{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JOG4AQLFIGXDTHAZGMFE7QCGRD","short_pith_number":"pith:JOG4AQLF","canonical_record":{"source":{"id":"1901.10309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T14:29:49Z","cross_cats_sorted":[],"title_canon_sha256":"c2e064e36f3a473c5d078c4be2a6d93755c258df88d126ea8f82ea06be322231","abstract_canon_sha256":"dc8d31e61dfbb2206727b21f64e3836ed9f60f1699ce52d01f931211ebe59c33"},"schema_version":"1.0"},"canonical_sha256":"4b8dc0416541ae399c19330a4fc04688f1f7fe46bfdd40ee8c19e42d4cbee11f","source":{"kind":"arxiv","id":"1901.10309","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10309","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10309v1","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10309","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"JOG4AQLFIGXD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JOG4AQLFIGXDTHAZ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JOG4AQLF","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JOG4AQLFIGXDTHAZGMFE7QCGRD","target":"record","payload":{"canonical_record":{"source":{"id":"1901.10309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T14:29:49Z","cross_cats_sorted":[],"title_canon_sha256":"c2e064e36f3a473c5d078c4be2a6d93755c258df88d126ea8f82ea06be322231","abstract_canon_sha256":"dc8d31e61dfbb2206727b21f64e3836ed9f60f1699ce52d01f931211ebe59c33"},"schema_version":"1.0"},"canonical_sha256":"4b8dc0416541ae399c19330a4fc04688f1f7fe46bfdd40ee8c19e42d4cbee11f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:15.631385Z","signature_b64":"wrwHJ9UMT4OAPQsVsra/76fw4oX7ZZFL5wVs0ogOfmcmTmTwviZ03PnUTN40Iajx+YC/bjMpl9CZVJxo9T+uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b8dc0416541ae399c19330a4fc04688f1f7fe46bfdd40ee8c19e42d4cbee11f","last_reissued_at":"2026-05-17T23:55:15.630891Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:15.630891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.10309","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":"2026-05-17T23:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSZVAyLuZGAIskN+V+8zzJaHcDVTfMjjixTQ1dsvtqHwTMLus/IOPVAWSkoLfgGPpco+BqRXft7I1dbDStD+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:35:18.193085Z"},"content_sha256":"8d2d37c61df31e6201ddd39200e1386e41ffe76e3e53a6bbea1047b5c983985d","schema_version":"1.0","event_id":"sha256:8d2d37c61df31e6201ddd39200e1386e41ffe76e3e53a6bbea1047b5c983985d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JOG4AQLFIGXDTHAZGMFE7QCGRD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence theory for well-balanced Euler model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shuyang Xiang, Yangyang Cao","submitted_at":"2019-01-29T14:29:49Z","abstract_excerpt":"We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the existence of shock waves. Our proof relies on a well-balanced random choice method called Glimm method which preserves the fluid equilibria and we construct a sequence of approximate weak solutions which converges to the exact weak solution of the initial value problem, based on the construction of exact solutions of the generalized Riemann problem associated with i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10309","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":"2026-05-17T23:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6E7/bV2a3SwVeiwNGStlYB9vJPif47u72qH75Kyp7m/jON8s3tlYRmRRY9GS8swAXcHtriO1NLYH0ZECbALBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:35:18.193779Z"},"content_sha256":"3b02aa0e5e9f886c1e7de4a7e9ca38e8790211f5b14116ebdb12d16297893817","schema_version":"1.0","event_id":"sha256:3b02aa0e5e9f886c1e7de4a7e9ca38e8790211f5b14116ebdb12d16297893817"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD/bundle.json","state_url":"https://pith.science/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD/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":"2026-06-09T17:35:18Z","links":{"resolver":"https://pith.science/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD","bundle":"https://pith.science/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD/bundle.json","state":"https://pith.science/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOG4AQLFIGXDTHAZGMFE7QCGRD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JOG4AQLFIGXDTHAZGMFE7QCGRD","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":"dc8d31e61dfbb2206727b21f64e3836ed9f60f1699ce52d01f931211ebe59c33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T14:29:49Z","title_canon_sha256":"c2e064e36f3a473c5d078c4be2a6d93755c258df88d126ea8f82ea06be322231"},"schema_version":"1.0","source":{"id":"1901.10309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10309","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10309v1","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10309","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"JOG4AQLFIGXD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JOG4AQLFIGXDTHAZ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JOG4AQLF","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:3b02aa0e5e9f886c1e7de4a7e9ca38e8790211f5b14116ebdb12d16297893817","target":"graph","created_at":"2026-05-17T23:55:15Z","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":"We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the existence of shock waves. Our proof relies on a well-balanced random choice method called Glimm method which preserves the fluid equilibria and we construct a sequence of approximate weak solutions which converges to the exact weak solution of the initial value problem, based on the construction of exact solutions of the generalized Riemann problem associated with i","authors_text":"Shuyang Xiang, Yangyang Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T14:29:49Z","title":"Existence theory for well-balanced Euler model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10309","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":"sha256:8d2d37c61df31e6201ddd39200e1386e41ffe76e3e53a6bbea1047b5c983985d","target":"record","created_at":"2026-05-17T23:55:15Z","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":"dc8d31e61dfbb2206727b21f64e3836ed9f60f1699ce52d01f931211ebe59c33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T14:29:49Z","title_canon_sha256":"c2e064e36f3a473c5d078c4be2a6d93755c258df88d126ea8f82ea06be322231"},"schema_version":"1.0","source":{"id":"1901.10309","kind":"arxiv","version":1}},"canonical_sha256":"4b8dc0416541ae399c19330a4fc04688f1f7fe46bfdd40ee8c19e42d4cbee11f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b8dc0416541ae399c19330a4fc04688f1f7fe46bfdd40ee8c19e42d4cbee11f","first_computed_at":"2026-05-17T23:55:15.630891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:15.630891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrwHJ9UMT4OAPQsVsra/76fw4oX7ZZFL5wVs0ogOfmcmTmTwviZ03PnUTN40Iajx+YC/bjMpl9CZVJxo9T+uDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:15.631385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d2d37c61df31e6201ddd39200e1386e41ffe76e3e53a6bbea1047b5c983985d","sha256:3b02aa0e5e9f886c1e7de4a7e9ca38e8790211f5b14116ebdb12d16297893817"],"state_sha256":"edc0378075da8a9db530012555c5199394a53686432812417e249d341a586ba4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G2yvgkBqd8YiqII8beYZ2gzZN7dLDmlG16j+gCjRo84MNZMfHIrXZ6iI8EWznHGGMvmDYh3Ps2PzWanZLrBZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:35:18.198222Z","bundle_sha256":"30f5962f627f8142abe7d7352a2ef03c452625f4cdee3558061bef1413a88c31"}}