{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6UVHSW4C7SUOKQYA3CVZ6Z47IY","short_pith_number":"pith:6UVHSW4C","canonical_record":{"source":{"id":"1104.4377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-22T02:46:46Z","cross_cats_sorted":[],"title_canon_sha256":"09a0b96df18a581113333743c15a8a489c230686c7ddde3e8347f93ecfa608da","abstract_canon_sha256":"1a6f05b5ce980f87b03ed0ca7aee72f9cf1ae395f5d3616a1a48f9ac8b3dd358"},"schema_version":"1.0"},"canonical_sha256":"f52a795b82fca8e54300d8ab9f679f46219664c329bff74a44df29bb3388d2ba","source":{"kind":"arxiv","id":"1104.4377","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4377","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4377v2","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4377","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"6UVHSW4C7SUO","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6UVHSW4C7SUOKQYA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6UVHSW4C","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6UVHSW4C7SUOKQYA3CVZ6Z47IY","target":"record","payload":{"canonical_record":{"source":{"id":"1104.4377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-22T02:46:46Z","cross_cats_sorted":[],"title_canon_sha256":"09a0b96df18a581113333743c15a8a489c230686c7ddde3e8347f93ecfa608da","abstract_canon_sha256":"1a6f05b5ce980f87b03ed0ca7aee72f9cf1ae395f5d3616a1a48f9ac8b3dd358"},"schema_version":"1.0"},"canonical_sha256":"f52a795b82fca8e54300d8ab9f679f46219664c329bff74a44df29bb3388d2ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:42.470734Z","signature_b64":"LCrB+g6eW+EPnqrtz5ibgHdtQ9R+BLhbjFt3VuMbF0UTixYEI09ukmMdFZ0+Qi+LycPdNM4uy74eLuvTmOMHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f52a795b82fca8e54300d8ab9f679f46219664c329bff74a44df29bb3388d2ba","last_reissued_at":"2026-05-18T02:52:42.470268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:42.470268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.4377","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KaGIJaxezBp00Ui5Igw6Gzluz+8mA5CO912gaB5ApYVproGSNo4JuVPm8ZB8++l3RejDpSOS5YCUi5b9ay+dAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:05:56.243177Z"},"content_sha256":"d39bf581bd2ffd4c62454ba3b4d928e6c2ff52443d43e4bcd7248928fcda5e5c","schema_version":"1.0","event_id":"sha256:d39bf581bd2ffd4c62454ba3b4d928e6c2ff52443d43e4bcd7248928fcda5e5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6UVHSW4C7SUOKQYA3CVZ6Z47IY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incompressible Limit of the Compressible Nematic Liquid Crystal Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huanyao Wen, Jinrui Huang, Ruizhao Zi, Shijin Ding","submitted_at":"2011-04-22T02:46:46Z","abstract_excerpt":"This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N = 2, 3). It is rigorously shown that the local (and global) strong solution of the compressible system converges to the local (and global) strong solution of the incompressible system. Furthermore, the convergence rates are also obtained in some sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4377","kind":"arxiv","version":2},"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":"2026-05-18T02:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ed0q05Axyvkh02hb+GdR76us03wp4pGePDjmwZJIkZ8niiOuOMkJC0PFoZb2kr8LkGZZp1QWXlRyTOHYu2HzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:05:56.243821Z"},"content_sha256":"85800a07baf2cb7bf4766438c5330c3ea546d01a299f0037068e6b65c11331c9","schema_version":"1.0","event_id":"sha256:85800a07baf2cb7bf4766438c5330c3ea546d01a299f0037068e6b65c11331c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY/bundle.json","state_url":"https://pith.science/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY/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":"2026-05-27T18:05:56Z","links":{"resolver":"https://pith.science/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY","bundle":"https://pith.science/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY/bundle.json","state":"https://pith.science/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UVHSW4C7SUOKQYA3CVZ6Z47IY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6UVHSW4C7SUOKQYA3CVZ6Z47IY","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":"1a6f05b5ce980f87b03ed0ca7aee72f9cf1ae395f5d3616a1a48f9ac8b3dd358","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-22T02:46:46Z","title_canon_sha256":"09a0b96df18a581113333743c15a8a489c230686c7ddde3e8347f93ecfa608da"},"schema_version":"1.0","source":{"id":"1104.4377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4377","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4377v2","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4377","created_at":"2026-05-18T02:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"6UVHSW4C7SUO","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6UVHSW4C7SUOKQYA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6UVHSW4C","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:85800a07baf2cb7bf4766438c5330c3ea546d01a299f0037068e6b65c11331c9","target":"graph","created_at":"2026-05-18T02:52:42Z","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":"This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N = 2, 3). It is rigorously shown that the local (and global) strong solution of the compressible system converges to the local (and global) strong solution of the incompressible system. Furthermore, the convergence rates are also obtained in some sense.","authors_text":"Huanyao Wen, Jinrui Huang, Ruizhao Zi, Shijin Ding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-22T02:46:46Z","title":"Incompressible Limit of the Compressible Nematic Liquid Crystal Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4377","kind":"arxiv","version":2},"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:d39bf581bd2ffd4c62454ba3b4d928e6c2ff52443d43e4bcd7248928fcda5e5c","target":"record","created_at":"2026-05-18T02:52:42Z","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":"1a6f05b5ce980f87b03ed0ca7aee72f9cf1ae395f5d3616a1a48f9ac8b3dd358","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-22T02:46:46Z","title_canon_sha256":"09a0b96df18a581113333743c15a8a489c230686c7ddde3e8347f93ecfa608da"},"schema_version":"1.0","source":{"id":"1104.4377","kind":"arxiv","version":2}},"canonical_sha256":"f52a795b82fca8e54300d8ab9f679f46219664c329bff74a44df29bb3388d2ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f52a795b82fca8e54300d8ab9f679f46219664c329bff74a44df29bb3388d2ba","first_computed_at":"2026-05-18T02:52:42.470268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:42.470268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCrB+g6eW+EPnqrtz5ibgHdtQ9R+BLhbjFt3VuMbF0UTixYEI09ukmMdFZ0+Qi+LycPdNM4uy74eLuvTmOMHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:42.470734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d39bf581bd2ffd4c62454ba3b4d928e6c2ff52443d43e4bcd7248928fcda5e5c","sha256:85800a07baf2cb7bf4766438c5330c3ea546d01a299f0037068e6b65c11331c9"],"state_sha256":"074f1e6f42f5a57a1bcbe8f8972874556e42745711d3396369da8443b77bb9a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/pt8OmBiVfGVhR3cPdUfc/I7irwqxTMFxTj3JqCtGPzsS1vrZqTqf1N5tfAFCA6bGiLGpjkkBtWDhYsXDs6Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:05:56.246245Z","bundle_sha256":"8b356d1cc9337452e2adeaa108a97dfeec9d35e35928213cdd0f0d266b17c1fe"}}