{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YAF35AEJC5VSCUXFMG3WHK5KS2","short_pith_number":"pith:YAF35AEJ","canonical_record":{"source":{"id":"1504.05569","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-21T19:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"73492e7d33b686479dbdabb1bc448513fc0341cbb0ae068b79bbbfd0c21c81d1","abstract_canon_sha256":"5caaab52f8fb86df5ef134a543b6f4e5db96581237c9f4fb8a5937f6b9ef3bae"},"schema_version":"1.0"},"canonical_sha256":"c00bbe8089176b2152e561b763abaa96a91a73caac7badee0cf5eec5e8b048e2","source":{"kind":"arxiv","id":"1504.05569","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05569","created_at":"2026-05-18T01:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05569v4","created_at":"2026-05-18T01:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05569","created_at":"2026-05-18T01:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"YAF35AEJC5VS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YAF35AEJC5VSCUXF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YAF35AEJ","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YAF35AEJC5VSCUXFMG3WHK5KS2","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05569","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-21T19:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"73492e7d33b686479dbdabb1bc448513fc0341cbb0ae068b79bbbfd0c21c81d1","abstract_canon_sha256":"5caaab52f8fb86df5ef134a543b6f4e5db96581237c9f4fb8a5937f6b9ef3bae"},"schema_version":"1.0"},"canonical_sha256":"c00bbe8089176b2152e561b763abaa96a91a73caac7badee0cf5eec5e8b048e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:08.904605Z","signature_b64":"scj8+daK1kWa6/xzcoOgg42zw0g/yGiKOQNhywq6oc2Atq+3QB2FZ7Ozzen8fnwR97gyAjgAoWF6kGtNF6MgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c00bbe8089176b2152e561b763abaa96a91a73caac7badee0cf5eec5e8b048e2","last_reissued_at":"2026-05-18T01:01:08.903909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:08.903909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05569","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CfiP6tHa8k4gT3tYwZP8Eh9fr9ZipUxVtJvE8lTB46t5T0D5FrpTRnI4dt4pcdZKdCEi9HLPymW6VzvUArjjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:25:20.852740Z"},"content_sha256":"8e1fdb7f1ac46cccba3590fc3978b79c9e3990e134bba8e30ad42c5613ce652e","schema_version":"1.0","event_id":"sha256:8e1fdb7f1ac46cccba3590fc3978b79c9e3990e134bba8e30ad42c5613ce652e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YAF35AEJC5VSCUXFMG3WHK5KS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuity and density results for a one-phase nonlocal free boundary problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Serena Dipierro","submitted_at":"2015-04-21T19:53:28Z","abstract_excerpt":"We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are H\\\"older continuous and the free boundary has positive density from both sides.\n  For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05569","kind":"arxiv","version":4},"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":"2026-05-18T01:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKK80Z+KQmzHGiC77pOwQddsd9m/OE4ojTQPCHM//5jX4QjlevnTDrbDLw5oGT1IIZ1r8dVTGvlS6+6kDYHhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:25:20.853094Z"},"content_sha256":"b8e00406e72a844dc6ce2ce10ef296bd3e145b9107c7a78d37fe39703325f70b","schema_version":"1.0","event_id":"sha256:b8e00406e72a844dc6ce2ce10ef296bd3e145b9107c7a78d37fe39703325f70b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAF35AEJC5VSCUXFMG3WHK5KS2/bundle.json","state_url":"https://pith.science/pith/YAF35AEJC5VSCUXFMG3WHK5KS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAF35AEJC5VSCUXFMG3WHK5KS2/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":"2026-06-05T21:25:20Z","links":{"resolver":"https://pith.science/pith/YAF35AEJC5VSCUXFMG3WHK5KS2","bundle":"https://pith.science/pith/YAF35AEJC5VSCUXFMG3WHK5KS2/bundle.json","state":"https://pith.science/pith/YAF35AEJC5VSCUXFMG3WHK5KS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAF35AEJC5VSCUXFMG3WHK5KS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YAF35AEJC5VSCUXFMG3WHK5KS2","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":"5caaab52f8fb86df5ef134a543b6f4e5db96581237c9f4fb8a5937f6b9ef3bae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-21T19:53:28Z","title_canon_sha256":"73492e7d33b686479dbdabb1bc448513fc0341cbb0ae068b79bbbfd0c21c81d1"},"schema_version":"1.0","source":{"id":"1504.05569","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05569","created_at":"2026-05-18T01:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05569v4","created_at":"2026-05-18T01:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05569","created_at":"2026-05-18T01:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"YAF35AEJC5VS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YAF35AEJC5VSCUXF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YAF35AEJ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:b8e00406e72a844dc6ce2ce10ef296bd3e145b9107c7a78d37fe39703325f70b","target":"graph","created_at":"2026-05-18T01:01:08Z","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 one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are H\\\"older continuous and the free boundary has positive density from both sides.\n  For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.","authors_text":"Enrico Valdinoci, Serena Dipierro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-21T19:53:28Z","title":"Continuity and density results for a one-phase nonlocal free boundary problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05569","kind":"arxiv","version":4},"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":"sha256:8e1fdb7f1ac46cccba3590fc3978b79c9e3990e134bba8e30ad42c5613ce652e","target":"record","created_at":"2026-05-18T01:01:08Z","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":"5caaab52f8fb86df5ef134a543b6f4e5db96581237c9f4fb8a5937f6b9ef3bae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-21T19:53:28Z","title_canon_sha256":"73492e7d33b686479dbdabb1bc448513fc0341cbb0ae068b79bbbfd0c21c81d1"},"schema_version":"1.0","source":{"id":"1504.05569","kind":"arxiv","version":4}},"canonical_sha256":"c00bbe8089176b2152e561b763abaa96a91a73caac7badee0cf5eec5e8b048e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c00bbe8089176b2152e561b763abaa96a91a73caac7badee0cf5eec5e8b048e2","first_computed_at":"2026-05-18T01:01:08.903909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:08.903909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"scj8+daK1kWa6/xzcoOgg42zw0g/yGiKOQNhywq6oc2Atq+3QB2FZ7Ozzen8fnwR97gyAjgAoWF6kGtNF6MgCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:08.904605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05569","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e1fdb7f1ac46cccba3590fc3978b79c9e3990e134bba8e30ad42c5613ce652e","sha256:b8e00406e72a844dc6ce2ce10ef296bd3e145b9107c7a78d37fe39703325f70b"],"state_sha256":"a9e308033b773527a78156a4524f4ac5be0f69cbd0ffdf3ca7c9bbe3fecf25c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9TF37DpB3Oyvp5/v9Muxryd3IoM6YSyWIrUlMOSKBuMeVpTnb1w1w5PMk3y+35TklmCTOnb+u8PYX9XUh1c0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:25:20.855644Z","bundle_sha256":"6503de29669c9d8654477a93b6df9b5ce38a6d8c13c82036d63d6d1612e93d43"}}