{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JCXKQAY626XYQ4JBFESXTOADYT","short_pith_number":"pith:JCXKQAY6","canonical_record":{"source":{"id":"1010.2960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-14T15:59:14Z","cross_cats_sorted":[],"title_canon_sha256":"4fcfada059919fe11ce740bd97fefc56c1439d94103fa6d434b3bab8ab6ca4c4","abstract_canon_sha256":"498f616b4596fd5754c39a9e58e073f8f85a65a440d50446885b74f9becdb638"},"schema_version":"1.0"},"canonical_sha256":"48aea8031ed7af887121292579b803c4e91a983d7c75831293b70b9466e6e22c","source":{"kind":"arxiv","id":"1010.2960","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2960","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2960v1","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2960","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"JCXKQAY626XY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JCXKQAY626XYQ4JB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JCXKQAY6","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JCXKQAY626XYQ4JBFESXTOADYT","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-14T15:59:14Z","cross_cats_sorted":[],"title_canon_sha256":"4fcfada059919fe11ce740bd97fefc56c1439d94103fa6d434b3bab8ab6ca4c4","abstract_canon_sha256":"498f616b4596fd5754c39a9e58e073f8f85a65a440d50446885b74f9becdb638"},"schema_version":"1.0"},"canonical_sha256":"48aea8031ed7af887121292579b803c4e91a983d7c75831293b70b9466e6e22c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:18.776262Z","signature_b64":"JNFj1Y65/NS+AwQPzfnPoHkVbAJDscFAPNMr+f+2rWPtC12iWTR7ZquwPRgYi+cOUPkl6qjxf9RQGHUmoM8GAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48aea8031ed7af887121292579b803c4e91a983d7c75831293b70b9466e6e22c","last_reissued_at":"2026-05-18T04:39:18.775661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:18.775661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2960","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":"2026-05-18T04:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2CQW1YG0KnQPDKgkUx+NjOyy7CYiHDjRGnk8dzz9ChfLPP2XCz3q2aQ1bbNsG9juz0HaKEVCce1ytpVzLg4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:32:51.531898Z"},"content_sha256":"1f2640305f398cc71b07f659ceaf7f662192211de3198c4d9d56779fbc8845a1","schema_version":"1.0","event_id":"sha256:1f2640305f398cc71b07f659ceaf7f662192211de3198c4d9d56779fbc8845a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JCXKQAY626XYQ4JBFESXTOADYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convexity of the free boundary for an exterior free boundary problem involving the perimeter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hayk Mikayelyan, Henrik Shahgholian","submitted_at":"2010-10-14T15:59:14Z","abstract_excerpt":"We prove that if the given compact set $K$ is convex then a minimizer of the functional $$ I(v)=\\int_{B_R} |\\nabla v|^p dx+\\text{Per}(\\{v>0\\}),\\,1<p<\\infty, $$ over the set $\\{v\\in H^1_0(B_R)|\\,\\, v\\equiv 1\\,\\,\\text{on}\\,\\, K\\subset B_R\\}$ has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2960","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":"2026-05-18T04:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeXKqQPqEuRCdXf0955xymyHQY0Pkv/hS6aQk3nr/Z1W6+QYy3XonYOi6S9vTUG/3ecgnYecxjT0ISpT32b3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:32:51.532219Z"},"content_sha256":"00c94464574a85a752e8776b77e0f61668c1d85e40c0c9ed2408f674d4d68474","schema_version":"1.0","event_id":"sha256:00c94464574a85a752e8776b77e0f61668c1d85e40c0c9ed2408f674d4d68474"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCXKQAY626XYQ4JBFESXTOADYT/bundle.json","state_url":"https://pith.science/pith/JCXKQAY626XYQ4JBFESXTOADYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCXKQAY626XYQ4JBFESXTOADYT/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":"2026-06-20T18:32:51Z","links":{"resolver":"https://pith.science/pith/JCXKQAY626XYQ4JBFESXTOADYT","bundle":"https://pith.science/pith/JCXKQAY626XYQ4JBFESXTOADYT/bundle.json","state":"https://pith.science/pith/JCXKQAY626XYQ4JBFESXTOADYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCXKQAY626XYQ4JBFESXTOADYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JCXKQAY626XYQ4JBFESXTOADYT","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":"498f616b4596fd5754c39a9e58e073f8f85a65a440d50446885b74f9becdb638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-14T15:59:14Z","title_canon_sha256":"4fcfada059919fe11ce740bd97fefc56c1439d94103fa6d434b3bab8ab6ca4c4"},"schema_version":"1.0","source":{"id":"1010.2960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2960","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2960v1","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2960","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"JCXKQAY626XY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JCXKQAY626XYQ4JB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JCXKQAY6","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:00c94464574a85a752e8776b77e0f61668c1d85e40c0c9ed2408f674d4d68474","target":"graph","created_at":"2026-05-18T04:39:18Z","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 prove that if the given compact set $K$ is convex then a minimizer of the functional $$ I(v)=\\int_{B_R} |\\nabla v|^p dx+\\text{Per}(\\{v>0\\}),\\,1<p<\\infty, $$ over the set $\\{v\\in H^1_0(B_R)|\\,\\, v\\equiv 1\\,\\,\\text{on}\\,\\, K\\subset B_R\\}$ has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.","authors_text":"Hayk Mikayelyan, Henrik Shahgholian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-14T15:59:14Z","title":"Convexity of the free boundary for an exterior free boundary problem involving the perimeter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2960","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":"sha256:1f2640305f398cc71b07f659ceaf7f662192211de3198c4d9d56779fbc8845a1","target":"record","created_at":"2026-05-18T04:39:18Z","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":"498f616b4596fd5754c39a9e58e073f8f85a65a440d50446885b74f9becdb638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-14T15:59:14Z","title_canon_sha256":"4fcfada059919fe11ce740bd97fefc56c1439d94103fa6d434b3bab8ab6ca4c4"},"schema_version":"1.0","source":{"id":"1010.2960","kind":"arxiv","version":1}},"canonical_sha256":"48aea8031ed7af887121292579b803c4e91a983d7c75831293b70b9466e6e22c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48aea8031ed7af887121292579b803c4e91a983d7c75831293b70b9466e6e22c","first_computed_at":"2026-05-18T04:39:18.775661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:18.775661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JNFj1Y65/NS+AwQPzfnPoHkVbAJDscFAPNMr+f+2rWPtC12iWTR7ZquwPRgYi+cOUPkl6qjxf9RQGHUmoM8GAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:18.776262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f2640305f398cc71b07f659ceaf7f662192211de3198c4d9d56779fbc8845a1","sha256:00c94464574a85a752e8776b77e0f61668c1d85e40c0c9ed2408f674d4d68474"],"state_sha256":"7adcca7cedfab98abc898c68dffbb26b89d85646822ecca8fb966459ff0f43bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTC/RhNr8nlYSVbVnVpx5ZILtNXTAshnipWlx2uyR2hSvv1RV8TpVVqKSTee0Cq7a0kn/nEWDOsz3BexR3/zBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:32:51.533940Z","bundle_sha256":"a9a5fbf05abee4055f8ddbfeba834c7400576d1542f4a34ab8df4ac85f5503b7"}}