{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DXYXUXEVO4WWC4GP4AT5MODBW3","short_pith_number":"pith:DXYXUXEV","canonical_record":{"source":{"id":"2608.03139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-08-04T05:10:34Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1ccb13b59eca52139b8d3d915e9f0bacca1eef907c514647820a0c6ddb709ae1","abstract_canon_sha256":"7b0c010fab7c68b13fefbe57fe36bd56656cc54e6dadecce3bb0cd2ee2143e59"},"schema_version":"1.0"},"canonical_sha256":"1df17a5c95772d6170cfe027d63861b6c6010842edae9f56787df74eca9a53b9","source":{"kind":"arxiv","id":"2608.03139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03139","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03139v1","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03139","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"DXYXUXEVO4WW","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"DXYXUXEVO4WWC4GP","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"DXYXUXEV","created_at":"2026-08-05T00:45:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DXYXUXEVO4WWC4GP4AT5MODBW3","target":"record","payload":{"canonical_record":{"source":{"id":"2608.03139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-08-04T05:10:34Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1ccb13b59eca52139b8d3d915e9f0bacca1eef907c514647820a0c6ddb709ae1","abstract_canon_sha256":"7b0c010fab7c68b13fefbe57fe36bd56656cc54e6dadecce3bb0cd2ee2143e59"},"schema_version":"1.0"},"canonical_sha256":"1df17a5c95772d6170cfe027d63861b6c6010842edae9f56787df74eca9a53b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-05T00:45:47.056947Z","signature_b64":"6Oif3H/CkN9xRzrloA+hY1/ilKZn9ur6A40P66veCBRuWFSTB0m68jkiPlTPRxMiOLsAIKbh0KUlPsDq1+5yCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1df17a5c95772d6170cfe027d63861b6c6010842edae9f56787df74eca9a53b9","last_reissued_at":"2026-08-05T00:45:47.054702Z","signature_status":"signed_v1","first_computed_at":"2026-08-05T00:45:47.054702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.03139","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":"2026-08-05T00:45:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7TQRffJM1U84tvkPbspx7SX+1t4w4g95usht6Xaz0N+1WFz0MiPmyLy9+bzGmTzWyq9Lxlvm/Yq/2zzSpuVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:32:40.343232Z"},"content_sha256":"6c29176908b5284b8356449317aa9aad449ea2bc10dab8c8fe669509b9b88536","schema_version":"1.0","event_id":"sha256:6c29176908b5284b8356449317aa9aad449ea2bc10dab8c8fe669509b9b88536"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DXYXUXEVO4WWC4GP4AT5MODBW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The co-directional overtaking collision problem between a dispersive shock wave and a rarefaction wave for the Hirota equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Rui Guo, Yuan Xiang","submitted_at":"2026-08-04T05:10:34Z","abstract_excerpt":"In this paper, we mainly investigate the overtaking collision problem between a dispersive shock wave (DSW) and a rarefaction wave (RW) propagating in the same direction in the defocusing Hirota equation framework. Based on the Whitham theory, the zero-phase and single-phase modulation systems corresponding to the defocusing Hirota equation are given, along with explicit expressions of Riemann invariants. For step-type initial conditions with left-side DSW and right-side RW propagating identically, the global initial configuration is constructed.~The modulation solution within the nonlinear co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03139","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/2608.03139/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":"2026-08-05T00:45:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZiKsiJa37SH0DkrHnJI2g5Tkbau7geC69epeOsy2DleGj5rXxd1X78yJvdPjMGPcDmcIFVjQypWMqOYbxHVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:32:40.344147Z"},"content_sha256":"561f8e6548be5f308d50d65fc23fef81e072085cf697ec2e2e2948d51703126b","schema_version":"1.0","event_id":"sha256:561f8e6548be5f308d50d65fc23fef81e072085cf697ec2e2e2948d51703126b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DXYXUXEVO4WWC4GP4AT5MODBW3/bundle.json