{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:362J6RSMUYX4MRENMV3PWK4EOI","short_pith_number":"pith:362J6RSM","canonical_record":{"source":{"id":"2204.00692","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-01T20:44:03Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"2a0770ad98d205c27cf4ac79e44279c1fa0c5afc98571c8fec4a31ff4242b1e5","abstract_canon_sha256":"5add3a749c8a23bad37742b8c049f3464a638cf71bdd69652436c8b441f6f87c"},"schema_version":"1.0"},"canonical_sha256":"dfb49f464ca62fc6448d6576fb2b84722c9edfd18e030aa327197e587dbbd18d","source":{"kind":"arxiv","id":"2204.00692","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.00692","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2204.00692v2","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00692","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"362J6RSMUYX4","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"362J6RSMUYX4MREN","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"362J6RSM","created_at":"2026-07-05T06:14:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:362J6RSMUYX4MRENMV3PWK4EOI","target":"record","payload":{"canonical_record":{"source":{"id":"2204.00692","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-01T20:44:03Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"2a0770ad98d205c27cf4ac79e44279c1fa0c5afc98571c8fec4a31ff4242b1e5","abstract_canon_sha256":"5add3a749c8a23bad37742b8c049f3464a638cf71bdd69652436c8b441f6f87c"},"schema_version":"1.0"},"canonical_sha256":"dfb49f464ca62fc6448d6576fb2b84722c9edfd18e030aa327197e587dbbd18d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:14:03.854856Z","signature_b64":"k38Jl8WoGdPo/GhWB5bAvjpINapAinwDr84RiiHyxzsS9od2qtMNCtfiWEhYv3Aa3P1qY1qeNvMELmlgW68UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfb49f464ca62fc6448d6576fb2b84722c9edfd18e030aa327197e587dbbd18d","last_reissued_at":"2026-07-05T06:14:03.854516Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:14:03.854516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.00692","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":"2026-07-05T06:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qOg5MZfF+cbfGrC5wLEMfBp4QaBEGIwjRH0iLlhYamsq1Clk79rvjJYwZlSIf3leXZ+fo271KugnlBIwDClDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:09:03.304639Z"},"content_sha256":"50b09cccb0825ce8271cef61cfdc4d72e9553bbb32aa90142b2831bbadaec34e","schema_version":"1.0","event_id":"sha256:50b09cccb0825ce8271cef61cfdc4d72e9553bbb32aa90142b2831bbadaec34e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:362J6RSMUYX4MRENMV3PWK4EOI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS","physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"G. Chen, Gui-Qiang","submitted_at":"2022-04-01T20:44:03Z","abstract_excerpt":"We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further multidimensional Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different two-dimensional Riemann problems through these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00692","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/2204.00692/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":"2026-07-05T06:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"inOUUZYcDFLgArqf1NqPt4hoG+V6lNk6MezZZoolEJExIzaWvCqT+M8smjGAonrRWilNem/ptoeu3i0tb3R3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:09:03.305025Z"},"content_sha256":"0b1514d8528bd8e7796e7c5706f1b84ea02265d63cd6b413eb5818800f532159","schema_version":"1.0","event_id":"sha256:0b1514d8528bd8e7796e7c5706f1b84ea02265d63cd6b413eb5818800f532159"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/362J6RSMUYX4MRENMV3PWK4EOI/bundle.json","state_url":"https://pith.science/pith/362J6RSMUYX4MRENMV3PWK4EOI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/362J6RSMUYX4MRENMV3PWK4EOI/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":"2026-07-07T11:09:03Z","links":{"resolver":"https://pith.science/pith/362J6RSMUYX4MRENMV3PWK4EOI","bundle":"https://pith.science/pith/362J6RSMUYX4MRENMV3PWK4EOI/bundle.json","state":"https://pith.science/pith/362J6RSMUYX4MRENMV3PWK4EOI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/362J6RSMUYX4MRENMV3PWK4EOI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:362J6RSMUYX4MRENMV3PWK4EOI","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":"5add3a749c8a23bad37742b8c049f3464a638cf71bdd69652436c8b441f6f87c","cross_cats_sorted":["math-ph","math.MP","nlin.PS","physics.comp-ph","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-01T20:44:03Z","title_canon_sha256":"2a0770ad98d205c27cf4ac79e44279c1fa0c5afc98571c8fec4a31ff4242b1e5"},"schema_version":"1.0","source":{"id":"2204.00692","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.00692","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2204.00692v2","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00692","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"362J6RSMUYX4","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"362J6RSMUYX4MREN","created_at":"2026-07-05T06:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"362J6RSM","created_at":"2026-07-05T06:14:03Z"}],"graph_snapshots":[{"event_id":"sha256:0b1514d8528bd8e7796e7c5706f1b84ea02265d63cd6b413eb5818800f532159","target":"graph","created_at":"2026-07-05T06:14:03Z","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/2204.00692/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further multidimensional Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different two-dimensional Riemann problems through these ","authors_text":"G. Chen, Gui-Qiang","cross_cats":["math-ph","math.MP","nlin.PS","physics.comp-ph","physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-01T20:44:03Z","title":"Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00692","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":"sha256:50b09cccb0825ce8271cef61cfdc4d72e9553bbb32aa90142b2831bbadaec34e","target":"record","created_at":"2026-07-05T06:14:03Z","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":"5add3a749c8a23bad37742b8c049f3464a638cf71bdd69652436c8b441f6f87c","cross_cats_sorted":["math-ph","math.MP","nlin.PS","physics.comp-ph","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-01T20:44:03Z","title_canon_sha256":"2a0770ad98d205c27cf4ac79e44279c1fa0c5afc98571c8fec4a31ff4242b1e5"},"schema_version":"1.0","source":{"id":"2204.00692","kind":"arxiv","version":2}},"canonical_sha256":"dfb49f464ca62fc6448d6576fb2b84722c9edfd18e030aa327197e587dbbd18d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfb49f464ca62fc6448d6576fb2b84722c9edfd18e030aa327197e587dbbd18d","first_computed_at":"2026-07-05T06:14:03.854516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:14:03.854516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k38Jl8WoGdPo/GhWB5bAvjpINapAinwDr84RiiHyxzsS9od2qtMNCtfiWEhYv3Aa3P1qY1qeNvMELmlgW68UDw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:14:03.854856Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.00692","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50b09cccb0825ce8271cef61cfdc4d72e9553bbb32aa90142b2831bbadaec34e","sha256:0b1514d8528bd8e7796e7c5706f1b84ea02265d63cd6b413eb5818800f532159"],"state_sha256":"0caa524a0fbf20e2df4988e2aab4ead1e0f3c449e4a53ff96742b8e46119ef1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QwvHsXO9XfVnjDLIAgXrQj73paDqvnjjQprOstZ5YNvukEjMRTcXeEY9JTwrQzIjMxE/qSPr82BRwpOiaRYjAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:09:03.307038Z","bundle_sha256":"4c43183d1380956d67362144e1279e9a51e7d96e2ebbd7f5e4c4cb361fe0aa8d"}}