{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ADODUAB6FN4GRHFOCKTUTR4NYG","short_pith_number":"pith:ADODUAB6","canonical_record":{"source":{"id":"1603.04473","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-03-14T21:03:27Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"f10704d23018c5ffaf42adca3b10bfa03a90baff6cf1648ab852ba413e192c02","abstract_canon_sha256":"835e3f21580529aca276933d2df19554c0fb81b60aaebd0bebe1b1943be1e093"},"schema_version":"1.0"},"canonical_sha256":"00dc3a003e2b78689cae12a749c78dc192802ea9dfe4b64fbb492347ac2b7bf7","source":{"kind":"arxiv","id":"1603.04473","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04473","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04473v2","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04473","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"ADODUAB6FN4G","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ADODUAB6FN4GRHFO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ADODUAB6","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ADODUAB6FN4GRHFOCKTUTR4NYG","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04473","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-03-14T21:03:27Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"f10704d23018c5ffaf42adca3b10bfa03a90baff6cf1648ab852ba413e192c02","abstract_canon_sha256":"835e3f21580529aca276933d2df19554c0fb81b60aaebd0bebe1b1943be1e093"},"schema_version":"1.0"},"canonical_sha256":"00dc3a003e2b78689cae12a749c78dc192802ea9dfe4b64fbb492347ac2b7bf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:24.988244Z","signature_b64":"lEbbFVokxnnY3UltsByaNvmVlsx726u66fckUv7BvUi8gACoXdAM0OlA2/3YMFabpRJFKk6RDLe2c9QTRi9nDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00dc3a003e2b78689cae12a749c78dc192802ea9dfe4b64fbb492347ac2b7bf7","last_reissued_at":"2026-05-18T01:12:24.987911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:24.987911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04473","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FfLsWaHsFk+mL1cawEY7tWtnj+5yQOQ/baCmRmjAijGIELkLm313mGyMQ/axCpxQ6hz644qKn8j7PuHwJMbOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:29:48.755943Z"},"content_sha256":"1c922fe3fd2f87c04ee56e21aec824c454619a9ac93eecc0b564261399db0652","schema_version":"1.0","event_id":"sha256:1c922fe3fd2f87c04ee56e21aec824c454619a9ac93eecc0b564261399db0652"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ADODUAB6FN4GRHFOCKTUTR4NYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distance distribution in configuration model networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Eytan Katzav, Mor Nitzan, Ofer Biham, Reimer K\\\"uhn","submitted_at":"2016-03-14T21:03:27Z","abstract_excerpt":"We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial and power-law degree distributions. The mean, mode and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illumin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04473","kind":"arxiv","version":2},"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":"2026-05-18T01:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQVQX52IXV0p9zTzBJt9IsBSwsOGxP9j5csx/keGEN4GDPUHtxp5R7ILOCCIO1M4X8Ht5BvHQGpAnTYY8nEEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:29:48.756285Z"},"content_sha256":"93462d72dc1cbf90d84b7fd62c4ea44f6ad4ed9f6c61009e5bec4f606ce6b685","schema_version":"1.0","event_id":"sha256:93462d72dc1cbf90d84b7fd62c4ea44f6ad4ed9f6c61009e5bec4f606ce6b685"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ADODUAB6FN4GRHFOCKTUTR4NYG/bundle.json","state_url":"https://pith.science/pith/ADODUAB6FN4GRHFOCKTUTR4NYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ADODUAB6FN4GRHFOCKTUTR4NYG/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":"2026-05-28T01:29:48Z","links":{"resolver":"https://pith.science/pith/ADODUAB6FN4GRHFOCKTUTR4NYG","bundle":"https://pith.science/pith/ADODUAB6FN4GRHFOCKTUTR4NYG/bundle.json","state":"https://pith.science/pith/ADODUAB6FN4GRHFOCKTUTR4NYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ADODUAB6FN4GRHFOCKTUTR4NYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ADODUAB6FN4GRHFOCKTUTR4NYG","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":"835e3f21580529aca276933d2df19554c0fb81b60aaebd0bebe1b1943be1e093","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-03-14T21:03:27Z","title_canon_sha256":"f10704d23018c5ffaf42adca3b10bfa03a90baff6cf1648ab852ba413e192c02"},"schema_version":"1.0","source":{"id":"1603.04473","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04473","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04473v2","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04473","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"ADODUAB6FN4G","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ADODUAB6FN4GRHFO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ADODUAB6","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:93462d72dc1cbf90d84b7fd62c4ea44f6ad4ed9f6c61009e5bec4f606ce6b685","target":"graph","created_at":"2026-05-18T01:12:24Z","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 present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial and power-law degree distributions. The mean, mode and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illumin","authors_text":"Eytan Katzav, Mor Nitzan, Ofer Biham, Reimer K\\\"uhn","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-03-14T21:03:27Z","title":"Distance distribution in configuration model networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04473","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":"sha256:1c922fe3fd2f87c04ee56e21aec824c454619a9ac93eecc0b564261399db0652","target":"record","created_at":"2026-05-18T01:12:24Z","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":"835e3f21580529aca276933d2df19554c0fb81b60aaebd0bebe1b1943be1e093","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-03-14T21:03:27Z","title_canon_sha256":"f10704d23018c5ffaf42adca3b10bfa03a90baff6cf1648ab852ba413e192c02"},"schema_version":"1.0","source":{"id":"1603.04473","kind":"arxiv","version":2}},"canonical_sha256":"00dc3a003e2b78689cae12a749c78dc192802ea9dfe4b64fbb492347ac2b7bf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00dc3a003e2b78689cae12a749c78dc192802ea9dfe4b64fbb492347ac2b7bf7","first_computed_at":"2026-05-18T01:12:24.987911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:24.987911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lEbbFVokxnnY3UltsByaNvmVlsx726u66fckUv7BvUi8gACoXdAM0OlA2/3YMFabpRJFKk6RDLe2c9QTRi9nDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:24.988244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04473","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c922fe3fd2f87c04ee56e21aec824c454619a9ac93eecc0b564261399db0652","sha256:93462d72dc1cbf90d84b7fd62c4ea44f6ad4ed9f6c61009e5bec4f606ce6b685"],"state_sha256":"244bce8e7a7febb786d731a073f2e2b6de607ab2a150e3df9ea554afc4e9a891"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0T+TYz5fdFR7qEoRmmfe6Gqyd8PydchmWkTdll7xsfDMaYchm3io4NXtul3ZSBaabokq4xJFH4IOLuMiFoObBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:29:48.758591Z","bundle_sha256":"4bba183614be5e3fad1c3367cdfba9dd9f998de30efad1c14e561f0b5564d79f"}}