{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:NOMI6HNPCQ6B2YQBIQ2G6MVJW5","short_pith_number":"pith:NOMI6HNP","canonical_record":{"source":{"id":"cond-mat/0510127","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-10-06T01:49:40Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"758d4c077657176da81f0f2a67ab1a7f1dbc78d11868a57637e488d4ecf06bde","abstract_canon_sha256":"9cc930b78b6f88dc0377eec6dc29a718f314bdb79eae546605ebcfa771261ece"},"schema_version":"1.0"},"canonical_sha256":"6b988f1daf143c1d620144346f32a9b74e61a2415706c11f71fde026744ddad9","source":{"kind":"arxiv","id":"cond-mat/0510127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0510127","created_at":"2026-05-18T01:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0510127v1","created_at":"2026-05-18T01:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0510127","created_at":"2026-05-18T01:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"NOMI6HNPCQ6B","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NOMI6HNPCQ6B2YQB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NOMI6HNP","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:NOMI6HNPCQ6B2YQBIQ2G6MVJW5","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0510127","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-10-06T01:49:40Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"758d4c077657176da81f0f2a67ab1a7f1dbc78d11868a57637e488d4ecf06bde","abstract_canon_sha256":"9cc930b78b6f88dc0377eec6dc29a718f314bdb79eae546605ebcfa771261ece"},"schema_version":"1.0"},"canonical_sha256":"6b988f1daf143c1d620144346f32a9b74e61a2415706c11f71fde026744ddad9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:57.980951Z","signature_b64":"Ne+mfrMGh3mq1Fg/rtPWLr/EeWvhRE1XxtmqQMVy6jnVBsRqWcfpOA8CUtXbNF3hJWHv7vE5unGGmR7sFDvkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b988f1daf143c1d620144346f32a9b74e61a2415706c11f71fde026744ddad9","last_reissued_at":"2026-05-18T01:08:57.980460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:57.980460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0510127","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k21N12I5nNX/T12fsczT3h3CNf+o8G/3NQX88ol+T5pJCeZkNv2JPznDXeBhzJk7nxFZiqUVbBArmGa1cmtjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:48:18.839685Z"},"content_sha256":"eaaa04bb1d73544856b9606d9f5a0d4bae44d1161818aa5e233a7229c25b31a7","schema_version":"1.0","event_id":"sha256:eaaa04bb1d73544856b9606d9f5a0d4bae44d1161818aa5e233a7229c25b31a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:NOMI6HNPCQ6B2YQBIQ2G6MVJW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Possible Connection between the Optimal Path and Flow in Percolation Clusters","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Eduardo L\\'opez, H. Eugene Stanley, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin","submitted_at":"2005-10-06T01:49:40Z","abstract_excerpt":"We study the behavior of the optimal path between two sites separated by a distance $r$ on a $d$-dimensional lattice of linear size $L$ with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution $P(\\ell_{\\rm opt}|r,L)$ of the optimal path length $\\ell_{\\rm opt}$, and find for $r\\ll L$ a power law decay with $\\ell_{\\rm opt}$, characterized by exponent $g_{\\rm opt}$. We determine the scaling form of $P(\\ell_{\\rm opt}|r,L)$ in two- and three-dimensional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0510127","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0qLhtkqv2zWdVsjPdKs/DvKi9obuwUndNR0vq3k16CCgMX988jpA9gXRoMDOspYsJYGjsyKn3cAI2v2MyLXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:48:18.840028Z"},"content_sha256":"d047f1c46885343fe88c107574fa588ede8694bebfd3d34447d42278365c1682","schema_version":"1.0","event_id":"sha256:d047f1c46885343fe88c107574fa588ede8694bebfd3d34447d42278365c1682"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5/bundle.json","state_url":"https://pith.science/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T07:48:18Z","links":{"resolver":"https://pith.science/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5","bundle":"https://pith.science/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5/bundle.json","state":"https://pith.science/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOMI6HNPCQ6B2YQBIQ2G6MVJW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NOMI6HNPCQ6B2YQBIQ2G6MVJW5","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":"9cc930b78b6f88dc0377eec6dc29a718f314bdb79eae546605ebcfa771261ece","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-10-06T01:49:40Z","title_canon_sha256":"758d4c077657176da81f0f2a67ab1a7f1dbc78d11868a57637e488d4ecf06bde"},"schema_version":"1.0","source":{"id":"cond-mat/0510127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0510127","created_at":"2026-05-18T01:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0510127v1","created_at":"2026-05-18T01:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0510127","created_at":"2026-05-18T01:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"NOMI6HNPCQ6B","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NOMI6HNPCQ6B2YQB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NOMI6HNP","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d047f1c46885343fe88c107574fa588ede8694bebfd3d34447d42278365c1682","target":"graph","created_at":"2026-05-18T01:08:57Z","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 behavior of the optimal path between two sites separated by a distance $r$ on a $d$-dimensional lattice of linear size $L$ with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution $P(\\ell_{\\rm opt}|r,L)$ of the optimal path length $\\ell_{\\rm opt}$, and find for $r\\ll L$ a power law decay with $\\ell_{\\rm opt}$, characterized by exponent $g_{\\rm opt}$. We determine the scaling form of $P(\\ell_{\\rm opt}|r,L)$ in two- and three-dimensional","authors_text":"Eduardo L\\'opez, H. Eugene Stanley, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-10-06T01:49:40Z","title":"Possible Connection between the Optimal Path and Flow in Percolation Clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0510127","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:eaaa04bb1d73544856b9606d9f5a0d4bae44d1161818aa5e233a7229c25b31a7","target":"record","created_at":"2026-05-18T01:08:57Z","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":"9cc930b78b6f88dc0377eec6dc29a718f314bdb79eae546605ebcfa771261ece","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-10-06T01:49:40Z","title_canon_sha256":"758d4c077657176da81f0f2a67ab1a7f1dbc78d11868a57637e488d4ecf06bde"},"schema_version":"1.0","source":{"id":"cond-mat/0510127","kind":"arxiv","version":1}},"canonical_sha256":"6b988f1daf143c1d620144346f32a9b74e61a2415706c11f71fde026744ddad9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b988f1daf143c1d620144346f32a9b74e61a2415706c11f71fde026744ddad9","first_computed_at":"2026-05-18T01:08:57.980460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:57.980460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ne+mfrMGh3mq1Fg/rtPWLr/EeWvhRE1XxtmqQMVy6jnVBsRqWcfpOA8CUtXbNF3hJWHv7vE5unGGmR7sFDvkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:57.980951Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0510127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eaaa04bb1d73544856b9606d9f5a0d4bae44d1161818aa5e233a7229c25b31a7","sha256:d047f1c46885343fe88c107574fa588ede8694bebfd3d34447d42278365c1682"],"state_sha256":"d442e575d03e6186c3e2b9335c83d5ea58e8f485ab7aff0aeaecd619f0acbafc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MFZj3ETzV2TO6UvuYQ63OF9eCFzgzto4quqLljQozujH9u5q5bujR4pkTMf4aGniCSLU1/7VxrPwNyFO0NFhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:48:18.842121Z","bundle_sha256":"510112fb4a853404b2d711d2c77cff1711bc7ec613d4aee71b2dcabfe4d512e2"}}