{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6DJNRTC7LU3SVW5V2XV7YKZNX4","short_pith_number":"pith:6DJNRTC7","canonical_record":{"source":{"id":"1301.4420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T16:20:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4fe738bb9d9cd54b583ebb4f1b69a8ff233f115d424723369a4eb5ddc6319de8","abstract_canon_sha256":"933efbccf8523a5a0a23ba0763c42b61e42aa804fcb2698472d1476fd93d25b6"},"schema_version":"1.0"},"canonical_sha256":"f0d2d8cc5f5d372adbb5d5ebfc2b2dbf19490c3533ab94242a38365f2d33f992","source":{"kind":"arxiv","id":"1301.4420","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4420","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4420v1","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4420","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"6DJNRTC7LU3S","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6DJNRTC7LU3SVW5V","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6DJNRTC7","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6DJNRTC7LU3SVW5V2XV7YKZNX4","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T16:20:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4fe738bb9d9cd54b583ebb4f1b69a8ff233f115d424723369a4eb5ddc6319de8","abstract_canon_sha256":"933efbccf8523a5a0a23ba0763c42b61e42aa804fcb2698472d1476fd93d25b6"},"schema_version":"1.0"},"canonical_sha256":"f0d2d8cc5f5d372adbb5d5ebfc2b2dbf19490c3533ab94242a38365f2d33f992","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:05.799282Z","signature_b64":"FJLS2QA0P4ee+1T2TmOnzv2BS4iBlQ5vvjStxD18dmQlFyezmEqde5b2SsX0QiFwfz3f1GWpfBzgkaWr3o98DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0d2d8cc5f5d372adbb5d5ebfc2b2dbf19490c3533ab94242a38365f2d33f992","last_reissued_at":"2026-05-18T01:52:05.798839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:05.798839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4420","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":"2026-05-18T01:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QaGVRtZoJYY6//KimZPWZ5CV52bBT5CBVSytpy0nGyNhzJu8YAJ4aYuCW1zbo24qrieJlO8f7C5MYgYELnGACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:51:23.853674Z"},"content_sha256":"529ffc90c454427218a9e93abb098bc2fadc008a74a6a52cf749d8532e24987a","schema_version":"1.0","event_id":"sha256:529ffc90c454427218a9e93abb098bc2fadc008a74a6a52cf749d8532e24987a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6DJNRTC7LU3SVW5V2XV7YKZNX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-time behavior for the two-dimensional motion of a disk in a viscous fluid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Christophe Lacave (IMJ-PRG), Matthieu Hillairet (CEREMADE), Sylvain Ervedoza (IMT)","submitted_at":"2013-01-18T16:20:07Z","abstract_excerpt":"In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive $L^p$-$L^q$ decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier-Stokes fluid-rigid disk system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4420","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":"2026-05-18T01:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LdwMPsVQpXHs4GH6zBBSuVz6LHffMjCxPuHvLBuxzcVy2kC51HxO+qwzhnjV87qkKuJC9bg/o76vioW1DQkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:51:23.854488Z"},"content_sha256":"2fcb831dcb22d6bc9f1a49a34af00db893c35b7170362fbd6a86a21246e1a06f","schema_version":"1.0","event_id":"sha256:2fcb831dcb22d6bc9f1a49a34af00db893c35b7170362fbd6a86a21246e1a06f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4/bundle.json","state_url":"https://pith.science/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4/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":"2026-06-09T07:51:23Z","links":{"resolver":"https://pith.science/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4","bundle":"https://pith.science/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4/bundle.json","state":"https://pith.science/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DJNRTC7LU3SVW5V2XV7YKZNX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6DJNRTC7LU3SVW5V2XV7YKZNX4","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":"933efbccf8523a5a0a23ba0763c42b61e42aa804fcb2698472d1476fd93d25b6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T16:20:07Z","title_canon_sha256":"4fe738bb9d9cd54b583ebb4f1b69a8ff233f115d424723369a4eb5ddc6319de8"},"schema_version":"1.0","source":{"id":"1301.4420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4420","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4420v1","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4420","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"6DJNRTC7LU3S","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6DJNRTC7LU3SVW5V","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6DJNRTC7","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:2fcb831dcb22d6bc9f1a49a34af00db893c35b7170362fbd6a86a21246e1a06f","target":"graph","created_at":"2026-05-18T01:52:05Z","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":"In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive $L^p$-$L^q$ decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier-Stokes fluid-rigid disk system.","authors_text":"Christophe Lacave (IMJ-PRG), Matthieu Hillairet (CEREMADE), Sylvain Ervedoza (IMT)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T16:20:07Z","title":"Long-time behavior for the two-dimensional motion of a disk in a viscous fluid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4420","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":"sha256:529ffc90c454427218a9e93abb098bc2fadc008a74a6a52cf749d8532e24987a","target":"record","created_at":"2026-05-18T01:52:05Z","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":"933efbccf8523a5a0a23ba0763c42b61e42aa804fcb2698472d1476fd93d25b6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-18T16:20:07Z","title_canon_sha256":"4fe738bb9d9cd54b583ebb4f1b69a8ff233f115d424723369a4eb5ddc6319de8"},"schema_version":"1.0","source":{"id":"1301.4420","kind":"arxiv","version":1}},"canonical_sha256":"f0d2d8cc5f5d372adbb5d5ebfc2b2dbf19490c3533ab94242a38365f2d33f992","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0d2d8cc5f5d372adbb5d5ebfc2b2dbf19490c3533ab94242a38365f2d33f992","first_computed_at":"2026-05-18T01:52:05.798839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:05.798839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJLS2QA0P4ee+1T2TmOnzv2BS4iBlQ5vvjStxD18dmQlFyezmEqde5b2SsX0QiFwfz3f1GWpfBzgkaWr3o98DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:05.799282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:529ffc90c454427218a9e93abb098bc2fadc008a74a6a52cf749d8532e24987a","sha256:2fcb831dcb22d6bc9f1a49a34af00db893c35b7170362fbd6a86a21246e1a06f"],"state_sha256":"22a32400100165d7e9545c309ebb0b62bb8b5918b4cc81436a06fcd1b5177507"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVlCo/GJ/y2Bm1Rf2NjMGPAWRQUCyvs4/ltZAUA3qTg3GcYJLEMll3yefhfeEwVX8Tm1H+2v7UqjUjgelBOQDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:51:23.858996Z","bundle_sha256":"18aa180d21c3954acbc0c093eea8702842dee02236e83b30fe7f066c1d48f032"}}