{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CPDBFTMJ75JADPBAUNGXRDW3AD","short_pith_number":"pith:CPDBFTMJ","canonical_record":{"source":{"id":"1808.00611","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T00:36:14Z","cross_cats_sorted":[],"title_canon_sha256":"141f9626ded0290e0fa8ed74782f08b855a0c4697ca4f37f59a7148dfa4e4a46","abstract_canon_sha256":"464b42159622afa484220ec13b062f7740c8bbd64ccc49e2161e0117fc0a2a62"},"schema_version":"1.0"},"canonical_sha256":"13c612cd89ff5201bc20a34d788edb00c17697ebbdbe6977e29f497033e38c7f","source":{"kind":"arxiv","id":"1808.00611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00611","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00611v1","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00611","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"CPDBFTMJ75JA","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CPDBFTMJ75JADPBA","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CPDBFTMJ","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CPDBFTMJ75JADPBAUNGXRDW3AD","target":"record","payload":{"canonical_record":{"source":{"id":"1808.00611","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T00:36:14Z","cross_cats_sorted":[],"title_canon_sha256":"141f9626ded0290e0fa8ed74782f08b855a0c4697ca4f37f59a7148dfa4e4a46","abstract_canon_sha256":"464b42159622afa484220ec13b062f7740c8bbd64ccc49e2161e0117fc0a2a62"},"schema_version":"1.0"},"canonical_sha256":"13c612cd89ff5201bc20a34d788edb00c17697ebbdbe6977e29f497033e38c7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:04.751881Z","signature_b64":"rGs2tdUL/Gkdwk9HB/T8gLD77HYdssi9JUsNulvEmGxSu5p8y3ta+EmBK850+AQxpIczYUQe27eRyxJ1QEGUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13c612cd89ff5201bc20a34d788edb00c17697ebbdbe6977e29f497033e38c7f","last_reissued_at":"2026-05-18T00:09:04.751353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:04.751353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.00611","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":"2026-05-18T00:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/2s4j4gho/2OOGwLTV9ja5TaLPgfUxdrKkfDA6w9mLjVMjw+IgnsYWGOZy+IVL3OyPqz1wynuD6Q+M8UUHg+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:18:05.906703Z"},"content_sha256":"e714a697e0167a83caff9a3603c3379b2f2c4afffc72279b8ac1a034ba1f5536","schema_version":"1.0","event_id":"sha256:e714a697e0167a83caff9a3603c3379b2f2c4afffc72279b8ac1a034ba1f5536"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CPDBFTMJ75JADPBAUNGXRDW3AD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embeddings for the space $LD_\\gamma^{p}$ on sets of finite perimeter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna L. Mazzucato, Nikolai V. Chemetov","submitted_at":"2018-08-02T00:36:14Z","abstract_excerpt":"Given an open set with finite perimeter $\\Omega\\subset \\mathbb{R}^n$, we consider the space $LD_\\gamma^{p}(\\Omega)$, $1\\leq p<\\infty$, of functions with $p$th-integrable deformation tensor on $\\Omega$ and with $p$ th-integrable trace value on the essential boundary of $\\Omega$. We establish the continuous embedding $LD_\\gamma^{p}(\\Omega)\\subset L^{pN/(N-1)}(\\Omega)$. The space $LD_\\gamma^{p}(\\Omega)$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00611","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":"2026-05-18T00:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"useR5t1HDx3k64BSDTTZ8V2vibgeNHr6UDIudDchWAUuTjzOfSK61urLQgdBTIM8NOSkHdISZ4jtuwSiDS0iAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:18:05.907278Z"},"content_sha256":"939ea7abe1a7d348589ac772ae21d7f8913d40dd614ff62bd6ca8f590962b08e","schema_version":"1.0","event_id":"sha256:939ea7abe1a7d348589ac772ae21d7f8913d40dd614ff62bd6ca8f590962b08e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPDBFTMJ75JADPBAUNGXRDW3AD/bundle.json","state_url":"https://pith.science