{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:AOIBGFCCZWT6MNOUL3TAVWX2RH","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":"25c9db59e8dd7a71d2c8da09b6074b5259708a34185526b04ac86dcf5eae3ed7","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-08-31T09:17:56Z","title_canon_sha256":"9c7c6bc868efef7d2294cbce9c18c0ed1fd3353f5f0b5cfa5b38be44aec1b047"},"schema_version":"1.0","source":{"id":"cond-mat/0508759","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0508759","created_at":"2026-05-18T01:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0508759v2","created_at":"2026-05-18T01:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0508759","created_at":"2026-05-18T01:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"AOIBGFCCZWT6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"AOIBGFCCZWT6MNOU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"AOIBGFCC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f4d36006514354e8ce26bcaf650e0c0e39b668afa1585e667e63908343f354da","target":"graph","created_at":"2026-05-18T01:08:58Z","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 study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter ($S \\equiv AL^{-1/\\nu}$ for $d$-dimensional lattices, and $S\\equiv AN^{-1/3}$ for random networks) determines the distributions of the optimal path length, including both strong and weak disorder regimes. Here $\\nu$ is the percolation connectivity exponent, and $A$ depends on the percolation threshold and $P(w)$. For $P(w)$ un","authors_text":"Eduardo L\\'opez, H.Eugene Stanley, Shlomo Havlin, Yiping Chen","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-08-31T09:17:56Z","title":"Universal behavior of optimal paths in weighted networks with general disorder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0508759","kind":"arxiv","version":2},"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":"sha256:82514f8ee43c167aeb6091f45dc3cf6af512fc5bcb1e634c2633085147fcf599","target":"record","created_at":"2026-05-18T01:08:58Z","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":"25c9db59e8dd7a71d2c8da09b6074b5259708a34185526b04ac86dcf5eae3ed7","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-08-31T09:17:56Z","title_canon_sha256":"9c7c6bc868efef7d2294cbce9c18c0ed1fd3353f5f0b5cfa5b38be44aec1b047"},"schema_version":"1.0","source":{"id":"cond-mat/0508759","kind":"arxiv","version":2}},"canonical_sha256":"0390131442cda7e635d45ee60adafa89d3c952a3799d0d91297eab2905084c8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0390131442cda7e635d45ee60adafa89d3c952a3799d0d91297eab2905084c8a","first_computed_at":"2026-05-18T01:08:58.043894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:58.043894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4x9/soSd3H/OBMAkF72aEPl1dHZCRK6mmiu0aenKwe9FVHlfrHAHzHJQYHJvsiXOJgBlDD9GzjlHsGHTCg/WDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:58.044422Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0508759","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82514f8ee43c167aeb6091f45dc3cf6af512fc5bcb1e634c2633085147fcf599","sha256:f4d36006514354e8ce26bcaf650e0c0e39b668afa1585e667e63908343f354da"],"state_sha256":"4e6268a5a6bd22d4e9e567a199bce7a648b32d427a67b33809b72532e29090a2"}