{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EMY4QTRYEXXVJD75KPBND7PYTJ","short_pith_number":"pith:EMY4QTRY","canonical_record":{"source":{"id":"1801.09077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-27T11:56:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0ae9752611a5eb8aa4e76ef1595fc84212e844430c449f837de5046e8b0707f1","abstract_canon_sha256":"57794c907abb9bb26a0d1620dd72c0823bcccdc45b782c5db8e6a6618bc6a469"},"schema_version":"1.0"},"canonical_sha256":"2331c84e3825ef548ffd53c2d1fdf89a4736fb386a69f853e0fee60f02ac0537","source":{"kind":"arxiv","id":"1801.09077","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09077","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09077v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09077","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"EMY4QTRYEXXV","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EMY4QTRYEXXVJD75","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EMY4QTRY","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EMY4QTRYEXXVJD75KPBND7PYTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-27T11:56:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0ae9752611a5eb8aa4e76ef1595fc84212e844430c449f837de5046e8b0707f1","abstract_canon_sha256":"57794c907abb9bb26a0d1620dd72c0823bcccdc45b782c5db8e6a6618bc6a469"},"schema_version":"1.0"},"canonical_sha256":"2331c84e3825ef548ffd53c2d1fdf89a4736fb386a69f853e0fee60f02ac0537","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:58.696458Z","signature_b64":"RSGUQwGXRQGgfAUWQb0FlddNBIWydmMlzSRtsJsvDNhTMy1EdzUfR9RhigmHak98qrxPpVsaZO8epbTjq5PiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2331c84e3825ef548ffd53c2d1fdf89a4736fb386a69f853e0fee60f02ac0537","last_reissued_at":"2026-05-18T00:24:58.695750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:58.695750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09077","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":"2026-05-18T00:24:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwSqgeZCS+n2/haLm1cOsDFDHnDIRnhmb7Jzrts1OXR6OLRXgmrInqMrI7Nzsa9NnY5hroui0B1ZhrOHwH9QCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:37:42.431536Z"},"content_sha256":"e7c8aeb4431b8a926e3468b76929dfbf2e47ca0591b55f8c7436ea2b65d6c15b","schema_version":"1.0","event_id":"sha256:e7c8aeb4431b8a926e3468b76929dfbf2e47ca0591b55f8c7436ea2b65d6c15b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EMY4QTRYEXXVJD75KPBND7PYTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and Uniqueness of Global Solutions to Euler Equations with Exothermic Reaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Kai Hu","submitted_at":"2018-01-27T11:56:15Z","abstract_excerpt":"We consider the Cauchy problems of a non-strictly hyperbolic system which describes the compressible Euler fluid with exothermic reaction. In this paper a Lyapunov-type functional is constructed for balance laws. By analysis of the flow generated by front tracking method, we prove the well-posedness theorems and present the local features of global solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09077","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":"2026-05-18T00:24:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"02p0punNiNXrkpfP2GlpmfJtl2popy471MJLrFsHQ3/SXONioLFHMxM1EQzDG2EnNad5x45SgrIYGllBmEbDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:37:42.432225Z"},"content_sha256":"444517da7c57a1648fc4a989174d488512420fb7c94d94b42ef36d51c67a5462","schema_version":"1.0","event_id":"sha256:444517da7c57a1648fc4a989174d488512420fb7c94d94b42ef36d51c67a5462"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMY4QTRYEXXVJD75KPBND7PYTJ/bundle.json","state_url":"https://pith.science/pith/EMY4QTRYEXXVJD75KPBND7PYTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMY4QTRYEXXVJD75KPBND7PYTJ/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":"2026-05-31T03:37:42Z","links":{"resolver":"https://pith.science/pith/EMY4QTRYEXXVJD75KPBND7PYTJ","bundle":"https://pith.science/pith/EMY4QTRYEXXVJD75KPBND7PYTJ/bundle.json","state":"https://pith.science/pith/EMY4QTRYEXXVJD75KPBND7PYTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMY4QTRYEXXVJD75KPBND7PYTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EMY4QTRYEXXVJD75KPBND7PYTJ","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":"57794c907abb9bb26a0d1620dd72c0823bcccdc45b782c5db8e6a6618bc6a469","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-27T11:56:15Z","title_canon_sha256":"0ae9752611a5eb8aa4e76ef1595fc84212e844430c449f837de5046e8b0707f1"},"schema_version":"1.0","source":{"id":"1801.09077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09077","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09077v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09077","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"EMY4QTRYEXXV","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EMY4QTRYEXXVJD75","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EMY4QTRY","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:444517da7c57a1648fc4a989174d488512420fb7c94d94b42ef36d51c67a5462","target":"graph","created_at":"2026-05-18T00:24:58Z","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 consider the Cauchy problems of a non-strictly hyperbolic system which describes the compressible Euler fluid with exothermic reaction. In this paper a Lyapunov-type functional is constructed for balance laws. By analysis of the flow generated by front tracking method, we prove the well-posedness theorems and present the local features of global solutions.","authors_text":"Kai Hu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-27T11:56:15Z","title":"Stability and Uniqueness of Global Solutions to Euler Equations with Exothermic Reaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09077","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:e7c8aeb4431b8a926e3468b76929dfbf2e47ca0591b55f8c7436ea2b65d6c15b","target":"record","created_at":"2026-05-18T00:24:58Z","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":"57794c907abb9bb26a0d1620dd72c0823bcccdc45b782c5db8e6a6618bc6a469","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-27T11:56:15Z","title_canon_sha256":"0ae9752611a5eb8aa4e76ef1595fc84212e844430c449f837de5046e8b0707f1"},"schema_version":"1.0","source":{"id":"1801.09077","kind":"arxiv","version":1}},"canonical_sha256":"2331c84e3825ef548ffd53c2d1fdf89a4736fb386a69f853e0fee60f02ac0537","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2331c84e3825ef548ffd53c2d1fdf89a4736fb386a69f853e0fee60f02ac0537","first_computed_at":"2026-05-18T00:24:58.695750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.695750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RSGUQwGXRQGgfAUWQb0FlddNBIWydmMlzSRtsJsvDNhTMy1EdzUfR9RhigmHak98qrxPpVsaZO8epbTjq5PiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.696458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7c8aeb4431b8a926e3468b76929dfbf2e47ca0591b55f8c7436ea2b65d6c15b","sha256:444517da7c57a1648fc4a989174d488512420fb7c94d94b42ef36d51c67a5462"],"state_sha256":"cf5a95116fbb189d51a0f2b1f1d9d40ee5c0396fe32a7bc4c7d912fc8d38b2f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDRcdARln3Razp+e2u/OulEa7INOCByCKjiM24I0GJAO3PAeKVuMrUkl+m3Ra0RacA8dI7+qkuguFEsPuwDJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:37:42.437103Z","bundle_sha256":"d718808bd6a3e36695e79c33d7e0e6ac1708bb40671e414deb60c6724fe8c933"}}