05T09:20:27Z","title_canon_sha256":"6ce9f3b4d04e3242cbc3ec88914abf7a47ae2a6094e5db8276e8601ebc651521"},"schema_version":"1.0","source":{"id":"1807.01910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01910","created_at":"2026-05-17T23:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01910v2","created_at":"2026-05-17T23:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01910","created_at":"2026-05-17T23:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"XY7CGAADXNQU","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XY7CGAADXNQURPVS","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XY7CGAAD","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:90db3f3ab5bde64f6732a0a058b3db925a3f9b1c02036e4a076d27d2a70205c6","target":"graph","created_at":"2026-05-17T23:51:58Z","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 derive explicit formulas for the characteristic curves associated with the multipeakon solutions of the Camassa-Holm, Degasperis-Procesi and Novikov equations. Such a curve traces the path of a fluid particle whose instantaneous velocity equals the elevation of the wave at that point (or the square of the elevation, in the Novikov case). The peakons themselves follow characteristic curves, and the remaining characteristic curves can be viewed as paths of 'ghostpeakons' with zero amplitude; hence, they can be obtained as solutions of the ODEs governing the dynamics of multipeakon solutions. ","authors_text":"Budor Shuaib, Hans Lundmark","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2018-07-05T09:20:27Z","title":"Ghostpeakons and Characteristic Curves for the Camassa-Holm, Degasperis-Procesi and Novikov Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01910","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":"sha256:85036e7042a5a0724bdfa711b67e9d051d45bb1632a5d4f69b98a0ee40db1bf2","target":"record","created_at":"2026-05-17T23:51:58Z","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":"68234e08713050c818f19529b839b2661cc4a4a080ae32d8eb7eaf015468c11d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2018-07-05T09:20:27Z","title_canon_sha256":"6ce9f3b4d04e3242cbc3ec88914abf7a47ae2a6094e5db8276e8601ebc651521"},"schema_version":"1.0","source":{"id":"1807.01910","kind":"arxiv","version":2}},"canonical_sha256":"be3e230003bb6148beb2fda2daeb972dfe5c9550597e00f56713a03915183bd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be3e230003bb6148beb2fda2daeb972dfe5c9550597e00f56713a03915183bd2","first_computed_at":"2026-05-17T23:51:58.971510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:58.971510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u7BcZ34grAeEx+nwRm/VWMMhMy06vIxe/3LNVHBF3wMx+Xk7BYspm6h9vYoPqQrvfxQ7+qxiQAbpbBlL9UO0Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:58.971922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85036e7042a5a0724bdfa711b67e9d051d45bb1632a5d4f69b98a0ee40db1bf2","sha256:90db3f3ab5bde64f6732a0a058b3db925a3f9b1c02036e4a076d27d2a70205c6"],"state_sha256":"43aab4e6529649910464de8d7b1c7da5777ca4a595fd43b727650f36733fff5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5dCIM2LjY19gYDohnF6T1NV9bV8XaCvQn1NJWd7UaKM2BkKym4DKOCrPDZlc+EtXdjddRSQFXQeocl+pxDnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:55:27.300786Z","bundle_sha256":"f83e768207ce38915ff1072f6595cac94044b63c65ade92cce9186de9141c36c"}}