{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MERKCT4E3WKG27XYWIHTBEAMVB","short_pith_number":"pith:MERKCT4E","canonical_record":{"source":{"id":"1705.06451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-05-18T07:59:49Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"a25869c7a5d55af8c2b02e14c0db31594af9b297af84cbc866333f46d4ecb505","abstract_canon_sha256":"8eea056f76c243240f824c136de130a5d51a2f8c155f3fe2a2d4348059c69b4e"},"schema_version":"1.0"},"canonical_sha256":"6122a14f84dd946d7ef8b20f30900ca84b1ca7bdcf65e63d5e7b2279082d7396","source":{"kind":"arxiv","id":"1705.06451","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06451","created_at":"2026-05-18T00:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06451v1","created_at":"2026-05-18T00:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06451","created_at":"2026-05-18T00:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"MERKCT4E3WKG","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MERKCT4E3WKG27XY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MERKCT4E","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MERKCT4E3WKG27XYWIHTBEAMVB","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-05-18T07:59:49Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"a25869c7a5d55af8c2b02e14c0db31594af9b297af84cbc866333f46d4ecb505","abstract_canon_sha256":"8eea056f76c243240f824c136de130a5d51a2f8c155f3fe2a2d4348059c69b4e"},"schema_version":"1.0"},"canonical_sha256":"6122a14f84dd946d7ef8b20f30900ca84b1ca7bdcf65e63d5e7b2279082d7396","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:38.814123Z","signature_b64":"Wo0fOb6loPl+79wv1DFKdt2yRTB9GSwu91SeYr3Mtjv36064xK+9cQaspR2gY+hl9piALZIO+09sBpStTUfTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6122a14f84dd946d7ef8b20f30900ca84b1ca7bdcf65e63d5e7b2279082d7396","last_reissued_at":"2026-05-18T00:23:38.813396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:38.813396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06451","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWR1OXfyipTTIIoq/FqXcJrgsJkp0p/qaK49T2ip2eDBBv9GU0Ee2/KJsR5OfiLJXHj6qHV8EqRQAWS5SihUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:48:01.100831Z"},"content_sha256":"da94b66b860b479bff875d5a7792467f411e5b4d1a2271cc6c1d510d0d88857c","schema_version":"1.0","event_id":"sha256:da94b66b860b479bff875d5a7792467f411e5b4d1a2271cc6c1d510d0d88857c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MERKCT4E3WKG27XYWIHTBEAMVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lax integrability and the peakon problem for the modified Camassa-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Jacek Szmigielski, Xiangke Chang","submitted_at":"2017-05-18T07:59:49Z","abstract_excerpt":"Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfyi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06451","kind":"arxiv","version":1},"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":"2026-05-18T00:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aMzh1MDwJcNt6/cuhmG5miUiWLkViJ2Ht63sasy0Tu7tQsYc3vaHvub4zYuKdLePU3g76jRJ5yLrOZfw1gvKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:48:01.101528Z"},"content_sha256":"52e1a50eb3ad9d1b10278791ee039e0ff747c206c7e82704fb8a30d5a3418027","schema_version":"1.0","event_id":"sha256:52e1a50eb3ad9d1b10278791ee039e0ff747c206c7e82704fb8a30d5a3418027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MERKCT4E3WKG27XYWIHTBEAMVB/bundle.json","state_url":"https://pith.science/pith/MERKCT4E3WKG27XYWIHTBEAMVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MERKCT4E3WKG27XYWIHTBEAMVB/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":"2026-05-27T07:48:01Z","links":{"resolver":"https://pith.science/pith/MERKCT4E3WKG27XYWIHTBEAMVB","bundle":"https://pith.science/pith/MERKCT4E3WKG27XYWIHTBEAMVB/bundle.json","state":"https://pith.science/pith/MERKCT4E3WKG27XYWIHTBEAMVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MERKCT4E3WKG27XYWIHTBEAMVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MERKCT4E3WKG27XYWIHTBEAMVB","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":"8eea056f76c243240f824c136de130a5d51a2f8c155f3fe2a2d4348059c69b4e","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-05-18T07:59:49Z","title_canon_sha256":"a25869c7a5d55af8c2b02e14c0db31594af9b297af84cbc866333f46d4ecb505"},"schema_version":"1.0","source":{"id":"1705.06451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06451","created_at":"2026-05-18T00:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06451v1","created_at":"2026-05-18T00:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06451","created_at":"2026-05-18T00:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"MERKCT4E3WKG","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MERKCT4E3WKG27XY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MERKCT4E","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:52e1a50eb3ad9d1b10278791ee039e0ff747c206c7e82704fb8a30d5a3418027","target":"graph","created_at":"2026-05-18T00:23:38Z","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":"Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfyi","authors_text":"Jacek Szmigielski, Xiangke Chang","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-05-18T07:59:49Z","title":"Lax integrability and the peakon problem for the modified Camassa-Holm equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06451","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:da94b66b860b479bff875d5a7792467f411e5b4d1a2271cc6c1d510d0d88857c","target":"record","created_at":"2026-05-18T00:23:38Z","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":"8eea056f76c243240f824c136de130a5d51a2f8c155f3fe2a2d4348059c69b4e","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-05-18T07:59:49Z","title_canon_sha256":"a25869c7a5d55af8c2b02e14c0db31594af9b297af84cbc866333f46d4ecb505"},"schema_version":"1.0","source":{"id":"1705.06451","kind":"arxiv","version":1}},"canonical_sha256":"6122a14f84dd946d7ef8b20f30900ca84b1ca7bdcf65e63d5e7b2279082d7396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6122a14f84dd946d7ef8b20f30900ca84b1ca7bdcf65e63d5e7b2279082d7396","first_computed_at":"2026-05-18T00:23:38.813396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:38.813396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wo0fOb6loPl+79wv1DFKdt2yRTB9GSwu91SeYr3Mtjv36064xK+9cQaspR2gY+hl9piALZIO+09sBpStTUfTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:38.814123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da94b66b860b479bff875d5a7792467f411e5b4d1a2271cc6c1d510d0d88857c","sha256:52e1a50eb3ad9d1b10278791ee039e0ff747c206c7e82704fb8a30d5a3418027"],"state_sha256":"fae43e1c8e3fe2200078bb0f502c16dd8cd42264d09bcd1ced07abd5f27d065a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hehPBzVM6/ulffuUkCINn5KyLWAOFoADdbz2eKkuKPMJN5Iv3zLh6nV+XJG0QWQEYhHe4ZuBkH98ocEiYLF4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:48:01.106816Z","bundle_sha256":"6736ec16c28ddb7bc2327e5d8cf7f6c1d66c56aef6943bfe41c899eafe238f08"}}