{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:M4MRKXGSKEBQK3M6SA2BQMDL2N","short_pith_number":"pith:M4MRKXGS","canonical_record":{"source":{"id":"2412.07283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-10T08:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"1a26c018b932d6bc5e90e493db7d19072cbb945f7b4ec0461a5bb3d406d96f06","abstract_canon_sha256":"29fa929f85977ee334527064c9eb98712c1b5abda91177f3716f9dd61f9ef28b"},"schema_version":"1.0"},"canonical_sha256":"6719155cd25103056d9e903418306bd3553d9bf1f0ee7a65fc78514d48174f09","source":{"kind":"arxiv","id":"2412.07283","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.07283","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"2412.07283v2","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.07283","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"M4MRKXGSKEBQ","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"pith_short_16","alias_value":"M4MRKXGSKEBQK3M6","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"pith_short_8","alias_value":"M4MRKXGS","created_at":"2026-07-05T10:14:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:M4MRKXGSKEBQK3M6SA2BQMDL2N","target":"record","payload":{"canonical_record":{"source":{"id":"2412.07283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-10T08:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"1a26c018b932d6bc5e90e493db7d19072cbb945f7b4ec0461a5bb3d406d96f06","abstract_canon_sha256":"29fa929f85977ee334527064c9eb98712c1b5abda91177f3716f9dd61f9ef28b"},"schema_version":"1.0"},"canonical_sha256":"6719155cd25103056d9e903418306bd3553d9bf1f0ee7a65fc78514d48174f09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:48.895562Z","signature_b64":"BqWZNvkS3stI85TUmRatF+mnhFKkic0x3aNMA0T4Sors20RrhQQe529OjZ4h3uVAyZUfcB/jA3lttsFXihSPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6719155cd25103056d9e903418306bd3553d9bf1f0ee7a65fc78514d48174f09","last_reissued_at":"2026-07-05T10:14:48.894976Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:48.894976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.07283","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":"2026-07-05T10:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A51Tkm6jEXYovm44ObsAkZu+/9KxZY2BxWws6PVOGR3r79FkNk1rRk9NHI3h4CFUyAwGEZXfGZGN8TO+DvYmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:42:15.202462Z"},"content_sha256":"13c9294a930e3d69a25db5bab3433dbfde11139d4776d97cd32d943fc90e85df","schema_version":"1.0","event_id":"sha256:13c9294a930e3d69a25db5bab3433dbfde11139d4776d97cd32d943fc90e85df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:M4MRKXGSKEBQK3M6SA2BQMDL2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Similar Solutions to the steady Navier-Stokes Equations in a two-dimensional sector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changfeng Gui, Chunjing Xie, Hao Liu, Jeaheang Bang, Yun Wang","submitted_at":"2024-12-10T08:13:57Z","abstract_excerpt":"This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the flux to guarantee the existence of self-similar solutions of a given type. We also investigate the uniqueness and non-uniqueness of flows with a given type, which not only give rigorous justifications for some statements in \\cite{Rosenhead40} but also show that some numerical computations in \\cite{Rosenhead40} may not be precise. The non-uniqueness result is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.07283","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/2412.07283/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":"2026-07-05T10:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyIxP3xURKslPTnD0KsYtHP9jHbfEp04YLrFHNzjqtJQvbvTBKA59iC6HKX23L2F99QzGLzn4Ecl6UwRc8GlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:42:15.203346Z"},"content_sha256":"37599175397f443530dfa92456f7291194b06bfad5f62a5d1e20485f48a20b56","schema_version":"1.0","event_id":"sha256:37599175397f443530dfa92456f7291194b06bfad5f62a5d1e20485f48a20b56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N/bundle.json","state_url":"https://pith.science/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N/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":"2026-08-06T02:42:15Z","links":{"resolver":"https://pith.science/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N","bundle":"https://pith.science/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N/bundle.json","state":"https://pith.science/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4MRKXGSKEBQK3M6SA2BQMDL2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:M4MRKXGSKEBQK3M6SA2BQMDL2N","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":"29fa929f85977ee334527064c9eb98712c1b5abda91177f3716f9dd61f9ef28b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-10T08:13:57Z","title_canon_sha256":"1a26c018b932d6bc5e90e493db7d19072cbb945f7b4ec0461a5bb3d406d96f06"},"schema_version":"1.0","source":{"id":"2412.07283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.07283","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"2412.07283v2","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.07283","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"M4MRKXGSKEBQ","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"pith_short_16","alias_value":"M4MRKXGSKEBQK3M6","created_at":"2026-07-05T10:14:48Z"},{"alias_kind":"pith_short_8","alias_value":"M4MRKXGS","created_at":"2026-07-05T10:14:48Z"}],"graph_snapshots":[{"event_id":"sha256:37599175397f443530dfa92456f7291194b06bfad5f62a5d1e20485f48a20b56","target":"graph","created_at":"2026-07-05T10:14:48Z","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/2412.07283/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the flux to guarantee the existence of self-similar solutions of a given type. We also investigate the uniqueness and non-uniqueness of flows with a given type, which not only give rigorous justifications for some statements in \\cite{Rosenhead40} but also show that some numerical computations in \\cite{Rosenhead40} may not be precise. The non-uniqueness result is","authors_text":"Changfeng Gui, Chunjing Xie, Hao Liu, Jeaheang Bang, Yun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-10T08:13:57Z","title":"Self-Similar Solutions to the steady Navier-Stokes Equations in a two-dimensional sector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.07283","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":"sha256:13c9294a930e3d69a25db5bab3433dbfde11139d4776d97cd32d943fc90e85df","target":"record","created_at":"2026-07-05T10:14:48Z","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":"29fa929f85977ee334527064c9eb98712c1b5abda91177f3716f9dd61f9ef28b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-10T08:13:57Z","title_canon_sha256":"1a26c018b932d6bc5e90e493db7d19072cbb945f7b4ec0461a5bb3d406d96f06"},"schema_version":"1.0","source":{"id":"2412.07283","kind":"arxiv","version":2}},"canonical_sha256":"6719155cd25103056d9e903418306bd3553d9bf1f0ee7a65fc78514d48174f09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6719155cd25103056d9e903418306bd3553d9bf1f0ee7a65fc78514d48174f09","first_computed_at":"2026-07-05T10:14:48.894976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:48.894976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BqWZNvkS3stI85TUmRatF+mnhFKkic0x3aNMA0T4Sors20RrhQQe529OjZ4h3uVAyZUfcB/jA3lttsFXihSPCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:48.895562Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.07283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13c9294a930e3d69a25db5bab3433dbfde11139d4776d97cd32d943fc90e85df","sha256:37599175397f443530dfa92456f7291194b06bfad5f62a5d1e20485f48a20b56"],"state_sha256":"8805fb8ebe318344123fb3e20591adea95dcacec0c4dc74664e184ae22541a5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ZsoXjqvWZbQ9G7XMVNV4wYL/mjqB3nyt9KmbT5V3Ps7yKwHDFlE7GCyb5WQuZkpE2ZA0vW5lDuLYOeHUNtVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T02:42:15.210459Z","bundle_sha256":"0602f8350f146a46b1bf5afaecf361cebec2d23ecf32d9c40781f3a35b5a144a"}}