{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AILUJX64OPEUE2OW27ETFDOLVT","short_pith_number":"pith:AILUJX64","canonical_record":{"source":{"id":"1012.3212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-15T02:10:32Z","cross_cats_sorted":[],"title_canon_sha256":"e03227948a990e759075f46a042559760264b100673dd70dc54978d28cddb30d","abstract_canon_sha256":"e692b4cd91c7236ead6f7f2eba921c6c2dc34f22f00309b26788f545378bf097"},"schema_version":"1.0"},"canonical_sha256":"021744dfdc73c94269d6d7c9328dcbacc0cddbf41a97f2a5737313a274f3d703","source":{"kind":"arxiv","id":"1012.3212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3212","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3212v1","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3212","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"AILUJX64OPEU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AILUJX64OPEUE2OW","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AILUJX64","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AILUJX64OPEUE2OW27ETFDOLVT","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-15T02:10:32Z","cross_cats_sorted":[],"title_canon_sha256":"e03227948a990e759075f46a042559760264b100673dd70dc54978d28cddb30d","abstract_canon_sha256":"e692b4cd91c7236ead6f7f2eba921c6c2dc34f22f00309b26788f545378bf097"},"schema_version":"1.0"},"canonical_sha256":"021744dfdc73c94269d6d7c9328dcbacc0cddbf41a97f2a5737313a274f3d703","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:29.155280Z","signature_b64":"EG0r540xU098XTF0/craykBmU2MwwEUZYaHqUdmwGilHF4A3WY3OtMguGMx0/R930dNuzY9W5CNf2AtinR9GCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"021744dfdc73c94269d6d7c9328dcbacc0cddbf41a97f2a5737313a274f3d703","last_reissued_at":"2026-05-18T01:22:29.154845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:29.154845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3212","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":"2026-05-18T01:22:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IhipBSbS4o7c57YhUlmtn+xgRoXJ0tPX79k1/9h6hSMz9Eb2hnCoGh4doY4juGx3+PZJNGdPTWpIfJyNKdAqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:36:11.642095Z"},"content_sha256":"2a295b41800340e9aa3c29789bf2ebf3dda6e106f3517eec94063f292ff4f911","schema_version":"1.0","event_id":"sha256:2a295b41800340e9aa3c29789bf2ebf3dda6e106f3517eec94063f292ff4f911"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AILUJX64OPEUE2OW27ETFDOLVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J\\'er\\^ome Le Rousseau, Nicolas Lerner","submitted_at":"2010-12-15T02:10:32Z","abstract_excerpt":"We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are necessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3212","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":"2026-05-18T01:22:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2gU3J3aDUw3PfRA/IN9D/quYwNYZGG7eP695SN3kw/YmQOnxFmtZFqZqP7acgTk0Bcl41L3aHp3+K5ZWjzYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:36:11.642455Z"},"content_sha256":"13728269c8757313c184d63b20ebe8d69e8bc87809190d9601f3efa45cf99e9a","schema_version":"1.0","event_id":"sha256:13728269c8757313c184d63b20ebe8d69e8bc87809190d9601f3efa45cf99e9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AILUJX64OPEUE2OW27ETFDOLVT/bundle.json","state_url":"https://pith.science/pith/AILUJX64OPEUE2OW27ETFDOLVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AILUJX64OPEUE2OW27ETFDOLVT/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":"2026-06-20T04:36:11Z","links":{"resolver":"https://pith.science/pith/AILUJX64OPEUE2OW27ETFDOLVT","bundle":"https://pith.science/pith/AILUJX64OPEUE2OW27ETFDOLVT/bundle.json","state":"https://pith.science/pith/AILUJX64OPEUE2OW27ETFDOLVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AILUJX64OPEUE2OW27ETFDOLVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AILUJX64OPEUE2OW27ETFDOLVT","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":"e692b4cd91c7236ead6f7f2eba921c6c2dc34f22f00309b26788f545378bf097","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-15T02:10:32Z","title_canon_sha256":"e03227948a990e759075f46a042559760264b100673dd70dc54978d28cddb30d"},"schema_version":"1.0","source":{"id":"1012.3212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3212","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3212v1","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3212","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"AILUJX64OPEU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AILUJX64OPEUE2OW","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AILUJX64","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:13728269c8757313c184d63b20ebe8d69e8bc87809190d9601f3efa45cf99e9a","target":"graph","created_at":"2026-05-18T01:22:29Z","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 consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are necessary.","authors_text":"J\\'er\\^ome Le Rousseau, Nicolas Lerner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-15T02:10:32Z","title":"Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3212","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":"sha256:2a295b41800340e9aa3c29789bf2ebf3dda6e106f3517eec94063f292ff4f911","target":"record","created_at":"2026-05-18T01:22:29Z","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":"e692b4cd91c7236ead6f7f2eba921c6c2dc34f22f00309b26788f545378bf097","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-15T02:10:32Z","title_canon_sha256":"e03227948a990e759075f46a042559760264b100673dd70dc54978d28cddb30d"},"schema_version":"1.0","source":{"id":"1012.3212","kind":"arxiv","version":1}},"canonical_sha256":"021744dfdc73c94269d6d7c9328dcbacc0cddbf41a97f2a5737313a274f3d703","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021744dfdc73c94269d6d7c9328dcbacc0cddbf41a97f2a5737313a274f3d703","first_computed_at":"2026-05-18T01:22:29.154845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:29.154845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EG0r540xU098XTF0/craykBmU2MwwEUZYaHqUdmwGilHF4A3WY3OtMguGMx0/R930dNuzY9W5CNf2AtinR9GCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:29.155280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a295b41800340e9aa3c29789bf2ebf3dda6e106f3517eec94063f292ff4f911","sha256:13728269c8757313c184d63b20ebe8d69e8bc87809190d9601f3efa45cf99e9a"],"state_sha256":"e06a7c9ca600621b2d98f793f2f4e76c2423a509b4d476541af93bebfe53b238"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ti5H5hDQAU4PAadcRX8LOhaAg8HTZgP3Sm3389iTBp1ELuI9iaBTFZGTkVjypD2Dkn9Eh2GX542F970HD7TpAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:36:11.644346Z","bundle_sha256":"b771eca40c2d1391549614db3a16f2eace19cdf48bd51b7b7f1b53189528d4f2"}}