{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WNGV4IHOND7OB7SZ2TASZ664RZ","short_pith_number":"pith:WNGV4IHO","canonical_record":{"source":{"id":"2511.03973","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-06T01:55:21Z","cross_cats_sorted":[],"title_canon_sha256":"97f4dcb73b6e3ed32dac251e555f8bd320800db9d0b7c4bca794149cc451c20b","abstract_canon_sha256":"3f795a419d3ca1c9c34dfa0f51830fb343178f70e46d4661b55aee03fc64ed11"},"schema_version":"1.0"},"canonical_sha256":"b34d5e20ee68fee0fe59d4c12cfbdc8e48d4acdbcbcb6ecfd1867d0f67ae7119","source":{"kind":"arxiv","id":"2511.03973","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.03973","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"2511.03973v2","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.03973","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"WNGV4IHOND7O","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"pith_short_16","alias_value":"WNGV4IHOND7OB7SZ","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"pith_short_8","alias_value":"WNGV4IHO","created_at":"2026-07-28T01:23:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WNGV4IHOND7OB7SZ2TASZ664RZ","target":"record","payload":{"canonical_record":{"source":{"id":"2511.03973","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-06T01:55:21Z","cross_cats_sorted":[],"title_canon_sha256":"97f4dcb73b6e3ed32dac251e555f8bd320800db9d0b7c4bca794149cc451c20b","abstract_canon_sha256":"3f795a419d3ca1c9c34dfa0f51830fb343178f70e46d4661b55aee03fc64ed11"},"schema_version":"1.0"},"canonical_sha256":"b34d5e20ee68fee0fe59d4c12cfbdc8e48d4acdbcbcb6ecfd1867d0f67ae7119","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:23:26.877909Z","signature_b64":"VbIc2gZkp3fgNa0Zm0dYZOgy3kh9/MHrG3be10WyiPxyc92GAI4QEDIUOARz2vjb6aVA9XePtK6l5NiDaJKHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b34d5e20ee68fee0fe59d4c12cfbdc8e48d4acdbcbcb6ecfd1867d0f67ae7119","last_reissued_at":"2026-07-28T01:23:26.876947Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:23:26.876947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2511.03973","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":"2026-07-28T01:23:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyXx9gHer6IywEZxi5NqBcWIRs9mHM/AwbY58z33uXiyMEc62eqkrwDC9p5O+zProa4jEvUyL5OBvDyGkIdBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:06:56.955323Z"},"content_sha256":"7146307ec9e8348e2734b2bbe49b4c8fb78bec3ef12ba1bef6444a87685b5930","schema_version":"1.0","event_id":"sha256:7146307ec9e8348e2734b2bbe49b4c8fb78bec3ef12ba1bef6444a87685b5930"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WNGV4IHOND7OB7SZ2TASZ664RZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcation analysis of Stokes waves with piecewise smooth vorticity in deep water","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changfeng Gui, Jun Wang, Wen Yang, Yong Zhang","submitted_at":"2025-11-06T01:55:21Z","abstract_excerpt":"In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite cylinder, where the vorticity may exhibit discontinuities. The analysis is carried out by applying a hodograph transformation, which reformulates the original free boundary problem into an abstract elliptic boundary value problem. Compared to previously studied steady water waves, the present setting introduces several novel features: the presence of an inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.03973","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.03973/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":"2026-07-28T01:23:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrHdU7yYrucqePBBmyLvuJUVXKLqJGkwZ4Ui20QiCNs2qIo7fPhw8266enu4JdhjaxPGkxhg75vhimx7x8boDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:06:56.955849Z"},"content_sha256":"f82b4894b279002d89ce9f1c22b635c2923462a7ac79dc6c3b577bc340c3d465","schema_version":"1.0","event_id":"sha256:f82b4894b279002d89ce9f1c22b635c2923462a7ac79dc6c3b577bc340c3d465"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNGV4IHOND7OB7SZ2TASZ664RZ/bundle