{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WNFM2H7O3Z7NZY2L6FVSA3FQB7","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":"26d5a6efa5148c875bf43c0db1663a1f076734ec3c70f54af24cadae53a8e43f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-15T12:40:08Z","title_canon_sha256":"a7956a432e1ce8ef9b9e2a84a839082a4acc31b7a15b443af0c295c3427916b3"},"schema_version":"1.0","source":{"id":"1010.3144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3144","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3144v1","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3144","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"pith_short_12","alias_value":"WNFM2H7O3Z7N","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WNFM2H7O3Z7NZY2L","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WNFM2H7O","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:16c87e343eb5fe1066453827df1ab39a0ea02200ac0ebc09f5844323184ca93a","target":"graph","created_at":"2026-05-18T04:33:28Z","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":"A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\\Om$ is constrained to lie in the half space determined by $x_1\\geq 0$ and its boundary to contain a segment of the hyperplane $\\{x_1=0\\}$ where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic propertie","authors_text":"Antoine Laurain, Yannick Privat (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-15T12:40:08Z","title":"On a Bernoulli problem with geometric constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3144","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":"sha256:9f7001410cbc8d277e743601a30125ab752be64b744c548c4a2f81f20cea4edf","target":"record","created_at":"2026-05-18T04:33:28Z","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":"26d5a6efa5148c875bf43c0db1663a1f076734ec3c70f54af24cadae53a8e43f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-15T12:40:08Z","title_canon_sha256":"a7956a432e1ce8ef9b9e2a84a839082a4acc31b7a15b443af0c295c3427916b3"},"schema_version":"1.0","source":{"id":"1010.3144","kind":"arxiv","version":1}},"canonical_sha256":"b34acd1feede7edce34bf16b206cb00fd29e76573cd26ca97d5076302b83be78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b34acd1feede7edce34bf16b206cb00fd29e76573cd26ca97d5076302b83be78","first_computed_at":"2026-05-18T04:33:28.897636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:28.897636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fKUrjHiRsmGkVezhvBdaD0KmMbomgVtg/F4thZu2QclP+ytt1+kgKJ1vzVLybNbdsIVg7A3vhGybHAZkPpAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:28.898094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f7001410cbc8d277e743601a30125ab752be64b744c548c4a2f81f20cea4edf","sha256:16c87e343eb5fe1066453827df1ab39a0ea02200ac0ebc09f5844323184ca93a"],"state_sha256":"a837d292f8591bb6d6a5ed44a09be120c083cc628f4d5a585b22b447e238d34e"}