{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7HMZNCYFMOMTXEV4ORNVW47Y4V","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":"6cf8e06637632a8647017eeca62a9c1db1d9953dd479be8c3615fb0d3cb8b7a9","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-28T22:50:13Z","title_canon_sha256":"42c7a351e50185cb446a8cfc058de55340830d90e4df5f400e9e37588ddec7d4"},"schema_version":"1.0","source":{"id":"1103.0048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0048","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0048v1","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0048","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"7HMZNCYFMOMT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7HMZNCYFMOMTXEV4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7HMZNCYF","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4a621209867dd404db501b75575486db7b0a0d1c5c1dbe59a1d6292cf38f48f3","target":"graph","created_at":"2026-05-18T04:27:37Z","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":"We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the original SWN model. These short-range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for $r \\ll 1$ indicating that global shortcuts are not necessary for the small-world effect. For short-range SWNs, the average path length changes nonmonotonically with system size, whereas for th","authors_text":"Rahul V. Kulkarni, Tao Jia","cross_cats":["cond-mat.dis-nn","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-28T22:50:13Z","title":"On the structural properties of small-world networks with finite range of shortcut links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0048","kind":"arxiv","version":1},"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":"sha256:5328bc2db903c930b780cbde44b563fec122f4c92144d4dee5f04b676cce2189","target":"record","created_at":"2026-05-18T04:27:37Z","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":"6cf8e06637632a8647017eeca62a9c1db1d9953dd479be8c3615fb0d3cb8b7a9","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-28T22:50:13Z","title_canon_sha256":"42c7a351e50185cb446a8cfc058de55340830d90e4df5f400e9e37588ddec7d4"},"schema_version":"1.0","source":{"id":"1103.0048","kind":"arxiv","version":1}},"canonical_sha256":"f9d9968b0563993b92bc745b5b73f8e54cf2ed011f80bbb7e51265bf347264bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d9968b0563993b92bc745b5b73f8e54cf2ed011f80bbb7e51265bf347264bd","first_computed_at":"2026-05-18T04:27:37.479203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:37.479203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"34oPVWpCaZ4PUpmF3WtqrwoZQtRcx0Scq95rS9yWZeEIMVGTsc1WzyRWx3Dnad9r8RFNzDC04GGTLe0TcrsgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:37.479739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5328bc2db903c930b780cbde44b563fec122f4c92144d4dee5f04b676cce2189","sha256:4a621209867dd404db501b75575486db7b0a0d1c5c1dbe59a1d6292cf38f48f3"],"state_sha256":"77b3123c88fdd9858e7ae6bbe83c5607ed8650864ef44531f3c9f5c5111fd400"}