{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HO4OAQTRHM2K4DHZEHB5Y4XKXC","short_pith_number":"pith:HO4OAQTR","schema_version":"1.0","canonical_sha256":"3bb8e042713b34ae0cf921c3dc72eab8b350c45e73e8a3e3fe8ddf4d9d9c198e","source":{"kind":"arxiv","id":"1509.03568","version":1},"attestation_state":"computed","paper":{"title":"Connectivity and giant component in random distance graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Briana Oshiro, Joshua Flynn, Mary Radcliffe","submitted_at":"2015-09-11T15:50:11Z","abstract_excerpt":"Various different random graph models have been proposed in which the vertices of the graph are seen as members of a metric space, and edges between vertices are determined as a function of the distance between the corresponding metric space elements. We here propose a model $G=G(X, f)$, in which $(X, d)$ is a metric space, $V(G)=X$, and $\\mathbb{P}(u\\sim v) = f(d(u, v))$, where $f$ is a decreasing function on the set of possible distances in $X$. We consider the case that $X$ is the $n\\times n \\times \\dots\\times n$ integer lattice in dimension $r$, with $d$ the $\\ell_1$ metric, and $f(d) = \\f"},"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":"1509.03568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-11T15:50:11Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"458d839420d8bdf15c74cdc0ead34c1c1cc455f685d874ca9e758c4a2e635764","abstract_canon_sha256":"85e40c4a07e1af5e41acb1cfe9894b7cfb13254e5b9525943aef58f701b0626a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:17.483812Z","signature_b64":"pITf9xGeNkzN0aSiXDBz1faxboKXzAmym0DXgt95zhyqd1iWxzSB6p3weUg4tgo3UXTQP7KfzqJrT83mvlgPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bb8e042713b34ae0cf921c3dc72eab8b350c45e73e8a3e3fe8ddf4d9d9c198e","last_reissued_at":"2026-05-18T01:33:17.483103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:17.483103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectivity and giant component in random distance graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Briana Oshiro, Joshua Flynn, Mary Radcliffe","submitted_at":"2015-09-11T15:50:11Z","abstract_excerpt":"Various different random graph models have been proposed in which the vertices of the graph are seen as members of a metric space, and edges between vertices are determined as a function of the distance between the corresponding metric space elements. We here propose a model $G=G(X, f)$, in which $(X, d)$ is a metric space, $V(G)=X$, and $\\mathbb{P}(u\\sim v) = f(d(u, v))$, where $f$ is a decreasing function on the set of possible distances in $X$. We consider the case that $X$ is the $n\\times n \\times \\dots\\times n$ integer lattice in dimension $r$, with $d$ the $\\ell_1$ metric, and $f(d) = \\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03568","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":"1509.03568","created_at":"2026-05-18T01:33:17.483227+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.03568v1","created_at":"2026-05-18T01:33:17.483227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03568","created_at":"2026-05-18T01:33:17.483227+00:00"},{"alias_kind":"pith_short_12","alias_value":"HO4OAQTRHM2K","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HO4OAQTRHM2K4DHZ","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HO4OAQTR","created_at":"2026-05-18T12:29:25.134429+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/HO4OAQTRHM2K4DHZEHB5Y4XKXC","json":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC.json","graph_json":"https://pith.science/api/pith-number/HO4OAQTRHM2K4DHZEHB5Y4XKXC/graph.json","events_json":"https://pith.science/api/pith-number/HO4OAQTRHM2K4DHZEHB5Y4XKXC/events.json","paper":"https://pith.science/paper/HO4OAQTR"},"agent_actions":{"view_html":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC","download_json":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC.json","view_paper":"https://pith.science/paper/HO4OAQTR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.03568&json=true","fetch_graph":"https://pith.science/api/pith-number/HO4OAQTRHM2K4DHZEHB5Y4XKXC/graph.json","fetch_events":"https://pith.science/api/pith-number/HO4OAQTRHM2K4DHZEHB5Y4XKXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC/action/storage_attestation","attest_author":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC/action/author_attestation","sign_citation":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC/action/citation_signature","submit_replication":"https://pith.science/pith/HO4OAQTRHM2K4DHZEHB5Y4XKXC/action/replication_record"}},"created_at":"2026-05-18T01:33:17.483227+00:00","updated_at":"2026-05-18T01:33:17.483227+00:00"}