{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HOTHQ23XZARPY4DBWUBXGRGFRD","short_pith_number":"pith:HOTHQ23X","schema_version":"1.0","canonical_sha256":"3ba6786b77c822fc7061b5037344c588c7bfc5fd77eeee7b22b56949958cd86a","source":{"kind":"arxiv","id":"1709.08706","version":2},"attestation_state":"computed","paper":{"title":"Topology-dependent density optima for efficient simultaneous network exploration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR","physics.bio-ph"],"primary_cat":"math.OC","authors_text":"Daniel B. Wilson, Francis G. Woodhouse, Ruth E. Baker","submitted_at":"2017-09-25T19:58:58Z","abstract_excerpt":"A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric "},"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":"1709.08706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-25T19:58:58Z","cross_cats_sorted":["cond-mat.stat-mech","math.PR","physics.bio-ph"],"title_canon_sha256":"bd2f87c4cdb591e8cdf63e0aed2384728182f6f1a8bf09eddf3a48de289be256","abstract_canon_sha256":"29203a7f70e381f3bf271aed3470c5bf2965598bd57bcd9028be9a3a0b5941bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:31.933334Z","signature_b64":"v60mGUc5BnEIYXpRgCPwA57qzy7eyQxur4byZI0/1hpML/19qB3GRz77s0nm3YYJSV8Bw2mv3Q2uRq/mvsFzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ba6786b77c822fc7061b5037344c588c7bfc5fd77eeee7b22b56949958cd86a","last_reissued_at":"2026-05-18T00:13:31.932609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:31.932609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology-dependent density optima for efficient simultaneous network exploration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR","physics.bio-ph"],"primary_cat":"math.OC","authors_text":"Daniel B. Wilson, Francis G. Woodhouse, Ruth E. Baker","submitted_at":"2017-09-25T19:58:58Z","abstract_excerpt":"A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08706","kind":"arxiv","version":2},"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":"1709.08706","created_at":"2026-05-18T00:13:31.932699+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.08706v2","created_at":"2026-05-18T00:13:31.932699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08706","created_at":"2026-05-18T00:13:31.932699+00:00"},{"alias_kind":"pith_short_12","alias_value":"HOTHQ23XZARP","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HOTHQ23XZARPY4DB","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HOTHQ23X","created_at":"2026-05-18T12:31:18.294218+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/HOTHQ23XZARPY4DBWUBXGRGFRD","json":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD.json","graph_json":"https://pith.science/api/pith-number/HOTHQ23XZARPY4DBWUBXGRGFRD/graph.json","events_json":"https://pith.science/api/pith-number/HOTHQ23XZARPY4DBWUBXGRGFRD/events.json","paper":"https://pith.science/paper/HOTHQ23X"},"agent_actions":{"view_html":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD","download_json":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD.json","view_paper":"https://pith.science/paper/HOTHQ23X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.08706&json=true","fetch_graph":"https://pith.science/api/pith-number/HOTHQ23XZARPY4DBWUBXGRGFRD/graph.json","fetch_events":"https://pith.science/api/pith-number/HOTHQ23XZARPY4DBWUBXGRGFRD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD/action/storage_attestation","attest_author":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD/action/author_attestation","sign_citation":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD/action/citation_signature","submit_replication":"https://pith.science/pith/HOTHQ23XZARPY4DBWUBXGRGFRD/action/replication_record"}},"created_at":"2026-05-18T00:13:31.932699+00:00","updated_at":"2026-05-18T00:13:31.932699+00:00"}