{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2UJ67ZHXU2YWCKPIOU2JHCFNO7","short_pith_number":"pith:2UJ67ZHX","canonical_record":{"source":{"id":"1411.7971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T18:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"6681346828a595b9b5e711f4fe8ae0a8bf259422cdfccbe4da0eab6856ad4333","abstract_canon_sha256":"3f477f789cf592a51f00eb94be9e92ff58ab834caddf2f1dacd141a19421dca4"},"schema_version":"1.0"},"canonical_sha256":"d513efe4f7a6b16129e875349388ad77fa1e11bfd17ef98bd123fa03a44f4b7d","source":{"kind":"arxiv","id":"1411.7971","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7971","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7971v2","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7971","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"2UJ67ZHXU2YW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2UJ67ZHXU2YWCKPI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2UJ67ZHX","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2UJ67ZHXU2YWCKPIOU2JHCFNO7","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T18:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"6681346828a595b9b5e711f4fe8ae0a8bf259422cdfccbe4da0eab6856ad4333","abstract_canon_sha256":"3f477f789cf592a51f00eb94be9e92ff58ab834caddf2f1dacd141a19421dca4"},"schema_version":"1.0"},"canonical_sha256":"d513efe4f7a6b16129e875349388ad77fa1e11bfd17ef98bd123fa03a44f4b7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:19.869832Z","signature_b64":"w04iUt/+JdHZ3iB7n/CxFJaAzVV+xgXKrVLw/xpwj2C0eXlgsdRrCMFNhn3iA+mZp0mNcTztgEO3Ej78CuT3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d513efe4f7a6b16129e875349388ad77fa1e11bfd17ef98bd123fa03a44f4b7d","last_reissued_at":"2026-05-18T01:31:19.869211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:19.869211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7971","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":"2026-05-18T01:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9w52QYXYmhvAufSFhVadz6RRfZ4w8w+CrGEwCnZB2e2tdZIKdqKpZrIRcq82FAcIRB1m+rglJh55el1Vvz6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:24:49.528487Z"},"content_sha256":"0c9287bb551c7f2abd863afb6aa8afb71c294d8f2299db1fc08e552b5dd7fcd0","schema_version":"1.0","event_id":"sha256:0c9287bb551c7f2abd863afb6aa8afb71c294d8f2299db1fc08e552b5dd7fcd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2UJ67ZHXU2YWCKPIOU2JHCFNO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A nonlocal free boundary problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Ovidiu Savin, Serena Dipierro","submitted_at":"2014-11-28T18:42:30Z","abstract_excerpt":"Given~$s,\\sigma\\in(0,1)$ and a bounded domain~$\\Omega\\subset\\R^n$, we consider the following minimization problem of $s$-Dirichlet plus $\\sigma$-perimeter type $$ [u]_{ H^s(\\R^{2n}\\setminus(\\Omega^c)^2) }\n  + \\Per_\\sigma\\left(\\{u>0\\},\\Omega\\right), $$ where~$[ \\cdot]_{H^s}$ is the fractional Gagliardo seminorm and $\\Per_\\sigma$ is the fractional perimeter.\n  Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case.\n  Several classic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7971","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":"2026-05-18T01:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ECfgAmIjxDtnwZpk0czUEtEBqIVF1CmpWjWqSC8jAel+gwRk3Y8TyM7DUSiThJ0ffoZBtTILD79ZkACXj0MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:24:49.529190Z"},"content_sha256":"c9af6712aa7b482b3846bc7cad93d448f36b4d426a82069d362b225cadbfe3c1","schema_version":"1.0","event_id":"sha256:c9af6712aa7b482b3846bc7cad93d448f36b4d426a82069d362b225cadbfe3c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7/bundle.json","state_url":"https://pith.science/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7/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":"2026-06-06T05:24:49Z","links":{"resolver":"https://pith.science/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7","bundle":"https://pith.science/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7/bundle.json","state":"https://pith.science/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UJ67ZHXU2YWCKPIOU2JHCFNO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2UJ67ZHXU2YWCKPIOU2JHCFNO7","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":"3f477f789cf592a51f00eb94be9e92ff58ab834caddf2f1dacd141a19421dca4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T18:42:30Z","title_canon_sha256":"6681346828a595b9b5e711f4fe8ae0a8bf259422cdfccbe4da0eab6856ad4333"},"schema_version":"1.0","source":{"id":"1411.7971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7971","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7971v2","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7971","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"2UJ67ZHXU2YW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2UJ67ZHXU2YWCKPI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2UJ67ZHX","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:c9af6712aa7b482b3846bc7cad93d448f36b4d426a82069d362b225cadbfe3c1","target":"graph","created_at":"2026-05-18T01:31:19Z","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~$s,\\sigma\\in(0,1)$ and a bounded domain~$\\Omega\\subset\\R^n$, we consider the following minimization problem of $s$-Dirichlet plus $\\sigma$-perimeter type $$ [u]_{ H^s(\\R^{2n}\\setminus(\\Omega^c)^2) }\n  + \\Per_\\sigma\\left(\\{u>0\\},\\Omega\\right), $$ where~$[ \\cdot]_{H^s}$ is the fractional Gagliardo seminorm and $\\Per_\\sigma$ is the fractional perimeter.\n  Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case.\n  Several classic","authors_text":"Enrico Valdinoci, Ovidiu Savin, Serena Dipierro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T18:42:30Z","title":"A nonlocal free boundary problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7971","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":"sha256:0c9287bb551c7f2abd863afb6aa8afb71c294d8f2299db1fc08e552b5dd7fcd0","target":"record","created_at":"2026-05-18T01:31:19Z","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":"3f477f789cf592a51f00eb94be9e92ff58ab834caddf2f1dacd141a19421dca4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T18:42:30Z","title_canon_sha256":"6681346828a595b9b5e711f4fe8ae0a8bf259422cdfccbe4da0eab6856ad4333"},"schema_version":"1.0","source":{"id":"1411.7971","kind":"arxiv","version":2}},"canonical_sha256":"d513efe4f7a6b16129e875349388ad77fa1e11bfd17ef98bd123fa03a44f4b7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d513efe4f7a6b16129e875349388ad77fa1e11bfd17ef98bd123fa03a44f4b7d","first_computed_at":"2026-05-18T01:31:19.869211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:19.869211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w04iUt/+JdHZ3iB7n/CxFJaAzVV+xgXKrVLw/xpwj2C0eXlgsdRrCMFNhn3iA+mZp0mNcTztgEO3Ej78CuT3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:19.869832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c9287bb551c7f2abd863afb6aa8afb71c294d8f2299db1fc08e552b5dd7fcd0","sha256:c9af6712aa7b482b3846bc7cad93d448f36b4d426a82069d362b225cadbfe3c1"],"state_sha256":"e142e781f7ca0d59724c349654f3a03da802287ec7cf434435eed50b04a489e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3zud+KZiTVa9AckiqvNccyoz0C41eKkTM5fPP73yloJH2BnLj2VTi/7lRNZtvA2+9cD1LYISANtfDsyG1IJrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T05:24:49.533016Z","bundle_sha256":"bed8ad54f00b79eef826c75a712d6fbcd39157cbf67b770d022f2d84d15731b1"}}