{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N6VG43QTFVC4G7MRFWEVP5BRRE","short_pith_number":"pith:N6VG43QT","canonical_record":{"source":{"id":"1508.06241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T18:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"f4ed1203391c9ef55f7bec478868f9d617f84965ae5acc6cfd0391721d031ec1","abstract_canon_sha256":"0d961f57328b53fc4c1454a41a45f37a8cf803888eb854d353cc1f0d4b4e1a13"},"schema_version":"1.0"},"canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","source":{"kind":"arxiv","id":"1508.06241","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06241","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06241v1","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06241","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"N6VG43QTFVC4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6VG43QTFVC4G7MR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6VG43QT","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N6VG43QTFVC4G7MRFWEVP5BRRE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T18:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"f4ed1203391c9ef55f7bec478868f9d617f84965ae5acc6cfd0391721d031ec1","abstract_canon_sha256":"0d961f57328b53fc4c1454a41a45f37a8cf803888eb854d353cc1f0d4b4e1a13"},"schema_version":"1.0"},"canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:46.347693Z","signature_b64":"csR1DM9vervxj1Q4TX6bg5LbDHv3iNW3MhDhybehvyI+vFqgGwfCYeaFygNlLsKqZVDLmBxyuZs84GxqfItUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","last_reissued_at":"2026-05-18T01:34:46.347178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:46.347178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06241","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":"2026-05-18T01:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jJaAunLwol+uKc7ghxjq4rLVTcxhV6UyHMQgLgE3nTzxbNKTT1d3vRGunNdNzLa0dOLAJkyyrKAXwDY1QyzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:34:55.540595Z"},"content_sha256":"ff40cd4b78d250fb86f347f7ca26eeceaf1beb30e664ca1e8f14693f9f90e81e","schema_version":"1.0","event_id":"sha256:ff40cd4b78d250fb86f347f7ca26eeceaf1beb30e664ca1e8f14693f9f90e81e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N6VG43QTFVC4G7MRFWEVP5BRRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Perimeter and Nonlocal Minimal Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lombardini","submitted_at":"2015-08-25T18:26:05Z","abstract_excerpt":"This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give full detailed proofs for all the Theorems contained in the article \"Nonlocal Minimal Surfaces\" by Caffarelli, Roquejoffre and Savin, where these s-minimal sets were introduced and studied for the first time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06241","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":"2026-05-18T01:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkHw+QWhX2Hd+SAH0tI1IWD06ZqxJKBt0sOW7g/k20gZEKS09TCQy2YTgkXtUquGGBbooUUUYB9L1A1yZ7RWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:34:55.541123Z"},"content_sha256":"50659a153445582c23969213d088aac01a536b09541863715164768b4b6802ca","schema_version":"1.0","event_id":"sha256:50659a153445582c23969213d088aac01a536b09541863715164768b4b6802ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/bundle.json","state_url":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/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":"2026-06-23T16:34:55Z","links":{"resolver":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE","bundle":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/bundle.json","state":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N6VG43QTFVC4G7MRFWEVP5BRRE","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":"0d961f57328b53fc4c1454a41a45f37a8cf803888eb854d353cc1f0d4b4e1a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T18:26:05Z","title_canon_sha256":"f4ed1203391c9ef55f7bec478868f9d617f84965ae5acc6cfd0391721d031ec1"},"schema_version":"1.0","source":{"id":"1508.06241","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06241","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06241v1","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06241","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"N6VG43QTFVC4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6VG43QTFVC4G7MR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6VG43QT","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:50659a153445582c23969213d088aac01a536b09541863715164768b4b6802ca","target":"graph","created_at":"2026-05-18T01:34:46Z","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":"This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give full detailed proofs for all the Theorems contained in the article \"Nonlocal Minimal Surfaces\" by Caffarelli, Roquejoffre and Savin, where these s-minimal sets were introduced and studied for the first time.","authors_text":"Luca Lombardini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T18:26:05Z","title":"Fractional Perimeter and Nonlocal Minimal Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06241","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:ff40cd4b78d250fb86f347f7ca26eeceaf1beb30e664ca1e8f14693f9f90e81e","target":"record","created_at":"2026-05-18T01:34:46Z","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":"0d961f57328b53fc4c1454a41a45f37a8cf803888eb854d353cc1f0d4b4e1a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T18:26:05Z","title_canon_sha256":"f4ed1203391c9ef55f7bec478868f9d617f84965ae5acc6cfd0391721d031ec1"},"schema_version":"1.0","source":{"id":"1508.06241","kind":"arxiv","version":1}},"canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","first_computed_at":"2026-05-18T01:34:46.347178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:46.347178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csR1DM9vervxj1Q4TX6bg5LbDHv3iNW3MhDhybehvyI+vFqgGwfCYeaFygNlLsKqZVDLmBxyuZs84GxqfItUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:46.347693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06241","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff40cd4b78d250fb86f347f7ca26eeceaf1beb30e664ca1e8f14693f9f90e81e","sha256:50659a153445582c23969213d088aac01a536b09541863715164768b4b6802ca"],"state_sha256":"6c9dcf12d359590c1884c091f89227b7a19d40feffdb722744e4e4166c1c1463"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIjLzbVOVuqONM25xVrfCXRZcS1IbEcQU/3/PL6X6rg1jkPpgyKB46JTjkW89ubdLwVmlsHhIt2B+J6LOJ+bCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:34:55.694145Z","bundle_sha256":"8ac22434d01a055ebbeba2e019ad0ad9c7cc6228681e60ae19b08175dfdeae31"}}