","state_url":"https://pith.science/pith/DXYXUXEVO4WWC4GP4AT5MODBW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DXYXUXEVO4WWC4GP4AT5MODBW3/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":"2026-08-12T22:32:40Z","links":{"resolver":"https://pith.science/pith/DXYXUXEVO4WWC4GP4AT5MODBW3","bundle":"https://pith.science/pith/DXYXUXEVO4WWC4GP4AT5MODBW3/bundle.json","state":"https://pith.science/pith/DXYXUXEVO4WWC4GP4AT5MODBW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DXYXUXEVO4WWC4GP4AT5MODBW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DXYXUXEVO4WWC4GP4AT5MODBW3","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":"7b0c010fab7c68b13fefbe57fe36bd56656cc54e6dadecce3bb0cd2ee2143e59","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-08-04T05:10:34Z","title_canon_sha256":"1ccb13b59eca52139b8d3d915e9f0bacca1eef907c514647820a0c6ddb709ae1"},"schema_version":"1.0","source":{"id":"2608.03139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03139","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03139v1","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03139","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"DXYXUXEVO4WW","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"DXYXUXEVO4WWC4GP","created_at":"2026-08-05T00:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"DXYXUXEV","created_at":"2026-08-05T00:45:47Z"}],"graph_snapshots":[{"event_id":"sha256:561f8e6548be5f308d50d65fc23fef81e072085cf697ec2e2e2948d51703126b","target":"graph","created_at":"2026-08-05T00:45:47Z","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/2608.03139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we mainly investigate the overtaking collision problem between a dispersive shock wave (DSW) and a rarefaction wave (RW) propagating in the same direction in the defocusing Hirota equation framework. Based on the Whitham theory, the zero-phase and single-phase modulation systems corresponding to the defocusing Hirota equation are given, along with explicit expressions of Riemann invariants. For step-type initial conditions with left-side DSW and right-side RW propagating identically, the global initial configuration is constructed.~The modulation solution within the nonlinear co","authors_text":"Rui Guo, Yuan Xiang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-08-04T05:10:34Z","title":"The co-directional overtaking collision problem between a dispersive shock wave and a rarefaction wave for the Hirota equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03139","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":"sha256:6c29176908b5284b8356449317aa9aad449ea2bc10dab8c8fe669509b9b88536","target":"record","created_at":"2026-08-05T00:45:47Z","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":"7b0c010fab7c68b13fefbe57fe36bd56656cc54e6dadecce3bb0cd2ee2143e59","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-08-04T05:10:34Z","title_canon_sha256":"1ccb13b59eca52139b8d3d915e9f0bacca1eef907c514647820a0c6ddb709ae1"},"schema_version":"1.0","source":{"id":"2608.03139","kind":"arxiv","version":1}},"canonical_sha256":"1df17a5c95772d6170cfe027d63861b6c6010842edae9f56787df74eca9a53b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1df17a5c95772d6170cfe027d63861b6c6010842edae9f56787df74eca9a53b9","first_computed_at":"2026-08-05T00:45:47.054702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T00:45:47.054702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Oif3H/CkN9xRzrloA+hY1/ilKZn9ur6A40P66veCBRuWFSTB0m68jkiPlTPRxMiOLsAIKbh0KUlPsDq1+5yCQ==","signature_status":"signed_v1","signed_at":"2026-08-05T00:45:47.056947Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c29176908b5284b8356449317aa9aad449ea2bc10dab8c8fe669509b9b88536","sha256:561f8e6548be5f308d50d65fc23fef81e072085cf697ec2e2e2948d51703126b"],"state_sha256":"6ce6ea8cc85bd101c768592d232e19a07d8155dd43a3d7458d12aa5cbe110cc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIGuXgGv2eP3SlyOA8xH21ItpAxzQFjkAGzsdMCy0sbx4byeDFPxg6o8PEDKzonNVfEVabPumwbqDUwNihV8DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:32:40.349943Z","bundle_sha256":"4469f0b9153379e8a4650d90189b02bf31523e0968902a0ac9f78d07454ac4ff"}}