{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OEE7DQYMGTJRGGGAV3KGYVLWDY","short_pith_number":"pith:OEE7DQYM","canonical_record":{"source":{"id":"2109.11339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-23T12:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"544bd0fc411d1171ed9872a96e14e3d696a952d5b7d0122013c8468bfe8441e3","abstract_canon_sha256":"5bcca5a17b0000e4cd4dab988854d963e2b608730a247ac9671ae9a8bba39aeb"},"schema_version":"1.0"},"canonical_sha256":"7109f1c30c34d31318c0aed46c55761e12cfb316c2b07e772562f15e810ce258","source":{"kind":"arxiv","id":"2109.11339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11339","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11339v1","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11339","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"OEE7DQYMGTJR","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"pith_short_16","alias_value":"OEE7DQYMGTJRGGGA","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"pith_short_8","alias_value":"OEE7DQYM","created_at":"2026-07-05T04:09:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OEE7DQYMGTJRGGGAV3KGYVLWDY","target":"record","payload":{"canonical_record":{"source":{"id":"2109.11339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-23T12:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"544bd0fc411d1171ed9872a96e14e3d696a952d5b7d0122013c8468bfe8441e3","abstract_canon_sha256":"5bcca5a17b0000e4cd4dab988854d963e2b608730a247ac9671ae9a8bba39aeb"},"schema_version":"1.0"},"canonical_sha256":"7109f1c30c34d31318c0aed46c55761e12cfb316c2b07e772562f15e810ce258","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:09:37.256211Z","signature_b64":"zT5P42IqRZWGIA2KrJmCYs1NfhZb/CelqidtBG+daE4jwqh5TNOJAmh2jIsSSCgYdhtmnDc9dE0+FHvLguBSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7109f1c30c34d31318c0aed46c55761e12cfb316c2b07e772562f15e810ce258","last_reissued_at":"2026-07-05T04:09:37.255795Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:09:37.255795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.11339","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":"2026-07-05T04:09:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WAW0fa/KAVOZIH2cTYs8WwMxqoFn/K95oc+e30InbVFddAb6T8JdV5NFLOBpQanjTMRf3j3y/uPIx+WfYbLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T17:39:55.644075Z"},"content_sha256":"4a0179ca0aa73ce9325962e87c326d40a2438dd143a8e990d8bf6d04f2866aea","schema_version":"1.0","event_id":"sha256:4a0179ca0aa73ce9325962e87c326d40a2438dd143a8e990d8bf6d04f2866aea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OEE7DQYMGTJRGGGAV3KGYVLWDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well posedness for a Q-tensor model of nematic liquid crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miho Murata, Yoshihiro Shibata","submitted_at":"2021-09-23T12:40:27Z","abstract_excerpt":"In this paper, we prove the global well posedness and the decay estimates for a $\\mathbb Q$-tensor model of nematic liquid crystals in $\\mathbb R^N$, $N \\geq 3$. This system is coupled system by the Navier-Stokes equations with a parabolic-type equation describing the evolution of the director fields $\\mathbb Q$. The proof is based on the maximal $L_p$ -$L_q$ regularity and the $L_p$ -$L_q$ decay estimates to the linearized problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11339","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.11339/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:09:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aac1MlEW1M1Ctyxm21j69Eg5JYuOajbIY2jHMB7OiAi8ejJrLQO3ruQuNqetmaPzVAfcsHZ053bVX/hOuVQmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T17:39:55.644580Z"},"content_sha256":"cc9b6755509c48d9eb07d2efe2649981adee1870c6b2d8d15fd1badfa994ea90","schema_version":"1.0","event_id":"sha256:cc9b6755509c48d9eb07d2efe2649981adee1870c6b2d8d15fd1badfa994ea90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY/bundle.json","state_url":"https://pith.science/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY/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":"2026-08-22T17:39:55Z","links":{"resolver":"https://pith.science/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY","bundle":"https://pith.science/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY/bundle.json","state":"https://pith.science/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OEE7DQYMGTJRGGGAV3KGYVLWDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OEE7DQYMGTJRGGGAV3KGYVLWDY","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":"5bcca5a17b0000e4cd4dab988854d963e2b608730a247ac9671ae9a8bba39aeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-23T12:40:27Z","title_canon_sha256":"544bd0fc411d1171ed9872a96e14e3d696a952d5b7d0122013c8468bfe8441e3"},"schema_version":"1.0","source":{"id":"2109.11339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11339","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11339v1","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11339","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"OEE7DQYMGTJR","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"pith_short_16","alias_value":"OEE7DQYMGTJRGGGA","created_at":"2026-07-05T04:09:37Z"},{"alias_kind":"pith_short_8","alias_value":"OEE7DQYM","created_at":"2026-07-05T04:09:37Z"}],"graph_snapshots":[{"event_id":"sha256:cc9b6755509c48d9eb07d2efe2649981adee1870c6b2d8d15fd1badfa994ea90","target":"graph","created_at":"2026-07-05T04:09:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.11339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove the global well posedness and the decay estimates for a $\\mathbb Q$-tensor model of nematic liquid crystals in $\\mathbb R^N$, $N \\geq 3$. This system is coupled system by the Navier-Stokes equations with a parabolic-type equation describing the evolution of the director fields $\\mathbb Q$. The proof is based on the maximal $L_p$ -$L_q$ regularity and the $L_p$ -$L_q$ decay estimates to the linearized problem.","authors_text":"Miho Murata, Yoshihiro Shibata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-23T12:40:27Z","title":"Global well posedness for a Q-tensor model of nematic liquid crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11339","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":"sha256:4a0179ca0aa73ce9325962e87c326d40a2438dd143a8e990d8bf6d04f2866aea","target":"record","created_at":"2026-07-05T04:09:37Z","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":"5bcca5a17b0000e4cd4dab988854d963e2b608730a247ac9671ae9a8bba39aeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-23T12:40:27Z","title_canon_sha256":"544bd0fc411d1171ed9872a96e14e3d696a952d5b7d0122013c8468bfe8441e3"},"schema_version":"1.0","source":{"id":"2109.11339","kind":"arxiv","version":1}},"canonical_sha256":"7109f1c30c34d31318c0aed46c55761e12cfb316c2b07e772562f15e810ce258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7109f1c30c34d31318c0aed46c55761e12cfb316c2b07e772562f15e810ce258","first_computed_at":"2026-07-05T04:09:37.255795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:09:37.255795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zT5P42IqRZWGIA2KrJmCYs1NfhZb/CelqidtBG+daE4jwqh5TNOJAmh2jIsSSCgYdhtmnDc9dE0+FHvLguBSCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:09:37.256211Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a0179ca0aa73ce9325962e87c326d40a2438dd143a8e990d8bf6d04f2866aea","sha256:cc9b6755509c48d9eb07d2efe2649981adee1870c6b2d8d15fd1badfa994ea90"],"state_sha256":"8f04951653365c03fae81644cc7e34f2b14ff24e185e7f6b30d96ee3397039cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MjAEz37x6Q8A8D+kBVeoQ6h6L+5zulAjN9gWuZMLaloSVbWiakGKf+OVKwVEQ1ylzEt0RK830k5uzeg8ri0CAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T17:39:55.648454Z","bundle_sha256":"75d8c0436877c0449f2caa550dbbf3365df2cc6e386aed46038d805fb8dfde52"}}