{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TMVPZOCOV7WPHK6YLS2VTBKCDC","short_pith_number":"pith:TMVPZOCO","schema_version":"1.0","canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","source":{"kind":"arxiv","id":"1704.06400","version":3},"attestation_state":"computed","paper":{"title":"Counting k-Hop Paths in the Random Connection Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander P. Kartun-Giles, Sunwoo Kim","submitted_at":"2017-04-21T05:01:10Z","abstract_excerpt":"We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than determinist"},"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":"1704.06400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-21T05:01:10Z","cross_cats_sorted":[],"title_canon_sha256":"12a1b32b75789f83a1abcb27b655fc1559a198fecc4c2c9610dece609736fab2","abstract_canon_sha256":"a1781bcb46e337fc7afe4df4a39a772664e518a2a113f0f27a78e192bed154b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:10.272004Z","signature_b64":"tVX+c119en4JTa4wRONYvQHMI2Xv16UYYRAD0H53jCXeu83PpZpOWUX3Z4f0bvvRabLcTciiDDqH1XW+ygnlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","last_reissued_at":"2026-05-18T00:24:10.271371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:10.271371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting k-Hop Paths in the Random Connection Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander P. Kartun-Giles, Sunwoo Kim","submitted_at":"2017-04-21T05:01:10Z","abstract_excerpt":"We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than determinist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06400","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":"1704.06400","created_at":"2026-05-18T00:24:10.271464+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.06400v3","created_at":"2026-05-18T00:24:10.271464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06400","created_at":"2026-05-18T00:24:10.271464+00:00"},{"alias_kind":"pith_short_12","alias_value":"TMVPZOCOV7WP","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TMVPZOCOV7WPHK6Y","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TMVPZOCO","created_at":"2026-05-18T12:31:46.661854+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/TMVPZOCOV7WPHK6YLS2VTBKCDC","json":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC.json","graph_json":"https://pith.science/api/pith-number/TMVPZOCOV7WPHK6YLS2VTBKCDC/graph.json","events_json":"https://pith.science/api/pith-number/TMVPZOCOV7WPHK6YLS2VTBKCDC/events.json","paper":"https://pith.science/paper/TMVPZOCO"},"agent_actions":{"view_html":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC","download_json":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC.json","view_paper":"https://pith.science/paper/TMVPZOCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.06400&json=true","fetch_graph":"https://pith.science/api/pith-number/TMVPZOCOV7WPHK6YLS2VTBKCDC/graph.json","fetch_events":"https://pith.science/api/pith-number/TMVPZOCOV7WPHK6YLS2VTBKCDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/action/storage_attestation","attest_author":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/action/author_attestation","sign_citation":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/action/citation_signature","submit_replication":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/action/replication_record"}},"created_at":"2026-05-18T00:24:10.271464+00:00","updated_at":"2026-05-18T00:24:10.271464+00:00"}