{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:M2CRLFUMB5SFAJNR5STYAHEMTQ","short_pith_number":"pith:M2CRLFUM","canonical_record":{"source":{"id":"1107.4179","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-21T06:26:17Z","cross_cats_sorted":[],"title_canon_sha256":"b800c57bc00ee4306a8d52d330b0f287d115f1b69230952daf38da272b622ef4","abstract_canon_sha256":"cb9c4beccb95314780a231f9805122b7d7091e8b21073ecb6dca488ded49f318"},"schema_version":"1.0"},"canonical_sha256":"668515968c0f645025b1eca7801c8c9c0e03236cf1bfb270c47050244fb1d035","source":{"kind":"arxiv","id":"1107.4179","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4179","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4179v3","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4179","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"M2CRLFUMB5SF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M2CRLFUMB5SFAJNR","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M2CRLFUM","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:M2CRLFUMB5SFAJNR5STYAHEMTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4179","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-21T06:26:17Z","cross_cats_sorted":[],"title_canon_sha256":"b800c57bc00ee4306a8d52d330b0f287d115f1b69230952daf38da272b622ef4","abstract_canon_sha256":"cb9c4beccb95314780a231f9805122b7d7091e8b21073ecb6dca488ded49f318"},"schema_version":"1.0"},"canonical_sha256":"668515968c0f645025b1eca7801c8c9c0e03236cf1bfb270c47050244fb1d035","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:35.358815Z","signature_b64":"ONd9l3HiLbnOghaNI5FU6QKL7+7bb0YHdet8HD8hH7z6cmeRNDct3kMThKT6Pdp7yRDkjDddaVdB7M1r5LzaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"668515968c0f645025b1eca7801c8c9c0e03236cf1bfb270c47050244fb1d035","last_reissued_at":"2026-05-18T03:56:35.358338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:35.358338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4179","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fv3WULDtrqH4H7JVlhOmm2Lvz8+/fR0LjvLFDbkXa5qpoa16wrgxLshOlKab7Q2VgLZEMhEZgh1tsKvyWuF4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:43.262204Z"},"content_sha256":"107cb2b1a0883936cbb2b5e528740f3a5b7ccc33a5040a78872fe9f355435b4f","schema_version":"1.0","event_id":"sha256:107cb2b1a0883936cbb2b5e528740f3a5b7ccc33a5040a78872fe9f355435b4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:M2CRLFUMB5SFAJNR5STYAHEMTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness for a multi-dimensional viscous liquid-gas two-phase flow model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengchun Hao, Hai-Liang Li","submitted_at":"2011-07-21T06:26:17Z","abstract_excerpt":"The Cauchy problem of a multi-dimensional ($d\\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close to a stable equilibrium and the local in time existence and uniqueness of the solution with general initial data in the framework of Besov spaces. A continuation criterion is also obtained for the local solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4179","kind":"arxiv","version":3},"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":"2026-05-18T03:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkeIjOMMmZmo72R3aiWV2hO7EhxtjztaDvp5hUbpEZuZi1eE+UKVyMsWvbKWz6X2J4PUiBXXf8w2QNINtjikDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:43.262557Z"},"content_sha256":"e66cb9b14edf6507f113b49abff5e76a579d43c9558f83c7b734e852333d2aa3","schema_version":"1.0","event_id":"sha256:e66cb9b14edf6507f113b49abff5e76a579d43c9558f83c7b734e852333d2aa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ/bundle.json","state_url":"https://pith.science/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ/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":"2026-06-01T19:40:43Z","links":{"resolver":"https://pith.science/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ","bundle":"https://pith.science/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ/bundle.json","state":"https://pith.science/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2CRLFUMB5SFAJNR5STYAHEMTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:M2CRLFUMB5SFAJNR5STYAHEMTQ","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":"cb9c4beccb95314780a231f9805122b7d7091e8b21073ecb6dca488ded49f318","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-21T06:26:17Z","title_canon_sha256":"b800c57bc00ee4306a8d52d330b0f287d115f1b69230952daf38da272b622ef4"},"schema_version":"1.0","source":{"id":"1107.4179","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4179","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4179v3","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4179","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"M2CRLFUMB5SF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M2CRLFUMB5SFAJNR","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M2CRLFUM","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:e66cb9b14edf6507f113b49abff5e76a579d43c9558f83c7b734e852333d2aa3","target":"graph","created_at":"2026-05-18T03:56:35Z","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":"The Cauchy problem of a multi-dimensional ($d\\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close to a stable equilibrium and the local in time existence and uniqueness of the solution with general initial data in the framework of Besov spaces. A continuation criterion is also obtained for the local solution.","authors_text":"Chengchun Hao, Hai-Liang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-21T06:26:17Z","title":"Well-posedness for a multi-dimensional viscous liquid-gas two-phase flow model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4179","kind":"arxiv","version":3},"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":"sha256:107cb2b1a0883936cbb2b5e528740f3a5b7ccc33a5040a78872fe9f355435b4f","target":"record","created_at":"2026-05-18T03:56:35Z","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":"cb9c4beccb95314780a231f9805122b7d7091e8b21073ecb6dca488ded49f318","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-21T06:26:17Z","title_canon_sha256":"b800c57bc00ee4306a8d52d330b0f287d115f1b69230952daf38da272b622ef4"},"schema_version":"1.0","source":{"id":"1107.4179","kind":"arxiv","version":3}},"canonical_sha256":"668515968c0f645025b1eca7801c8c9c0e03236cf1bfb270c47050244fb1d035","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"668515968c0f645025b1eca7801c8c9c0e03236cf1bfb270c47050244fb1d035","first_computed_at":"2026-05-18T03:56:35.358338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:35.358338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ONd9l3HiLbnOghaNI5FU6QKL7+7bb0YHdet8HD8hH7z6cmeRNDct3kMThKT6Pdp7yRDkjDddaVdB7M1r5LzaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:35.358815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4179","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:107cb2b1a0883936cbb2b5e528740f3a5b7ccc33a5040a78872fe9f355435b4f","sha256:e66cb9b14edf6507f113b49abff5e76a579d43c9558f83c7b734e852333d2aa3"],"state_sha256":"0eed2c5c0d8439aacf38357e06bb4d093dde638dfc90120ecdc7ac0281a489cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zCwiNPKFH1PI5iJZwsUG86W5ZFhPjAq567K/19547+RhNoqFCX61w9bCslUzRcwJMey/pQgphcGE+oMTsynCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:40:43.264734Z","bundle_sha256":"7271fac90a55b00c5a20d9c8ced607811504d55482f62e63dec345c4ce8c99e5"}}