{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OZXEAW33JAW2QK45NDPTJRJFMB","short_pith_number":"pith:OZXEAW33","canonical_record":{"source":{"id":"2606.17238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-15T19:37:33Z","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS"],"title_canon_sha256":"7ba795521e29e16d75b305645e8cbdd490714740c44411e892daec3385d0012e","abstract_canon_sha256":"93fec61b97bcbe7f53185318b91af9b5361251b286c29e06b581c3a17bb713e3"},"schema_version":"1.0"},"canonical_sha256":"766e405b7b482da82b9d68df34c5256079969b20d55728e7b4393879a26770d7","source":{"kind":"arxiv","id":"2606.17238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17238","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17238v1","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17238","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"OZXEAW33JAW2","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_16","alias_value":"OZXEAW33JAW2QK45","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_8","alias_value":"OZXEAW33","created_at":"2026-06-19T16:10:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OZXEAW33JAW2QK45NDPTJRJFMB","target":"record","payload":{"canonical_record":{"source":{"id":"2606.17238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-15T19:37:33Z","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS"],"title_canon_sha256":"7ba795521e29e16d75b305645e8cbdd490714740c44411e892daec3385d0012e","abstract_canon_sha256":"93fec61b97bcbe7f53185318b91af9b5361251b286c29e06b581c3a17bb713e3"},"schema_version":"1.0"},"canonical_sha256":"766e405b7b482da82b9d68df34c5256079969b20d55728e7b4393879a26770d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:06.623730Z","signature_b64":"utTOmRCUv6yrg6GkFX0tbIdZ9Ah4SL08Oo+E23zRZuhqhJJ38bNvKmr60C2UqxgWk+JlU4Jyh/kze5nCLdNfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"766e405b7b482da82b9d68df34c5256079969b20d55728e7b4393879a26770d7","last_reissued_at":"2026-06-19T16:10:06.623337Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:06.623337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.17238","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":"2026-06-19T16:10:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+a2Rdq5RQ3gAMg2sArIFNpl9dIp0ByZEc1uPsdwGoRIs6X+g7DxsKEm9G5qt2FtjitJI6A7nJT8ANn5r971IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:43:22.195465Z"},"content_sha256":"76ee745f666a4ca77cd8b705480141ac9869e1cf56a3c8f1b4c5ac8a839a205a","schema_version":"1.0","event_id":"sha256:76ee745f666a4ca77cd8b705480141ac9869e1cf56a3c8f1b4c5ac8a839a205a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OZXEAW33JAW2QK45NDPTJRJFMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector peakon equations and isospectral flows in Clifford algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Andrew N.W. Hone, Jacek Szmigielski, Vladimir S. Novikov","submitted_at":"2026-06-15T19:37:33Z","abstract_excerpt":"Starting from a spectral problem posed in a Clifford algebra with $d$ generators and Euclidean signature, we study an integrable, coupled system of PDEs that can be viewed as a vector perturbation of the Camassa--Holm equation with residual orthogonal symmetry. In the two-component case $d=2$, we show that the travelling wave solutions correspond to a Liouville integrable Hamiltonian system with two degrees of freedom, making use of a reciprocal transformation linking the coupled PDEs to a symmetry of the Hirota--Satsuma system. We also present a symmetry classification of all integrable two-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17238","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-19T16:10:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R+ZWiXcWfgC3yFSqlOOy/jM27DYh0CnBlB8EXfpJLWqW9Z4Zi+kY/lkuBRfA40G5goGS0nCcAHSaTTFgrsTPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:43:22.195854Z"},"content_sha256":"5e3eac2ef1516f637abba38d89dcb801192ca36958784ec4b3d5ce517873b68a","schema_version":"1.0","event_id":"sha256:5e3eac2ef1516f637abba38d89dcb801192ca36958784ec4b3d5ce517873b68a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZXEAW33JAW2QK45NDPTJRJFMB/bundle.json","state_url":"https://pith.science/pith/OZXEAW33JAW2QK45NDPTJRJFMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZXEAW33JAW2QK45NDPTJRJFMB/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":"2026-06-20T21:43:22Z","links":{"resolver":"https://pith.science/pith/OZXEAW33JAW2QK45NDPTJRJFMB","bundle":"https://pith.science/pith/OZXEAW33JAW2QK45NDPTJRJFMB/bundle.json","state":"https://pith.science/pith/OZXEAW33JAW2QK45NDPTJRJFMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZXEAW33JAW2QK45NDPTJRJFMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OZXEAW33JAW2QK45NDPTJRJFMB","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":"93fec61b97bcbe7f53185318b91af9b5361251b286c29e06b581c3a17bb713e3","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-15T19:37:33Z","title_canon_sha256":"7ba795521e29e16d75b305645e8cbdd490714740c44411e892daec3385d0012e"},"schema_version":"1.0","source":{"id":"2606.17238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17238","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17238v1","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17238","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"OZXEAW33JAW2","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_16","alias_value":"OZXEAW33JAW2QK45","created_at":"2026-06-19T16:10:06Z"},{"alias_kind":"pith_short_8","alias_value":"OZXEAW33","created_at":"2026-06-19T16:10:06Z"}],"graph_snapshots":[{"event_id":"sha256:5e3eac2ef1516f637abba38d89dcb801192ca36958784ec4b3d5ce517873b68a","target":"graph","created_at":"2026-06-19T16:10:06Z","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/2606.17238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Starting from a spectral problem posed in a Clifford algebra with $d$ generators and Euclidean signature, we study an integrable, coupled system of PDEs that can be viewed as a vector perturbation of the Camassa--Holm equation with residual orthogonal symmetry. In the two-component case $d=2$, we show that the travelling wave solutions correspond to a Liouville integrable Hamiltonian system with two degrees of freedom, making use of a reciprocal transformation linking the coupled PDEs to a symmetry of the Hirota--Satsuma system. We also present a symmetry classification of all integrable two-c","authors_text":"Andrew N.W. Hone, Jacek Szmigielski, Vladimir S. Novikov","cross_cats":["math-ph","math.AP","math.MP","nlin.PS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-15T19:37:33Z","title":"Vector peakon equations and isospectral flows in Clifford algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17238","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":"sha256:76ee745f666a4ca77cd8b705480141ac9869e1cf56a3c8f1b4c5ac8a839a205a","target":"record","created_at":"2026-06-19T16:10:06Z","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":"93fec61b97bcbe7f53185318b91af9b5361251b286c29e06b581c3a17bb713e3","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-15T19:37:33Z","title_canon_sha256":"7ba795521e29e16d75b305645e8cbdd490714740c44411e892daec3385d0012e"},"schema_version":"1.0","source":{"id":"2606.17238","kind":"arxiv","version":1}},"canonical_sha256":"766e405b7b482da82b9d68df34c5256079969b20d55728e7b4393879a26770d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"766e405b7b482da82b9d68df34c5256079969b20d55728e7b4393879a26770d7","first_computed_at":"2026-06-19T16:10:06.623337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:06.623337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"utTOmRCUv6yrg6GkFX0tbIdZ9Ah4SL08Oo+E23zRZuhqhJJ38bNvKmr60C2UqxgWk+JlU4Jyh/kze5nCLdNfAg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:06.623730Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76ee745f666a4ca77cd8b705480141ac9869e1cf56a3c8f1b4c5ac8a839a205a","sha256:5e3eac2ef1516f637abba38d89dcb801192ca36958784ec4b3d5ce517873b68a"],"state_sha256":"94fcb825268b6341e2bbd9f526cfdb51cabb4cd28fdb3a8a16421e90bfbb34c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MCSISG/dHMKVwFPUrDcICyg6rTOJ23w52UF/ZleM6DeBMPTBYGbV2huT7Y27oXI+XsUBqRC/VB8csmXpl3zAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:43:22.197882Z","bundle_sha256":"162f305a91a269d04fe92b77b5b03c8754c16bca10edd495922a6c4fc538929a"}}