{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZGVVDT5FQUP5ICA3DPYTQ3DXIH","short_pith_number":"pith:ZGVVDT5F","schema_version":"1.0","canonical_sha256":"c9ab51cfa5851fd4081b1bf1386c7741c44544fd66015a2972cdb4b1c7bdb510","source":{"kind":"arxiv","id":"1212.1283","version":3},"attestation_state":"computed","paper":{"title":"A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multi-hop Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Jing Guo, Salman Durrani, Zubair Khalid","submitted_at":"2012-12-06T10:57:58Z","abstract_excerpt":"This paper presents a tractable analytical framework for the exact calculation of probability of node isolation and minimum node degree distribution when $N$ sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account for the boundary effects by partitioning the square into subregions, based on the transmission range and the node location. We show that for each subregion, the probability that a random node falls inside a disk centered at an arbitrary node located in that subregion can be expressed analytically in closed-"},"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":"1212.1283","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-06T10:57:58Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"c39898f6aa9462050cfb5e39f4a5eb36cbcc3b66466a8ec082c237ffd8e308f7","abstract_canon_sha256":"3b61bbba05743b0f30b2d42172fad13b881b4658925a9e052a16870d339740de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:11.704797Z","signature_b64":"KqRKR/QVpErUdUvqCvLtpowtkt7nawjebrUvu3c05FGlVl0T8DIkuQQqPHZhGj/NZ1U5cZ7u9xbJeE74hfW5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9ab51cfa5851fd4081b1bf1386c7741c44544fd66015a2972cdb4b1c7bdb510","last_reissued_at":"2026-05-18T01:37:11.704010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:11.704010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multi-hop Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Jing Guo, Salman Durrani, Zubair Khalid","submitted_at":"2012-12-06T10:57:58Z","abstract_excerpt":"This paper presents a tractable analytical framework for the exact calculation of probability of node isolation and minimum node degree distribution when $N$ sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account for the boundary effects by partitioning the square into subregions, based on the transmission range and the node location. We show that for each subregion, the probability that a random node falls inside a disk centered at an arbitrary node located in that subregion can be expressed analytically in closed-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1283","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":"1212.1283","created_at":"2026-05-18T01:37:11.704167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1283v3","created_at":"2026-05-18T01:37:11.704167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1283","created_at":"2026-05-18T01:37:11.704167+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGVVDT5FQUP5","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGVVDT5FQUP5ICA3","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGVVDT5F","created_at":"2026-05-18T12:27:30.460161+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/ZGVVDT5FQUP5ICA3DPYTQ3DXIH","json":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH.json","graph_json":"https://pith.science/api/pith-number/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/graph.json","events_json":"https://pith.science/api/pith-number/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/events.json","paper":"https://pith.science/paper/ZGVVDT5F"},"agent_actions":{"view_html":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH","download_json":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH.json","view_paper":"https://pith.science/paper/ZGVVDT5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1283&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/action/storage_attestation","attest_author":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/action/author_attestation","sign_citation":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/action/citation_signature","submit_replication":"https://pith.science/pith/ZGVVDT5FQUP5ICA3DPYTQ3DXIH/action/replication_record"}},"created_at":"2026-05-18T01:37:11.704167+00:00","updated_at":"2026-05-18T01:37:11.704167+00:00"}