{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6ROVH6YP7O5OSWBCMGKYLQRHI6","short_pith_number":"pith:6ROVH6YP","schema_version":"1.0","canonical_sha256":"f45d53fb0ffbbae95822619585c22747912c0dde73a4457ddb75a63836e8b795","source":{"kind":"arxiv","id":"1604.06474","version":1},"attestation_state":"computed","paper":{"title":"On Detection and Structural Reconstruction of Small-World Random Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander Rakhlin, Tengyuan Liang, T. Tony Cai","submitted_at":"2016-04-21T20:13:54Z","abstract_excerpt":"In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \\citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering and short average length properties. The WS model with neighborhood size $k$ and rewiring probability probability $\\beta$ can be viewed as a continuous interpolation between a deterministic ring lattice graph and the Erd\\H{o}s-R\\'{e}nyi random graph. We study both the computational and statistical aspects of detecting the deterministic ring lattice structure"},"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":"1604.06474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-21T20:13:54Z","cross_cats_sorted":["cs.LG","stat.TH"],"title_canon_sha256":"45ddaf8dba61340f37edb1aab5a3ade87fd518d540cda2f5a0d26c9e6096d6b9","abstract_canon_sha256":"b4242b4f348cec955036138384ea821801beeaee4bc5f830e4603549f16d520e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:21:44.335180Z","signature_b64":"M6cZlyCqDvVrbEKALhHcellUYbYq7Ixzo9DIqITarmEjPkNh5lr3VjbcvPi3of7LEV5R3cLRwckiKKP87LuqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f45d53fb0ffbbae95822619585c22747912c0dde73a4457ddb75a63836e8b795","last_reissued_at":"2026-07-05T01:21:44.334682Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:21:44.334682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Detection and Structural Reconstruction of Small-World Random Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander Rakhlin, Tengyuan Liang, T. Tony Cai","submitted_at":"2016-04-21T20:13:54Z","abstract_excerpt":"In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \\citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering and short average length properties. The WS model with neighborhood size $k$ and rewiring probability probability $\\beta$ can be viewed as a continuous interpolation between a deterministic ring lattice graph and the Erd\\H{o}s-R\\'{e}nyi random graph. We study both the computational and statistical aspects of detecting the deterministic ring lattice structure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1604.06474/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1604.06474","created_at":"2026-07-05T01:21:44.334736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06474v1","created_at":"2026-07-05T01:21:44.334736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06474","created_at":"2026-07-05T01:21:44.334736+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ROVH6YP7O5O","created_at":"2026-07-05T01:21:44.334736+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ROVH6YP7O5OSWBC","created_at":"2026-07-05T01:21:44.334736+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ROVH6YP","created_at":"2026-07-05T01:21:44.334736+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/6ROVH6YP7O5OSWBCMGKYLQRHI6","json":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6.json","graph_json":"https://pith.science/api/pith-number/6ROVH6YP7O5OSWBCMGKYLQRHI6/graph.json","events_json":"https://pith.science/api/pith-number/6ROVH6YP7O5OSWBCMGKYLQRHI6/events.json","paper":"https://pith.science/paper/6ROVH6YP"},"agent_actions":{"view_html":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6","download_json":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6.json","view_paper":"https://pith.science/paper/6ROVH6YP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06474&json=true","fetch_graph":"https://pith.science/api/pith-number/6ROVH6YP7O5OSWBCMGKYLQRHI6/graph.json","fetch_events":"https://pith.science/api/pith-number/6ROVH6YP7O5OSWBCMGKYLQRHI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6/action/storage_attestation","attest_author":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6/action/author_attestation","sign_citation":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6/action/citation_signature","submit_replication":"https://pith.science/pith/6ROVH6YP7O5OSWBCMGKYLQRHI6/action/replication_record"}},"created_at":"2026-07-05T01:21:44.334736+00:00","updated_at":"2026-07-05T01:21:44.334736+00:00"}