{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3RTRP2ACXXVW6YEJKODZGTOLHS","short_pith_number":"pith:3RTRP2AC","schema_version":"1.0","canonical_sha256":"dc6717e802bdeb6f60895387934dcb3c9714f3d9ba9c026bf8bb87ebb0f82621","source":{"kind":"arxiv","id":"1310.8430","version":1},"attestation_state":"computed","paper":{"title":"Size dependence of the largest distance between random points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"physics.comp-ph","authors_text":"Janusz Malinowski, Krzysztof Kulakowski, Malgorzata J. Krawczyk","submitted_at":"2013-10-31T09:17:05Z","abstract_excerpt":"A set of $N$ points is chosen randomly in a $D$-dimensional volume $V=a^D$, with periodic boundary conditions. For each point $i$, its distance $d_i$ is found to its nearest neighbour. Then, the maximal value is found, $d_{max}=max(d_i, i=1,...,N)$. Our numerical calculations indicate, that when the density $N/V$=const, $d_{max}$ scales with the linear system size as $d^2_{max}\\propto a^\\phi$, with $\\phi=0.24\\pm0.04$ for $D=1,2,3,4$."},"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":"1310.8430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2013-10-31T09:17:05Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"119c53c9a955ef6ce14e11af3251fb234ffd1ed32f1b6e37f800a3f67796bcd8","abstract_canon_sha256":"d84f9c4b73b6bf624795210c78ef6a1bf533076ca7e4f1368027db11203df91b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:31.779619Z","signature_b64":"dOdfK6g/32zfVi1W2WLtfvb1e/qxI+2MwOke4FKxRgVeDriGS1SWo4iFX2PflI0DRPRLxDsnSA8jelCCF6rdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc6717e802bdeb6f60895387934dcb3c9714f3d9ba9c026bf8bb87ebb0f82621","last_reissued_at":"2026-05-18T02:44:31.779142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:31.779142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Size dependence of the largest distance between random points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"physics.comp-ph","authors_text":"Janusz Malinowski, Krzysztof Kulakowski, Malgorzata J. Krawczyk","submitted_at":"2013-10-31T09:17:05Z","abstract_excerpt":"A set of $N$ points is chosen randomly in a $D$-dimensional volume $V=a^D$, with periodic boundary conditions. For each point $i$, its distance $d_i$ is found to its nearest neighbour. Then, the maximal value is found, $d_{max}=max(d_i, i=1,...,N)$. Our numerical calculations indicate, that when the density $N/V$=const, $d_{max}$ scales with the linear system size as $d^2_{max}\\propto a^\\phi$, with $\\phi=0.24\\pm0.04$ for $D=1,2,3,4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8430","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":"1310.8430","created_at":"2026-05-18T02:44:31.779218+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8430v1","created_at":"2026-05-18T02:44:31.779218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8430","created_at":"2026-05-18T02:44:31.779218+00:00"},{"alias_kind":"pith_short_12","alias_value":"3RTRP2ACXXVW","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3RTRP2ACXXVW6YEJ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3RTRP2AC","created_at":"2026-05-18T12:27:32.513160+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/3RTRP2ACXXVW6YEJKODZGTOLHS","json":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS.json","graph_json":"https://pith.science/api/pith-number/3RTRP2ACXXVW6YEJKODZGTOLHS/graph.json","events_json":"https://pith.science/api/pith-number/3RTRP2ACXXVW6YEJKODZGTOLHS/events.json","paper":"https://pith.science/paper/3RTRP2AC"},"agent_actions":{"view_html":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS","download_json":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS.json","view_paper":"https://pith.science/paper/3RTRP2AC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8430&json=true","fetch_graph":"https://pith.science/api/pith-number/3RTRP2ACXXVW6YEJKODZGTOLHS/graph.json","fetch_events":"https://pith.science/api/pith-number/3RTRP2ACXXVW6YEJKODZGTOLHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS/action/storage_attestation","attest_author":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS/action/author_attestation","sign_citation":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS/action/citation_signature","submit_replication":"https://pith.science/pith/3RTRP2ACXXVW6YEJKODZGTOLHS/action/replication_record"}},"created_at":"2026-05-18T02:44:31.779218+00:00","updated_at":"2026-05-18T02:44:31.779218+00:00"}