/pith/CPDBFTMJ75JADPBAUNGXRDW3AD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPDBFTMJ75JADPBAUNGXRDW3AD/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":"2026-05-28T06:18:05Z","links":{"resolver":"https://pith.science/pith/CPDBFTMJ75JADPBAUNGXRDW3AD","bundle":"https://pith.science/pith/CPDBFTMJ75JADPBAUNGXRDW3AD/bundle.json","state":"https://pith.science/pith/CPDBFTMJ75JADPBAUNGXRDW3AD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPDBFTMJ75JADPBAUNGXRDW3AD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CPDBFTMJ75JADPBAUNGXRDW3AD","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":"464b42159622afa484220ec13b062f7740c8bbd64ccc49e2161e0117fc0a2a62","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T00:36:14Z","title_canon_sha256":"141f9626ded0290e0fa8ed74782f08b855a0c4697ca4f37f59a7148dfa4e4a46"},"schema_version":"1.0","source":{"id":"1808.00611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00611","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00611v1","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00611","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"CPDBFTMJ75JA","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CPDBFTMJ75JADPBA","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CPDBFTMJ","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:939ea7abe1a7d348589ac772ae21d7f8913d40dd614ff62bd6ca8f590962b08e","target":"graph","created_at":"2026-05-18T00:09:04Z","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":"Given an open set with finite perimeter $\\Omega\\subset \\mathbb{R}^n$, we consider the space $LD_\\gamma^{p}(\\Omega)$, $1\\leq p<\\infty$, of functions with $p$th-integrable deformation tensor on $\\Omega$ and with $p$ th-integrable trace value on the essential boundary of $\\Omega$. We establish the continuous embedding $LD_\\gamma^{p}(\\Omega)\\subset L^{pN/(N-1)}(\\Omega)$. The space $LD_\\gamma^{p}(\\Omega)$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.","authors_text":"Anna L. Mazzucato, Nikolai V. Chemetov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T00:36:14Z","title":"Embeddings for the space $LD_\\gamma^{p}$ on sets of finite perimeter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00611","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:e714a697e0167a83caff9a3603c3379b2f2c4afffc72279b8ac1a034ba1f5536","target":"record","created_at":"2026-05-18T00:09:04Z","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":"464b42159622afa484220ec13b062f7740c8bbd64ccc49e2161e0117fc0a2a62","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T00:36:14Z","title_canon_sha256":"141f9626ded0290e0fa8ed74782f08b855a0c4697ca4f37f59a7148dfa4e4a46"},"schema_version":"1.0","source":{"id":"1808.00611","kind":"arxiv","version":1}},"canonical_sha256":"13c612cd89ff5201bc20a34d788edb00c17697ebbdbe6977e29f497033e38c7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13c612cd89ff5201bc20a34d788edb00c17697ebbdbe6977e29f497033e38c7f","first_computed_at":"2026-05-18T00:09:04.751353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:04.751353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGs2tdUL/Gkdwk9HB/T8gLD77HYdssi9JUsNulvEmGxSu5p8y3ta+EmBK850+AQxpIczYUQe27eRyxJ1QEGUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:04.751881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e714a697e0167a83caff9a3603c3379b2f2c4afffc72279b8ac1a034ba1f5536","sha256:939ea7abe1a7d348589ac772ae21d7f8913d40dd614ff62bd6ca8f590962b08e"],"state_sha256":"ea4097164728399de92955756e2e1a79e12cb4812910d04bd2b1101cb54b5a2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iugZoQgYo8K1dl4E7x5ye5y1YZ1TBPo/lI/GwVnIqgTlP3hFj3BQ2hXWfzsQvoFE6i8716842TRyLxT+5f6vAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:18:05.910028Z","bundle_sha256":"a0bc6956d84fa4a4cce02d4971f097e45f29dfb0d48be26ff0bbe15259c4df0a"}}