{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JTQUT3WYRNQ3EOXB3XF2MC2N3F","short_pith_number":"pith:JTQUT3WY","canonical_record":{"source":{"id":"1610.07051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-10-22T13:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"3fa5f2c6ee6ab007fa0e171b0525dfef5fdd6ad1dda41359defd54852b54b9bb","abstract_canon_sha256":"36e1c4fac85cd93846a80a3f12a18e17c9b017ce4dfbedb628a502bf94c6bbd9"},"schema_version":"1.0"},"canonical_sha256":"4ce149eed88b61b23ae1ddcba60b4dd95866f0d8dc69b9b315f67f2c1d769567","source":{"kind":"arxiv","id":"1610.07051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07051","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07051v1","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07051","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"JTQUT3WYRNQ3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTQUT3WYRNQ3EOXB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTQUT3WY","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JTQUT3WYRNQ3EOXB3XF2MC2N3F","target":"record","payload":{"canonical_record":{"source":{"id":"1610.07051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-10-22T13:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"3fa5f2c6ee6ab007fa0e171b0525dfef5fdd6ad1dda41359defd54852b54b9bb","abstract_canon_sha256":"36e1c4fac85cd93846a80a3f12a18e17c9b017ce4dfbedb628a502bf94c6bbd9"},"schema_version":"1.0"},"canonical_sha256":"4ce149eed88b61b23ae1ddcba60b4dd95866f0d8dc69b9b315f67f2c1d769567","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:35.342757Z","signature_b64":"TaqOFOzAbPXeTa7EbhMG+bSZI4UW63Uoh4ih7radUXKmGr/oNyvG2FxrZl2eDkjA0sUMvTa6/oBmM6YCY1uyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ce149eed88b61b23ae1ddcba60b4dd95866f0d8dc69b9b315f67f2c1d769567","last_reissued_at":"2026-05-18T01:01:35.342197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:35.342197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.07051","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":"2026-05-18T01:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"APy5UJCTe0seBlrYNQock9NAmzV8oJD4ujElyXvk3zzIklMoqcTHUi3JbACINLnLVMHlw9eznhZRKkcT+qURDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:36:37.221631Z"},"content_sha256":"7c3e51c377fe4f54129950cedea3c648709a74a30c0dd4fe1c4a2908f60b3f83","schema_version":"1.0","event_id":"sha256:7c3e51c377fe4f54129950cedea3c648709a74a30c0dd4fe1c4a2908f60b3f83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JTQUT3WYRNQ3EOXB3XF2MC2N3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The multiple soliton and peakon solutions of the Dullin-Gottwald-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Qilao Zha","submitted_at":"2016-10-22T13:54:01Z","abstract_excerpt":"Explicit multi-soliton and multi-peakon solutions of the Dullin-Gottwald-Holm equation are constructed via Darboux transformation and direct computation, respectively. To this end we first map the Dullin-Gottwald-Holm equation to a negative order KdV equation by a reciprocal transformation. Then we use the Darboux matrix approach to derive multi-soliton solutions of the Dullin-Gottwald-Holm equation from the solutions of the negative order KdV equation. Finally, we find multi-peakon solutions of the Dullin-Gottwald-Holm equation in weak sense. For $\\alpha=\\frac{1}{2}$ and $\\alpha\\neq \\frac{1}{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07051","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":"2026-05-18T01:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4CgEj7UOvCrg1WNqCz+ORIdsyUXEl8gq+Vc79QPbWpOyWTcn82SmbLboT333kx0iBF2wp9HmUREnnyi5B16aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:36:37.221970Z"},"content_sha256":"65276a184fe12d36885e2b7ec2d7160813357e385ec4b2ea509ce8b322c0348a","schema_version":"1.0","event_id":"sha256:65276a184fe12d36885e2b7ec2d7160813357e385ec4b2ea509ce8b322c0348a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F/bundle.json","state_url":"https://pith.science/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F/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":"2026-05-30T23:36:37Z","links":{"resolver":"https://pith.science/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F","bundle":"https://pith.science/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F/bundle.json","state":"https://pith.science/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTQUT3WYRNQ3EOXB3XF2MC2N3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JTQUT3WYRNQ3EOXB3XF2MC2N3F","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":"36e1c4fac85cd93846a80a3f12a18e17c9b017ce4dfbedb628a502bf94c6bbd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-10-22T13:54:01Z","title_canon_sha256":"3fa5f2c6ee6ab007fa0e171b0525dfef5fdd6ad1dda41359defd54852b54b9bb"},"schema_version":"1.0","source":{"id":"1610.07051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07051","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07051v1","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07051","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"JTQUT3WYRNQ3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTQUT3WYRNQ3EOXB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTQUT3WY","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:65276a184fe12d36885e2b7ec2d7160813357e385ec4b2ea509ce8b322c0348a","target":"graph","created_at":"2026-05-18T01:01:35Z","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":"Explicit multi-soliton and multi-peakon solutions of the Dullin-Gottwald-Holm equation are constructed via Darboux transformation and direct computation, respectively. To this end we first map the Dullin-Gottwald-Holm equation to a negative order KdV equation by a reciprocal transformation. Then we use the Darboux matrix approach to derive multi-soliton solutions of the Dullin-Gottwald-Holm equation from the solutions of the negative order KdV equation. Finally, we find multi-peakon solutions of the Dullin-Gottwald-Holm equation in weak sense. For $\\alpha=\\frac{1}{2}$ and $\\alpha\\neq \\frac{1}{","authors_text":"Qilao Zha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-10-22T13:54:01Z","title":"The multiple soliton and peakon solutions of the Dullin-Gottwald-Holm equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07051","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":"sha256:7c3e51c377fe4f54129950cedea3c648709a74a30c0dd4fe1c4a2908f60b3f83","target":"record","created_at":"2026-05-18T01:01:35Z","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":"36e1c4fac85cd93846a80a3f12a18e17c9b017ce4dfbedb628a502bf94c6bbd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-10-22T13:54:01Z","title_canon_sha256":"3fa5f2c6ee6ab007fa0e171b0525dfef5fdd6ad1dda41359defd54852b54b9bb"},"schema_version":"1.0","source":{"id":"1610.07051","kind":"arxiv","version":1}},"canonical_sha256":"4ce149eed88b61b23ae1ddcba60b4dd95866f0d8dc69b9b315f67f2c1d769567","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ce149eed88b61b23ae1ddcba60b4dd95866f0d8dc69b9b315f67f2c1d769567","first_computed_at":"2026-05-18T01:01:35.342197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:35.342197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TaqOFOzAbPXeTa7EbhMG+bSZI4UW63Uoh4ih7radUXKmGr/oNyvG2FxrZl2eDkjA0sUMvTa6/oBmM6YCY1uyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:35.342757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c3e51c377fe4f54129950cedea3c648709a74a30c0dd4fe1c4a2908f60b3f83","sha256:65276a184fe12d36885e2b7ec2d7160813357e385ec4b2ea509ce8b322c0348a"],"state_sha256":"b9362f0e59b0fc19665ba8bb39912a3d3004fb3309286740f68bfac5cd08f35e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XwUJnbrCV8GJO9SKvIPEsAD3R+AuVVbY+Eqfsr4xdqi8jxpiN5t6qdPdusFksrcUtq//tRbbISz3HS1LlPqBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:36:37.223883Z","bundle_sha256":"87eec57a26ace9663656283f52a31e435aebb46941ec3aec70c84fd0cd01356b"}}