{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BE3XOQDOHBQEKWOXHDIMTLZII5","short_pith_number":"pith:BE3XOQDO","canonical_record":{"source":{"id":"1207.0469","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-02T18:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"5c6fa4735dc9d2b5a7a658f05d6ba33dc07741dbd897c97b74b6123baef5ff07","abstract_canon_sha256":"f85551366a0f236bcbcb8a45a23cb90151d16fb7317a8d6c9ceacd840a96deb9"},"schema_version":"1.0"},"canonical_sha256":"093777406e38604559d738d0c9af28477949a5ebfc3a48ba68570d19bcacca37","source":{"kind":"arxiv","id":"1207.0469","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0469","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0469v2","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0469","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"BE3XOQDOHBQE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BE3XOQDOHBQEKWOX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BE3XOQDO","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BE3XOQDOHBQEKWOXHDIMTLZII5","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0469","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-02T18:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"5c6fa4735dc9d2b5a7a658f05d6ba33dc07741dbd897c97b74b6123baef5ff07","abstract_canon_sha256":"f85551366a0f236bcbcb8a45a23cb90151d16fb7317a8d6c9ceacd840a96deb9"},"schema_version":"1.0"},"canonical_sha256":"093777406e38604559d738d0c9af28477949a5ebfc3a48ba68570d19bcacca37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:06.943400Z","signature_b64":"ylmsvZ4vohtRXC0gujWtVaviol5Lhdad3PBTQS6WRk3E9QJysxdwrwP0B5+1Fv8FLUqIUZBx+lQ6Jo3OVmvcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"093777406e38604559d738d0c9af28477949a5ebfc3a48ba68570d19bcacca37","last_reissued_at":"2026-05-18T02:57:06.942981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:06.942981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0469","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":"2026-05-18T02:57:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RspfE027tfN0IcIAHqBnbgQX1vHrpVrajhVk8pDKrTIE1SsB/sDXGo046lCZQRuZWQzj+kdaD98sgIvhH/ZADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:15:35.256266Z"},"content_sha256":"c07a915fe31c2b2dd3e8d34ab6edf8045e729e8a85f397ef37ecb7f1126b6d1d","schema_version":"1.0","event_id":"sha256:c07a915fe31c2b2dd3e8d34ab6edf8045e729e8a85f397ef37ecb7f1126b6d1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BE3XOQDOHBQEKWOXHDIMTLZII5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of weak solutions up to collision for viscous fluid-solid systems with slip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David G\\'erard-Varet (IMJ), Matthieu Hillairet (CEREMADE)","submitted_at":"2012-07-02T18:52:58Z","abstract_excerpt":"We study in this paper the movement of a rigid solid inside an incompressible Navier-Stokes flow, within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface, through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no-slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0469","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":"2026-05-18T02:57:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BtDgVab6kCHc9o+rImEH7m8SVzKfpqzKMSnQpZe4TrIsqDloH6rd6i4/dzBmKYjnSJL5DMlHGQpgQXCE0c8XBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:15:35.256968Z"},"content_sha256":"1971d9f83d6ce6ce16b1661e576878eaa5779b2f9d1e80fbe28346a41b416c75","schema_version":"1.0","event_id":"sha256:1971d9f83d6ce6ce16b1661e576878eaa5779b2f9d1e80fbe28346a41b416c75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BE3XOQDOHBQEKWOXHDIMTLZII5/bundle.json","state_url":"https://pith.science/pith/BE3XOQDOHBQEKWOXHDIMTLZII5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BE3XOQDOHBQEKWOXHDIMTLZII5/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":"2026-05-26T11:15:35Z","links":{"resolver":"https://pith.science/pith/BE3XOQDOHBQEKWOXHDIMTLZII5","bundle":"https://pith.science/pith/BE3XOQDOHBQEKWOXHDIMTLZII5/bundle.json","state":"https://pith.science/pith/BE3XOQDOHBQEKWOXHDIMTLZII5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BE3XOQDOHBQEKWOXHDIMTLZII5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BE3XOQDOHBQEKWOXHDIMTLZII5","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":"f85551366a0f236bcbcb8a45a23cb90151d16fb7317a8d6c9ceacd840a96deb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-02T18:52:58Z","title_canon_sha256":"5c6fa4735dc9d2b5a7a658f05d6ba33dc07741dbd897c97b74b6123baef5ff07"},"schema_version":"1.0","source":{"id":"1207.0469","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0469","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0469v2","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0469","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"BE3XOQDOHBQE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BE3XOQDOHBQEKWOX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BE3XOQDO","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:1971d9f83d6ce6ce16b1661e576878eaa5779b2f9d1e80fbe28346a41b416c75","target":"graph","created_at":"2026-05-18T02:57:06Z","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 in this paper the movement of a rigid solid inside an incompressible Navier-Stokes flow, within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface, through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no-slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discon","authors_text":"David G\\'erard-Varet (IMJ), Matthieu Hillairet (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-02T18:52:58Z","title":"Existence of weak solutions up to collision for viscous fluid-solid systems with slip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0469","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:c07a915fe31c2b2dd3e8d34ab6edf8045e729e8a85f397ef37ecb7f1126b6d1d","target":"record","created_at":"2026-05-18T02:57:06Z","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":"f85551366a0f236bcbcb8a45a23cb90151d16fb7317a8d6c9ceacd840a96deb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-02T18:52:58Z","title_canon_sha256":"5c6fa4735dc9d2b5a7a658f05d6ba33dc07741dbd897c97b74b6123baef5ff07"},"schema_version":"1.0","source":{"id":"1207.0469","kind":"arxiv","version":2}},"canonical_sha256":"093777406e38604559d738d0c9af28477949a5ebfc3a48ba68570d19bcacca37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"093777406e38604559d738d0c9af28477949a5ebfc3a48ba68570d19bcacca37","first_computed_at":"2026-05-18T02:57:06.942981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:06.942981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ylmsvZ4vohtRXC0gujWtVaviol5Lhdad3PBTQS6WRk3E9QJysxdwrwP0B5+1Fv8FLUqIUZBx+lQ6Jo3OVmvcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:06.943400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0469","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c07a915fe31c2b2dd3e8d34ab6edf8045e729e8a85f397ef37ecb7f1126b6d1d","sha256:1971d9f83d6ce6ce16b1661e576878eaa5779b2f9d1e80fbe28346a41b416c75"],"state_sha256":"313d752f66f8b6dc047273ccbe89dbea8fde6bf21676f8c368714c262ab00444"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T4Q866iqR06U8wgyOz7EEGppegOGwIoc+PX2cInVb+18L3q1/QbP2WC1DM11cYwvN7SY43sT4OqlfyGlVJzgDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:15:35.260375Z","bundle_sha256":"d9f748499ea1a9e2664c4c9bae8c10b46d65b13008c73d3b61859884b8f59ed3"}}