{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PAAMF4UKHY4OCM7LS4ZK6TUBXS","short_pith_number":"pith:PAAMF4UK","schema_version":"1.0","canonical_sha256":"7800c2f28a3e38e133eb9732af4e81bcadeb16a85159b2b754d86c801030197e","source":{"kind":"arxiv","id":"1603.06088","version":1},"attestation_state":"computed","paper":{"title":"Fractional perimeter from a fractal perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lombardini","submitted_at":"2016-03-19T12:26:21Z","abstract_excerpt":"Following \\cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we give some examples of this kind of sets, explaining how to construct them starting from well known self-similar fractals. In particular, we show that in the case of the von Koch snowflake $S\\subset\\mathbb R^2$ this fractal dimension coincides with the Minkowski dimension, namely \\begin{equation*} P_s(S)<\\infty\\qquad\\Longleftrightarrow\\qquad s\\in\\Big(0,2-\\fra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.06088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-19T12:26:21Z","cross_cats_sorted":[],"title_canon_sha256":"e83cb2684aab4a4327a3bf98ae42842f65b6d27a444a286deb924456bab9aac4","abstract_canon_sha256":"c7f7d4abeb10d944667a7af72190ba716e2ce6161b80b8a27e16d18081dbfe3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:51.835294Z","signature_b64":"0Jhe82+tpO2YpaaUQEWjIX/1G6PBvvcwp9vo+wsm64g7H3J036rqt8vJ1WME228p0oZxj2gv+sSySZXGLN3oAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7800c2f28a3e38e133eb9732af4e81bcadeb16a85159b2b754d86c801030197e","last_reissued_at":"2026-05-18T01:18:51.834629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:51.834629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional perimeter from a fractal perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lombardini","submitted_at":"2016-03-19T12:26:21Z","abstract_excerpt":"Following \\cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we give some examples of this kind of sets, explaining how to construct them starting from well known self-similar fractals. In particular, we show that in the case of the von Koch snowflake $S\\subset\\mathbb R^2$ this fractal dimension coincides with the Minkowski dimension, namely \\begin{equation*} P_s(S)<\\infty\\qquad\\Longleftrightarrow\\qquad s\\in\\Big(0,2-\\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06088","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.06088","created_at":"2026-05-18T01:18:51.834732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06088v1","created_at":"2026-05-18T01:18:51.834732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06088","created_at":"2026-05-18T01:18:51.834732+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAAMF4UKHY4O","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAAMF4UKHY4OCM7L","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAAMF4UK","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS","json":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS.json","graph_json":"https://pith.science/api/pith-number/PAAMF4UKHY4OCM7LS4ZK6TUBXS/graph.json","events_json":"https://pith.science/api/pith-number/PAAMF4UKHY4OCM7LS4ZK6TUBXS/events.json","paper":"https://pith.science/paper/PAAMF4UK"},"agent_actions":{"view_html":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS","download_json":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS.json","view_paper":"https://pith.science/paper/PAAMF4UK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06088&json=true","fetch_graph":"https://pith.science/api/pith-number/PAAMF4UKHY4OCM7LS4ZK6TUBXS/graph.json","fetch_events":"https://pith.science/api/pith-number/PAAMF4UKHY4OCM7LS4ZK6TUBXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS/action/storage_attestation","attest_author":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS/action/author_attestation","sign_citation":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS/action/citation_signature","submit_replication":"https://pith.science/pith/PAAMF4UKHY4OCM7LS4ZK6TUBXS/action/replication_record"}},"created_at":"2026-05-18T01:18:51.834732+00:00","updated_at":"2026-05-18T01:18:51.834732+00:00"}