.json","state_url":"https://pith.science/pith/WNGV4IHOND7OB7SZ2TASZ664RZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNGV4IHOND7OB7SZ2TASZ664RZ/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":"2026-08-05T02:06:56Z","links":{"resolver":"https://pith.science/pith/WNGV4IHOND7OB7SZ2TASZ664RZ","bundle":"https://pith.science/pith/WNGV4IHOND7OB7SZ2TASZ664RZ/bundle.json","state":"https://pith.science/pith/WNGV4IHOND7OB7SZ2TASZ664RZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNGV4IHOND7OB7SZ2TASZ664RZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WNGV4IHOND7OB7SZ2TASZ664RZ","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":"3f795a419d3ca1c9c34dfa0f51830fb343178f70e46d4661b55aee03fc64ed11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-06T01:55:21Z","title_canon_sha256":"97f4dcb73b6e3ed32dac251e555f8bd320800db9d0b7c4bca794149cc451c20b"},"schema_version":"1.0","source":{"id":"2511.03973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.03973","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"2511.03973v2","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.03973","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"WNGV4IHOND7O","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"pith_short_16","alias_value":"WNGV4IHOND7OB7SZ","created_at":"2026-07-28T01:23:26Z"},{"alias_kind":"pith_short_8","alias_value":"WNGV4IHO","created_at":"2026-07-28T01:23:26Z"}],"graph_snapshots":[{"event_id":"sha256:f82b4894b279002d89ce9f1c22b635c2923462a7ac79dc6c3b577bc340c3d465","target":"graph","created_at":"2026-07-28T01:23:26Z","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/2511.03973/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite cylinder, where the vorticity may exhibit discontinuities. The analysis is carried out by applying a hodograph transformation, which reformulates the original free boundary problem into an abstract elliptic boundary value problem. Compared to previously studied steady water waves, the present setting introduces several novel features: the presence of an inter","authors_text":"Changfeng Gui, Jun Wang, Wen Yang, Yong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-06T01:55:21Z","title":"Bifurcation analysis of Stokes waves with piecewise smooth vorticity in deep water"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.03973","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":"sha256:7146307ec9e8348e2734b2bbe49b4c8fb78bec3ef12ba1bef6444a87685b5930","target":"record","created_at":"2026-07-28T01:23:26Z","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":"3f795a419d3ca1c9c34dfa0f51830fb343178f70e46d4661b55aee03fc64ed11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-06T01:55:21Z","title_canon_sha256":"97f4dcb73b6e3ed32dac251e555f8bd320800db9d0b7c4bca794149cc451c20b"},"schema_version":"1.0","source":{"id":"2511.03973","kind":"arxiv","version":2}},"canonical_sha256":"b34d5e20ee68fee0fe59d4c12cfbdc8e48d4acdbcbcb6ecfd1867d0f67ae7119","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b34d5e20ee68fee0fe59d4c12cfbdc8e48d4acdbcbcb6ecfd1867d0f67ae7119","first_computed_at":"2026-07-28T01:23:26.876947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:26.876947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VbIc2gZkp3fgNa0Zm0dYZOgy3kh9/MHrG3be10WyiPxyc92GAI4QEDIUOARz2vjb6aVA9XePtK6l5NiDaJKHAg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:26.877909Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.03973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7146307ec9e8348e2734b2bbe49b4c8fb78bec3ef12ba1bef6444a87685b5930","sha256:f82b4894b279002d89ce9f1c22b635c2923462a7ac79dc6c3b577bc340c3d465"],"state_sha256":"bc16d544016d1e97074eb0dc9d324107e78256bb7ad4adaa3b6d9246a62af522"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8CE5hyLZ6m2shFfyDFRe6OaVsvdK1Pri9hD/EbxjqI4qI6jUL5XhLU4s0nhYC8ufcKVr1v0vcUzCCOy4lbNAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:06:56.961967Z","bundle_sha256":"332787e5f6700e656a2419d13b1f2acf8600267f4a62e9d6026e466ffea73fe4"}}