{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XEWCXME7ISDBLU5HEQBKK5AM4C","short_pith_number":"pith:XEWCXME7","schema_version":"1.0","canonical_sha256":"b92c2bb09f448615d3a72402a5740ce0ba6a09d5f54b05e347f9f1cf509af776","source":{"kind":"arxiv","id":"1005.1808","version":3},"attestation_state":"computed","paper":{"title":"Dimension of the boundary in different metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Riku Kl\\'en, Ville Suomala","submitted_at":"2010-05-11T11:56:18Z","abstract_excerpt":"We consider metrics on Euclidean domains $\\Omega\\subset\\R^n$ that are induced by continuous densities $\\rho\\colon\\Omega\\rightarrow(0,\\infty)$ and study the Hausdorff and packing dimensions of the boundary of $\\Omega$ with respect to these metrics."},"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":"1005.1808","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-05-11T11:56:18Z","cross_cats_sorted":[],"title_canon_sha256":"f8f03ce5ddd2ee77a798242eeb427db7869baceed43eee4f933b9623592a7b59","abstract_canon_sha256":"54389a3cd5affefb256ad2f63518018ea8f05d3e895ff7beb389a112e0cb951e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.281810Z","signature_b64":"5qJtkfokthDxAmjyyYcYLpkk3f3ZzQFWk5D77m3RVdTayJBsyDs35Cb7d49jm5JWNcxnVTCiwFkEhQk37V+CDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b92c2bb09f448615d3a72402a5740ce0ba6a09d5f54b05e347f9f1cf509af776","last_reissued_at":"2026-05-18T03:12:58.281058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.281058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimension of the boundary in different metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Riku Kl\\'en, Ville Suomala","submitted_at":"2010-05-11T11:56:18Z","abstract_excerpt":"We consider metrics on Euclidean domains $\\Omega\\subset\\R^n$ that are induced by continuous densities $\\rho\\colon\\Omega\\rightarrow(0,\\infty)$ and study the Hausdorff and packing dimensions of the boundary of $\\Omega$ with respect to these metrics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1808","kind":"arxiv","version":3},"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":"1005.1808","created_at":"2026-05-18T03:12:58.281185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.1808v3","created_at":"2026-05-18T03:12:58.281185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1808","created_at":"2026-05-18T03:12:58.281185+00:00"},{"alias_kind":"pith_short_12","alias_value":"XEWCXME7ISDB","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XEWCXME7ISDBLU5H","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XEWCXME7","created_at":"2026-05-18T12:26:17.028572+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/XEWCXME7ISDBLU5HEQBKK5AM4C","json":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C.json","graph_json":"https://pith.science/api/pith-number/XEWCXME7ISDBLU5HEQBKK5AM4C/graph.json","events_json":"https://pith.science/api/pith-number/XEWCXME7ISDBLU5HEQBKK5AM4C/events.json","paper":"https://pith.science/paper/XEWCXME7"},"agent_actions":{"view_html":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C","download_json":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C.json","view_paper":"https://pith.science/paper/XEWCXME7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.1808&json=true","fetch_graph":"https://pith.science/api/pith-number/XEWCXME7ISDBLU5HEQBKK5AM4C/graph.json","fetch_events":"https://pith.science/api/pith-number/XEWCXME7ISDBLU5HEQBKK5AM4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C/action/storage_attestation","attest_author":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C/action/author_attestation","sign_citation":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C/action/citation_signature","submit_replication":"https://pith.science/pith/XEWCXME7ISDBLU5HEQBKK5AM4C/action/replication_record"}},"created_at":"2026-05-18T03:12:58.281185+00:00","updated_at":"2026-05-18T03:12:58.281185+00:00"}