{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5SYADNQ2QEC3IRIW44YV3P7PLT","short_pith_number":"pith:5SYADNQ2","canonical_record":{"source":{"id":"1812.07379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-14T19:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"4ac32582397e96ca161cd1f45245392bcc49c24d0ffb32277c632a17cc5c41d3","abstract_canon_sha256":"269f41c4bbae221b44f2bc0392e43268dfee9927dd6e50e54ad62f620431ec45"},"schema_version":"1.0"},"canonical_sha256":"ecb001b61a8105b44516e7315dbfef5ce2ae99aed5f307a92879ecaa217855ca","source":{"kind":"arxiv","id":"1812.07379","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07379","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07379v1","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07379","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"5SYADNQ2QEC3","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5SYADNQ2QEC3IRIW","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5SYADNQ2","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5SYADNQ2QEC3IRIW44YV3P7PLT","target":"record","payload":{"canonical_record":{"source":{"id":"1812.07379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-14T19:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"4ac32582397e96ca161cd1f45245392bcc49c24d0ffb32277c632a17cc5c41d3","abstract_canon_sha256":"269f41c4bbae221b44f2bc0392e43268dfee9927dd6e50e54ad62f620431ec45"},"schema_version":"1.0"},"canonical_sha256":"ecb001b61a8105b44516e7315dbfef5ce2ae99aed5f307a92879ecaa217855ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:00.686796Z","signature_b64":"V8hSkXVkqwk1MIP4h1/Rt8JWquteCclswPGjHW6DGiojpP4wvnnU3lLUhIpNo7HwcItiMROY8HT078Y0DetqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecb001b61a8105b44516e7315dbfef5ce2ae99aed5f307a92879ecaa217855ca","last_reissued_at":"2026-05-17T23:58:00.686227Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:00.686227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.07379","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRpr72hj7B2tmmxoeRIKI341he6BjmyikQC2z56pp4bsO3dUqxi/dt5mGJbeJDvwcw0HVYiey8hked1the0GCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:36:13.293002Z"},"content_sha256":"b58344166ebeac98b6cbe84fc0b74fadbb891942a8e72278956cd70a3577d2a3","schema_version":"1.0","event_id":"sha256:b58344166ebeac98b6cbe84fc0b74fadbb891942a8e72278956cd70a3577d2a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5SYADNQ2QEC3IRIW44YV3P7PLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal density lower bound on nonisentropic gas dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Geng Chen","submitted_at":"2018-12-14T19:34:48Z","abstract_excerpt":"In this paper, we prove a time dependent lower bound on density in the optimal order $O(1/(1+t))$ for the general smooth nonisentropic flow of compressible Euler equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07379","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZYhfTuRso18jKt/dHeAAPwcmoytam4JmnTYyWqBQ9TrehngkKtBV05XXAjCdCuwiR/ROjfnsIb0X4A1z4/pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:36:13.293810Z"},"content_sha256":"26836976dde53375deae551996b30554b93499d173e181348a0f6c5528061ee4","schema_version":"1.0","event_id":"sha256:26836976dde53375deae551996b30554b93499d173e181348a0f6c5528061ee4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SYADNQ2QEC3IRIW44YV3P7PLT/bundle.json","state_url":"https://pith.science/pith/5SYADNQ2QEC3IRIW44YV3P7PLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SYADNQ2QEC3IRIW44YV3P7PLT/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":"2026-06-01T02:36:13Z","links":{"resolver":"https://pith.science/pith/5SYADNQ2QEC3IRIW44YV3P7PLT","bundle":"https://pith.science/pith/5SYADNQ2QEC3IRIW44YV3P7PLT/bundle.json","state":"https://pith.science/pith/5SYADNQ2QEC3IRIW44YV3P7PLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SYADNQ2QEC3IRIW44YV3P7PLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5SYADNQ2QEC3IRIW44YV3P7PLT","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":"269f41c4bbae221b44f2bc0392e43268dfee9927dd6e50e54ad62f620431ec45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-14T19:34:48Z","title_canon_sha256":"4ac32582397e96ca161cd1f45245392bcc49c24d0ffb32277c632a17cc5c41d3"},"schema_version":"1.0","source":{"id":"1812.07379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07379","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07379v1","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07379","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"5SYADNQ2QEC3","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5SYADNQ2QEC3IRIW","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5SYADNQ2","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:26836976dde53375deae551996b30554b93499d173e181348a0f6c5528061ee4","target":"graph","created_at":"2026-05-17T23:58:00Z","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":"In this paper, we prove a time dependent lower bound on density in the optimal order $O(1/(1+t))$ for the general smooth nonisentropic flow of compressible Euler equations.","authors_text":"Geng Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-14T19:34:48Z","title":"Optimal density lower bound on nonisentropic gas dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07379","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:b58344166ebeac98b6cbe84fc0b74fadbb891942a8e72278956cd70a3577d2a3","target":"record","created_at":"2026-05-17T23:58:00Z","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":"269f41c4bbae221b44f2bc0392e43268dfee9927dd6e50e54ad62f620431ec45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-14T19:34:48Z","title_canon_sha256":"4ac32582397e96ca161cd1f45245392bcc49c24d0ffb32277c632a17cc5c41d3"},"schema_version":"1.0","source":{"id":"1812.07379","kind":"arxiv","version":1}},"canonical_sha256":"ecb001b61a8105b44516e7315dbfef5ce2ae99aed5f307a92879ecaa217855ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecb001b61a8105b44516e7315dbfef5ce2ae99aed5f307a92879ecaa217855ca","first_computed_at":"2026-05-17T23:58:00.686227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:00.686227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V8hSkXVkqwk1MIP4h1/Rt8JWquteCclswPGjHW6DGiojpP4wvnnU3lLUhIpNo7HwcItiMROY8HT078Y0DetqAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:00.686796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b58344166ebeac98b6cbe84fc0b74fadbb891942a8e72278956cd70a3577d2a3","sha256:26836976dde53375deae551996b30554b93499d173e181348a0f6c5528061ee4"],"state_sha256":"1f3d070ff5f878d2fc979d3085059932047b9c8aba3a902d0fdc7d381d455619"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQ08tXxkNS8vqWDwfFce7iFBEA/unQ3PL5uZq5WC8fIb0tN+b5MIDwL+xJtuIfxUt2YVYgvCbxLo1dFrfmOwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:36:13.297856Z","bundle_sha256":"7779939656229f8530708f688a5b5795ec82ff387ce58db3d458e437e6c1197b"}}