{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O7FB3AJNTZQGJ4OJSKG4FLZX5X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6a22f615666a5f687da6e0c15d900de9d66688d1a6eecb42c5f2b01889526ca3","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-11-15T01:31:37Z","title_canon_sha256":"5ae24c55e096c015994d2f0350d475312047a6f23e87947c6ba16bf064f1f8bb"},"schema_version":"1.0","source":{"id":"1411.4097","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4097","created_at":"2026-05-18T00:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4097v6","created_at":"2026-05-18T00:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4097","created_at":"2026-05-18T00:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"O7FB3AJNTZQG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O7FB3AJNTZQGJ4OJ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O7FB3AJN","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a76cf66051e69e5f2e7bdb927ac02edea47dc8d5144d14f4ba1ba2df8b5fafb5","target":"graph","created_at":"2026-05-18T00:19:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Kleinberg proposed a family of small-world networks to explain the navigability of large-scale real-world social networks. However, the underlying mechanism that drives real networks to be navigable is not yet well understood. In this paper, we present a game theoretic model for the formation of navigable small world networks. We model the network formation as a Distance-Reciprocity Balanced (DRB) game in which people seek for both high reciprocity and long-distance relationships. We show that the game has only two Nash equilibria: One is the navigable small-world network, and the other is the","authors_text":"Wei Chen, Zhi Yang","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-11-15T01:31:37Z","title":"A Game Theoretic Model for the Formation of Navigable Small-World Networks --- the Tradeoff between Distance and Reciprocity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4097","kind":"arxiv","version":6},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:81238dd81615f8120bf81dd4c1d9717a3e871e6945652d607c92ce1ddce2897c","target":"record","created_at":"2026-05-18T00:19:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6a22f615666a5f687da6e0c15d900de9d66688d1a6eecb42c5f2b01889526ca3","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-11-15T01:31:37Z","title_canon_sha256":"5ae24c55e096c015994d2f0350d475312047a6f23e87947c6ba16bf064f1f8bb"},"schema_version":"1.0","source":{"id":"1411.4097","kind":"arxiv","version":6}},"canonical_sha256":"77ca1d812d9e6064f1c9928dc2af37edc36c7b1a0eb40eb6576e6e1f12795c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77ca1d812d9e6064f1c9928dc2af37edc36c7b1a0eb40eb6576e6e1f12795c5c","first_computed_at":"2026-05-18T00:19:36.294198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:36.294198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ikmyd5MYWZYxpxinBBDJmN74W0ZZwEPI1F/Rut2suIiy1hdSRnNt5Q7Y9inQJpGv5zoNm7RsgAmxJV+fPU3gBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:36.294905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4097","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81238dd81615f8120bf81dd4c1d9717a3e871e6945652d607c92ce1ddce2897c","sha256:a76cf66051e69e5f2e7bdb927ac02edea47dc8d5144d14f4ba1ba2df8b5fafb5"],"state_sha256":"ffec0e0ec045f43390e9feea2e71cb60b461be4906b940669f0f195fb320c146"}