{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XS25XHTZHOT4N3PZM3HDCUXDXA","short_pith_number":"pith:XS25XHTZ","canonical_record":{"source":{"id":"1512.08300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-12-28T01:56:03Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"efb49b639cc16a2f82b683eac47ed490e1c90b52a77ff36a4b53c2f6de85c24c","abstract_canon_sha256":"06fe8a7124042815d4f51a03cae7a1774f2b953ea1baf5970598fcd2fc9303f2"},"schema_version":"1.0"},"canonical_sha256":"bcb5db9e793ba7c6edf966ce3152e3b807f0df4eeba4bf42fa7a06e92446d05e","source":{"kind":"arxiv","id":"1512.08300","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08300","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08300v2","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08300","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"XS25XHTZHOT4","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XS25XHTZHOT4N3PZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XS25XHTZ","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XS25XHTZHOT4N3PZM3HDCUXDXA","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-12-28T01:56:03Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"efb49b639cc16a2f82b683eac47ed490e1c90b52a77ff36a4b53c2f6de85c24c","abstract_canon_sha256":"06fe8a7124042815d4f51a03cae7a1774f2b953ea1baf5970598fcd2fc9303f2"},"schema_version":"1.0"},"canonical_sha256":"bcb5db9e793ba7c6edf966ce3152e3b807f0df4eeba4bf42fa7a06e92446d05e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:58.696294Z","signature_b64":"YuSllI4Bo37t3wKDfsOifK1I9c1mt47dwx8q0u7se3XwE+Kjj6Drq9abRre115Py6EFFgd1lNHBbJ7F3TQ0iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcb5db9e793ba7c6edf966ce3152e3b807f0df4eeba4bf42fa7a06e92446d05e","last_reissued_at":"2026-05-18T01:14:58.695706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:58.695706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08300","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":"2026-05-18T01:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1K3Ttz9CnWvgpZfSAr9tMLb2CCHvsD2FLNKJDEEKTiCozKA5mf4pX0dz97c4gsty1yeb5c5jYkkzl7WTip2VAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:46:10.364760Z"},"content_sha256":"2597c4c577a9fb89702c83f39603f6cd03b08b3b36c47ea83df4ded807ac90e4","schema_version":"1.0","event_id":"sha256:2597c4c577a9fb89702c83f39603f6cd03b08b3b36c47ea83df4ded807ac90e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XS25XHTZHOT4N3PZM3HDCUXDXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice","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, Xingbiao Hu","submitted_at":"2015-12-28T01:56:03Z","abstract_excerpt":"A spectral and the inverse spectral problem are studied for the two-component modified Camassa-Holm type for measures associated to interlacing peaks. It is shown that the spectral problem is equivalent to an inhomogenous string problem with Dirichlet/Neumann boundary conditions. The inverse problem is solved by Stieltjes' continued fraction expansion, leading to an explicit construction of peakon solutions. Sufficient conditions for the global existence in $t$ are given. The large time asymptotics reveals that, asymptotically, peakons pair up to form bound states moving with constant speeds. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08300","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":"2026-05-18T01:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yd+sVnxgtDiUOfCHwR18zl1zTFL9DqVKz0DHCDNtwcXxqMohUBCq79qAJ8mD+gfsp5LC+TU0vr6bMxc2Rs8LBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:46:10.365452Z"},"content_sha256":"781cef9145e5d89c4bb78776449798d6ac32f4622f99f1bb46a3ee0384d76e1a","schema_version":"1.0","event_id":"sha256:781cef9145e5d89c4bb78776449798d6ac32f4622f99f1bb46a3ee0384d76e1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XS25XHTZHOT4N3PZM3HDCUXDXA/bundle.json","state_url":"https://pith.science/pith/XS25XHTZHOT4N3PZM3HDCUXDXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XS25XHTZHOT4N3PZM3HDCUXDXA/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":"2026-05-27T01:46:10Z","links":{"resolver":"https://pith.science/pith/XS25XHTZHOT4N3PZM3HDCUXDXA","bundle":"https://pith.science/pith/XS25XHTZHOT4N3PZM3HDCUXDXA/bundle.json","state":"https://pith.science/pith/XS25XHTZHOT4N3PZM3HDCUXDXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XS25XHTZHOT4N3PZM3HDCUXDXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XS25XHTZHOT4N3PZM3HDCUXDXA","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":"06fe8a7124042815d4f51a03cae7a1774f2b953ea1baf5970598fcd2fc9303f2","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":"2015-12-28T01:56:03Z","title_canon_sha256":"efb49b639cc16a2f82b683eac47ed490e1c90b52a77ff36a4b53c2f6de85c24c"},"schema_version":"1.0","source":{"id":"1512.08300","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08300","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08300v2","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08300","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"XS25XHTZHOT4","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XS25XHTZHOT4N3PZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XS25XHTZ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:781cef9145e5d89c4bb78776449798d6ac32f4622f99f1bb46a3ee0384d76e1a","target":"graph","created_at":"2026-05-18T01:14:58Z","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":"A spectral and the inverse spectral problem are studied for the two-component modified Camassa-Holm type for measures associated to interlacing peaks. It is shown that the spectral problem is equivalent to an inhomogenous string problem with Dirichlet/Neumann boundary conditions. The inverse problem is solved by Stieltjes' continued fraction expansion, leading to an explicit construction of peakon solutions. Sufficient conditions for the global existence in $t$ are given. The large time asymptotics reveals that, asymptotically, peakons pair up to form bound states moving with constant speeds. ","authors_text":"Jacek Szmigielski, Xiangke Chang, Xingbiao Hu","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":"2015-12-28T01:56:03Z","title":"Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08300","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":"sha256:2597c4c577a9fb89702c83f39603f6cd03b08b3b36c47ea83df4ded807ac90e4","target":"record","created_at":"2026-05-18T01:14:58Z","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":"06fe8a7124042815d4f51a03cae7a1774f2b953ea1baf5970598fcd2fc9303f2","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":"2015-12-28T01:56:03Z","title_canon_sha256":"efb49b639cc16a2f82b683eac47ed490e1c90b52a77ff36a4b53c2f6de85c24c"},"schema_version":"1.0","source":{"id":"1512.08300","kind":"arxiv","version":2}},"canonical_sha256":"bcb5db9e793ba7c6edf966ce3152e3b807f0df4eeba4bf42fa7a06e92446d05e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcb5db9e793ba7c6edf966ce3152e3b807f0df4eeba4bf42fa7a06e92446d05e","first_computed_at":"2026-05-18T01:14:58.695706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:58.695706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YuSllI4Bo37t3wKDfsOifK1I9c1mt47dwx8q0u7se3XwE+Kjj6Drq9abRre115Py6EFFgd1lNHBbJ7F3TQ0iCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:58.696294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08300","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2597c4c577a9fb89702c83f39603f6cd03b08b3b36c47ea83df4ded807ac90e4","sha256:781cef9145e5d89c4bb78776449798d6ac32f4622f99f1bb46a3ee0384d76e1a"],"state_sha256":"559dd45b367138698152d2d37049719fd5f88291c36e73d0b6b4829b34e94637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOlmEOKZktgedsFHTnYQhdLEIg4PS99ERyWsdbV3cg+Dlo1AiAquLeHZQf8kgSWb7hZd+GrSJaZ0TRp6A5pbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:46:10.369084Z","bundle_sha256":"9da274794cf8942a0745d921dd2b30fe7164751a7203148d79784560a7c423b8"}}