{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NYPOGLOZ3D6UXOVXJ73FKU3SEA","short_pith_number":"pith:NYPOGLOZ","canonical_record":{"source":{"id":"1712.00223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-01T08:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"3ccc9636ad1e3f4cd9c30464cd4879dd37a8a1ec43ad64a35779fe7d259b5362","abstract_canon_sha256":"fc86599b0fa0ac4bb1783cc7ebc5c717dba60a7d4064710bf4fca7cae75659ca"},"schema_version":"1.0"},"canonical_sha256":"6e1ee32dd9d8fd4bbab74ff65553722024dbe202ce35c6fbe6bd002a439f83e2","source":{"kind":"arxiv","id":"1712.00223","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00223","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00223v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00223","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"NYPOGLOZ3D6U","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NYPOGLOZ3D6UXOVX","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NYPOGLOZ","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NYPOGLOZ3D6UXOVXJ73FKU3SEA","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-01T08:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"3ccc9636ad1e3f4cd9c30464cd4879dd37a8a1ec43ad64a35779fe7d259b5362","abstract_canon_sha256":"fc86599b0fa0ac4bb1783cc7ebc5c717dba60a7d4064710bf4fca7cae75659ca"},"schema_version":"1.0"},"canonical_sha256":"6e1ee32dd9d8fd4bbab74ff65553722024dbe202ce35c6fbe6bd002a439f83e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:06.901266Z","signature_b64":"wr7YotqPERnVV0Rvib0WtVuCUUQ7I4YCJs4qv4awEyuGgifYXWwx1+ma0TDKrd6AZDRrIyybqVR7f0zTi448CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e1ee32dd9d8fd4bbab74ff65553722024dbe202ce35c6fbe6bd002a439f83e2","last_reissued_at":"2026-05-18T00:29:06.900128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:06.900128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00223","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":"2026-05-18T00:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLPGTF443TrvW7Z+aHVn4CUZUDSOlRSsLwp8jN+QFDO2CsSfaEU/ZWNoj1PXRU9QVPJpoQ2z7OgQ/QKKwKYvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:55:16.637233Z"},"content_sha256":"bd4cd0617cef3d90e48662266c274a8d62a73c02aec0231aef9899313c692007","schema_version":"1.0","event_id":"sha256:bd4cd0617cef3d90e48662266c274a8d62a73c02aec0231aef9899313c692007"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NYPOGLOZ3D6UXOVXJ73FKU3SEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^p$-$L^q$ Maximal Regularity for some Operators Associated with Linearized Incompressible Fluid-Rigid Body Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debayan Maity, Marius Tucsnak","submitted_at":"2017-12-01T08:08:20Z","abstract_excerpt":"We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\\mathcal{R}$ sectorial in $L^q$ for every $q\\in (1,\\infty)$, thus it has the maximal $L^p$-$L^q$ regularity property. Moreover, we show that the generated semigroup is exponentially stable with respect to the $L^q$ norm. Finally, we use the results to prove the global existence for small initial data, in an $L^p$-$L^q$ setting, for the original nonlinear problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00223","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":"2026-05-18T00:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBrlvvADmRNsAIzEJh04I3obG3TFBP2ktKh52sDnv3EtZ/Wq/y6XwweIydp7/lYEIMj4Pe0pB7LkLajyGGo8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:55:16.637789Z"},"content_sha256":"f0a657e7eab2301bc4dfe26d69ab2707902a7c3f236026def37602df696fc99f","schema_version":"1.0","event_id":"sha256:f0a657e7eab2301bc4dfe26d69ab2707902a7c3f236026def37602df696fc99f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA/bundle.json","state_url":"https://pith.science/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA/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":"2026-06-02T10:55:16Z","links":{"resolver":"https://pith.science/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA","bundle":"https://pith.science/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA/bundle.json","state":"https://pith.science/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYPOGLOZ3D6UXOVXJ73FKU3SEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NYPOGLOZ3D6UXOVXJ73FKU3SEA","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":"fc86599b0fa0ac4bb1783cc7ebc5c717dba60a7d4064710bf4fca7cae75659ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-01T08:08:20Z","title_canon_sha256":"3ccc9636ad1e3f4cd9c30464cd4879dd37a8a1ec43ad64a35779fe7d259b5362"},"schema_version":"1.0","source":{"id":"1712.00223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00223","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00223v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00223","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"NYPOGLOZ3D6U","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NYPOGLOZ3D6UXOVX","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NYPOGLOZ","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:f0a657e7eab2301bc4dfe26d69ab2707902a7c3f236026def37602df696fc99f","target":"graph","created_at":"2026-05-18T00:29:06Z","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":"We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\\mathcal{R}$ sectorial in $L^q$ for every $q\\in (1,\\infty)$, thus it has the maximal $L^p$-$L^q$ regularity property. Moreover, we show that the generated semigroup is exponentially stable with respect to the $L^q$ norm. Finally, we use the results to prove the global existence for small initial data, in an $L^p$-$L^q$ setting, for the original nonlinear problem.","authors_text":"Debayan Maity, Marius Tucsnak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-01T08:08:20Z","title":"$L^p$-$L^q$ Maximal Regularity for some Operators Associated with Linearized Incompressible Fluid-Rigid Body Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00223","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:bd4cd0617cef3d90e48662266c274a8d62a73c02aec0231aef9899313c692007","target":"record","created_at":"2026-05-18T00:29:06Z","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":"fc86599b0fa0ac4bb1783cc7ebc5c717dba60a7d4064710bf4fca7cae75659ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-01T08:08:20Z","title_canon_sha256":"3ccc9636ad1e3f4cd9c30464cd4879dd37a8a1ec43ad64a35779fe7d259b5362"},"schema_version":"1.0","source":{"id":"1712.00223","kind":"arxiv","version":1}},"canonical_sha256":"6e1ee32dd9d8fd4bbab74ff65553722024dbe202ce35c6fbe6bd002a439f83e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e1ee32dd9d8fd4bbab74ff65553722024dbe202ce35c6fbe6bd002a439f83e2","first_computed_at":"2026-05-18T00:29:06.900128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:06.900128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wr7YotqPERnVV0Rvib0WtVuCUUQ7I4YCJs4qv4awEyuGgifYXWwx1+ma0TDKrd6AZDRrIyybqVR7f0zTi448CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:06.901266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd4cd0617cef3d90e48662266c274a8d62a73c02aec0231aef9899313c692007","sha256:f0a657e7eab2301bc4dfe26d69ab2707902a7c3f236026def37602df696fc99f"],"state_sha256":"b7775c7404246f3c1180d052eeb747702ddf59d8febf90b46cbd87fb1f0b7fcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eVCegQpH7MmEXwmlvjr1McV3Nj7bdZTHRPwOBZ/mAUlrAai44bx70kow7WL4Uq4TqmNZI3wLQZ3Z4U1nB6GSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:55:16.640422Z","bundle_sha256":"17a5e637812b552cfe4210af9157f298c1cdacdbf943b3a9f85c8dfa2b11a4cd"}}