{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:J6B4UMXEFPVZ7SKZAJRV7HLJMF","short_pith_number":"pith:J6B4UMXE","canonical_record":{"source":{"id":"1211.4569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-19T20:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"9f2525ab2af24f92e12821f83a4002048bd2e426f48d234ca34e1ced03913bfb","abstract_canon_sha256":"e2d880b3e3b871e304090fd1d2faf3ad40880e237f13782a7f185008724976c3"},"schema_version":"1.0"},"canonical_sha256":"4f83ca32e42beb9fc95902635f9d69615436ceee7d3d8c81244e979859dd4e5f","source":{"kind":"arxiv","id":"1211.4569","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4569","created_at":"2026-05-18T01:53:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4569v1","created_at":"2026-05-18T01:53:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4569","created_at":"2026-05-18T01:53:02Z"},{"alias_kind":"pith_short_12","alias_value":"J6B4UMXEFPVZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"J6B4UMXEFPVZ7SKZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"J6B4UMXE","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:J6B4UMXEFPVZ7SKZAJRV7HLJMF","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-19T20:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"9f2525ab2af24f92e12821f83a4002048bd2e426f48d234ca34e1ced03913bfb","abstract_canon_sha256":"e2d880b3e3b871e304090fd1d2faf3ad40880e237f13782a7f185008724976c3"},"schema_version":"1.0"},"canonical_sha256":"4f83ca32e42beb9fc95902635f9d69615436ceee7d3d8c81244e979859dd4e5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:02.809655Z","signature_b64":"m5LBBNpG55n86jITRKGKeBxA71MD/TNeDAbABaf2uSEWLxAWz/VDhXmp5eB2UvTrTmWdmwRbN1ww0PP9jTpgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f83ca32e42beb9fc95902635f9d69615436ceee7d3d8c81244e979859dd4e5f","last_reissued_at":"2026-05-18T01:53:02.808951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:02.808951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4569","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":"2026-05-18T01:53:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVr7MhLill1Xh8PW7144oxJ5FkLpSJahD6bvPX7Eqgo2FoJcDUwBtmcR9/KekBWdoVEsmnAZw4C8Mtv0FSkwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:34:34.031915Z"},"content_sha256":"3efadfaaf16e46db792641570c39f34b72adbe382d8bfc870b48abbc91e59314","schema_version":"1.0","event_id":"sha256:3efadfaaf16e46db792641570c39f34b72adbe382d8bfc870b48abbc91e59314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:J6B4UMXEFPVZ7SKZAJRV7HLJMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Short paths for first passage percolation on the complete graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesca R. Nardi, Jesse Goodman, Maren Eckhoff, Remco van der Hofstad","submitted_at":"2012-11-19T20:58:42Z","abstract_excerpt":"We study the complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W_n and the number of edges H_n of the minimal weight path between two distinct vertices in the weak disorder regime. We establish novel and simple first and second moment methods using path counting to derive first order asymptotics for the considered quantities. Our results are stated in terms of a sequence of parameters (s_n) that quantifies the extreme-value behaviour of the edge weights, and that describes different universality c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4569","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":"2026-05-18T01:53:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yg0NENM4lQnJpnt56NMF4neJFqSeZQtc2lhQuHUXWLXxLf200EIpRAozSFuY30znUajRresovtLPZ/DlrTKSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:34:34.032559Z"},"content_sha256":"9e613356efd00498ed695bf5460b16e0720ef1868c514dbcc1fcbaa85cb9c056","schema_version":"1.0","event_id":"sha256:9e613356efd00498ed695bf5460b16e0720ef1868c514dbcc1fcbaa85cb9c056"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF/bundle.json","state_url":"https://pith.science/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF/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":"2026-06-08T10:34:34Z","links":{"resolver":"https://pith.science/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF","bundle":"https://pith.science/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF/bundle.json","state":"https://pith.science/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6B4UMXEFPVZ7SKZAJRV7HLJMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J6B4UMXEFPVZ7SKZAJRV7HLJMF","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":"e2d880b3e3b871e304090fd1d2faf3ad40880e237f13782a7f185008724976c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-19T20:58:42Z","title_canon_sha256":"9f2525ab2af24f92e12821f83a4002048bd2e426f48d234ca34e1ced03913bfb"},"schema_version":"1.0","source":{"id":"1211.4569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4569","created_at":"2026-05-18T01:53:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4569v1","created_at":"2026-05-18T01:53:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4569","created_at":"2026-05-18T01:53:02Z"},{"alias_kind":"pith_short_12","alias_value":"J6B4UMXEFPVZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"J6B4UMXEFPVZ7SKZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"J6B4UMXE","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:9e613356efd00498ed695bf5460b16e0720ef1868c514dbcc1fcbaa85cb9c056","target":"graph","created_at":"2026-05-18T01:53:02Z","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 complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W_n and the number of edges H_n of the minimal weight path between two distinct vertices in the weak disorder regime. We establish novel and simple first and second moment methods using path counting to derive first order asymptotics for the considered quantities. Our results are stated in terms of a sequence of parameters (s_n) that quantifies the extreme-value behaviour of the edge weights, and that describes different universality c","authors_text":"Francesca R. Nardi, Jesse Goodman, Maren Eckhoff, Remco van der Hofstad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-19T20:58:42Z","title":"Short paths for first passage percolation on the complete graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4569","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":"sha256:3efadfaaf16e46db792641570c39f34b72adbe382d8bfc870b48abbc91e59314","target":"record","created_at":"2026-05-18T01:53:02Z","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":"e2d880b3e3b871e304090fd1d2faf3ad40880e237f13782a7f185008724976c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-19T20:58:42Z","title_canon_sha256":"9f2525ab2af24f92e12821f83a4002048bd2e426f48d234ca34e1ced03913bfb"},"schema_version":"1.0","source":{"id":"1211.4569","kind":"arxiv","version":1}},"canonical_sha256":"4f83ca32e42beb9fc95902635f9d69615436ceee7d3d8c81244e979859dd4e5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f83ca32e42beb9fc95902635f9d69615436ceee7d3d8c81244e979859dd4e5f","first_computed_at":"2026-05-18T01:53:02.808951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:02.808951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m5LBBNpG55n86jITRKGKeBxA71MD/TNeDAbABaf2uSEWLxAWz/VDhXmp5eB2UvTrTmWdmwRbN1ww0PP9jTpgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:02.809655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3efadfaaf16e46db792641570c39f34b72adbe382d8bfc870b48abbc91e59314","sha256:9e613356efd00498ed695bf5460b16e0720ef1868c514dbcc1fcbaa85cb9c056"],"state_sha256":"a29f9c87ca2e9c63368880c4c99473e2c93da22a4ff691313a82ebed6d92f82e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ytb7rxZibdLmhUtI4n+XQRPnt3myUjAD1hc9jLZRxR7Way5UwNgn2atkKoTNuajt4mLCPtM7+ROVtiq1uR/xBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:34:34.036855Z","bundle_sha256":"03dea73e779b96ead1039953caef949f1ebd8e9b32dff3e0f97b9af598518b06"}}