{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EVHB5ZSBHTK3M7L6WE3TUAY4I5","short_pith_number":"pith:EVHB5ZSB","canonical_record":{"source":{"id":"1410.3182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-13T03:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"492bf6e2cab38dd5ac437949eb465fe7c58e7a2827013843148d24d71523d038","abstract_canon_sha256":"75c0579d81c3c8016395a8c80413a7f1943caaaf935b76c20125b10be5cff5c7"},"schema_version":"1.0"},"canonical_sha256":"254e1ee6413cd5b67d7eb1373a031c476037661bbbabbde9f54f26d206d0fea8","source":{"kind":"arxiv","id":"1410.3182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3182","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3182v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3182","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"EVHB5ZSBHTK3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EVHB5ZSBHTK3M7L6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EVHB5ZSB","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EVHB5ZSBHTK3M7L6WE3TUAY4I5","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-13T03:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"492bf6e2cab38dd5ac437949eb465fe7c58e7a2827013843148d24d71523d038","abstract_canon_sha256":"75c0579d81c3c8016395a8c80413a7f1943caaaf935b76c20125b10be5cff5c7"},"schema_version":"1.0"},"canonical_sha256":"254e1ee6413cd5b67d7eb1373a031c476037661bbbabbde9f54f26d206d0fea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:11.947836Z","signature_b64":"IvlZuXhygLRB9EQtxl07OPzCoCE5YLxLT2I//IaBcozE7tUZYMTr0PIm48IsipQ07Rek2ObQGcHA8AMnglWmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"254e1ee6413cd5b67d7eb1373a031c476037661bbbabbde9f54f26d206d0fea8","last_reissued_at":"2026-05-18T02:40:11.947433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:11.947433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3182","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":"2026-05-18T02:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8Lk9O6xPkmeFSraCtDhz0Kag06rBEjUVkCU0NHR1u6ppMAIQZWTZZz1okOwWuaj8SPJ9hY397CXbfJJl5LnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:57:36.661567Z"},"content_sha256":"d638b297b0b351bd946c3a7c58615f2c18b2db446bc8d2cdcbfa604d9792a9eb","schema_version":"1.0","event_id":"sha256:d638b297b0b351bd946c3a7c58615f2c18b2db446bc8d2cdcbfa604d9792a9eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EVHB5ZSBHTK3M7L6WE3TUAY4I5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bound of density for Lipschitz continuous solutions in the isentropic gas dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Geng Chen, Ronghua Pan, Shengguo Zhu","submitted_at":"2014-10-13T03:40:57Z","abstract_excerpt":"For the Euler equations of isentropic gas dynamics in one space dimension, also knowns as p-system in Lagrangian coordinate, it is known that the density can be arbitrarily close to zero as time goes to infinity, even when initial density is uniformly away from zero. In this paper, for uniform positive initial density, we prove the density in any Lipschitz continuous solutions for Cauchy problem has a sharp positive lower bound in the order of O(1/(1+t)), which is identified by explicit examples in [9](Courant and Friedrichs, Supersonic Flow and Shock Waves, 1948.)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3182","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":"2026-05-18T02:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSTGuPFI3SgYbwDmTGrdovCH66O8yihounrViP7qHgVsV4qvMJdYn0rZMOjQ+DcmjdGA6GeNnhMSn6p+PWdRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:57:36.661954Z"},"content_sha256":"03e7b4b61fd1173702c2189bf3016e948a76ab9bfeb61150a503f33c4ee16592","schema_version":"1.0","event_id":"sha256:03e7b4b61fd1173702c2189bf3016e948a76ab9bfeb61150a503f33c4ee16592"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5/bundle.json","state_url":"https://pith.science/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5/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":"2026-05-26T13:57:36Z","links":{"resolver":"https://pith.science/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5","bundle":"https://pith.science/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5/bundle.json","state":"https://pith.science/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVHB5ZSBHTK3M7L6WE3TUAY4I5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EVHB5ZSBHTK3M7L6WE3TUAY4I5","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":"75c0579d81c3c8016395a8c80413a7f1943caaaf935b76c20125b10be5cff5c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-13T03:40:57Z","title_canon_sha256":"492bf6e2cab38dd5ac437949eb465fe7c58e7a2827013843148d24d71523d038"},"schema_version":"1.0","source":{"id":"1410.3182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3182","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3182v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3182","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"EVHB5ZSBHTK3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EVHB5ZSBHTK3M7L6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EVHB5ZSB","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:03e7b4b61fd1173702c2189bf3016e948a76ab9bfeb61150a503f33c4ee16592","target":"graph","created_at":"2026-05-18T02:40:11Z","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":"For the Euler equations of isentropic gas dynamics in one space dimension, also knowns as p-system in Lagrangian coordinate, it is known that the density can be arbitrarily close to zero as time goes to infinity, even when initial density is uniformly away from zero. In this paper, for uniform positive initial density, we prove the density in any Lipschitz continuous solutions for Cauchy problem has a sharp positive lower bound in the order of O(1/(1+t)), which is identified by explicit examples in [9](Courant and Friedrichs, Supersonic Flow and Shock Waves, 1948.).","authors_text":"Geng Chen, Ronghua Pan, Shengguo Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-13T03:40:57Z","title":"Lower bound of density for Lipschitz continuous solutions in the isentropic gas dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3182","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:d638b297b0b351bd946c3a7c58615f2c18b2db446bc8d2cdcbfa604d9792a9eb","target":"record","created_at":"2026-05-18T02:40:11Z","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":"75c0579d81c3c8016395a8c80413a7f1943caaaf935b76c20125b10be5cff5c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-13T03:40:57Z","title_canon_sha256":"492bf6e2cab38dd5ac437949eb465fe7c58e7a2827013843148d24d71523d038"},"schema_version":"1.0","source":{"id":"1410.3182","kind":"arxiv","version":1}},"canonical_sha256":"254e1ee6413cd5b67d7eb1373a031c476037661bbbabbde9f54f26d206d0fea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"254e1ee6413cd5b67d7eb1373a031c476037661bbbabbde9f54f26d206d0fea8","first_computed_at":"2026-05-18T02:40:11.947433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:11.947433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IvlZuXhygLRB9EQtxl07OPzCoCE5YLxLT2I//IaBcozE7tUZYMTr0PIm48IsipQ07Rek2ObQGcHA8AMnglWmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:11.947836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d638b297b0b351bd946c3a7c58615f2c18b2db446bc8d2cdcbfa604d9792a9eb","sha256:03e7b4b61fd1173702c2189bf3016e948a76ab9bfeb61150a503f33c4ee16592"],"state_sha256":"ed1918c14c8448580e401a3f19d58e4fee9af0672c4fcfb79e346e69a34e971c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyrjHWJs8Ec0DVb8wFGXfHpFOfchlL5lbImmMQ3rFVnTFT5PX3IS5aGMgQwvt61pJwgKxdJ5Pxeo4fB2oWheAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:57:36.664940Z","bundle_sha256":"3930f97dce7a56bbddd11bbbc8b273b814abe93c9c4534933848b9ed34a9d2b0"}}