{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:ZPT7HMBOPNJ7DTCNTU6EKOWCDB","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":"ccbcebaa445ed03c6df605ea9302f108d6add303b2a41b6408f4fd33422b74b5","cross_cats_sorted":[],"license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-12-14T20:51:57Z","title_canon_sha256":"14b42344d7e71cb5c61b01fc36cecb29338c68f0cb8ca1a11d18219436b8b86e"},"schema_version":"1.0","source":{"id":"physics/0612148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0612148","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0612148v2","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0612148","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZPT7HMBOPNJ7","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZPT7HMBOPNJ7DTCN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZPT7HMBO","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:2dc285e643b8069f8407aad5e23990fbbd9740c4b35bdcd45deabf25a83ff8f8","target":"graph","created_at":"2026-05-18T03:46:45Z","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":"A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when a new node enters the network, it either connects to a randomly selected node, or to the j -ancestor of this selected node. The j -ancestor is found by following j links from the randomly selected node. The system is shown to undergo a transition to a phase where condensates develop. We also find analytical predictions for the height statistics and show nume","authors_text":"M. Ausloos, R. Lambiotte","cross_cats":[],"headline":"","license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-12-14T20:51:57Z","title":"Growing network with j-redirection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0612148","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":"sha256:56e5a61db44428c0b499e27b9ad980c45d7cfa9e9d59da7590af9654a53e63a5","target":"record","created_at":"2026-05-18T03:46:45Z","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":"ccbcebaa445ed03c6df605ea9302f108d6add303b2a41b6408f4fd33422b74b5","cross_cats_sorted":[],"license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-12-14T20:51:57Z","title_canon_sha256":"14b42344d7e71cb5c61b01fc36cecb29338c68f0cb8ca1a11d18219436b8b86e"},"schema_version":"1.0","source":{"id":"physics/0612148","kind":"arxiv","version":2}},"canonical_sha256":"cbe7f3b02e7b53f1cc4d9d3c453ac218579ffd96feddf4c64b57e2d1478cf740","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbe7f3b02e7b53f1cc4d9d3c453ac218579ffd96feddf4c64b57e2d1478cf740","first_computed_at":"2026-05-18T03:46:45.934354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:45.934354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ysmx1DSrpO83wCKIWFtFVBRn5jg0TA3FEqCXOmZxySIOFh4Tjsg1IsknRiQvS1IdRJbTHSD1jzL5XC3gV/FADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:45.935181Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0612148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56e5a61db44428c0b499e27b9ad980c45d7cfa9e9d59da7590af9654a53e63a5","sha256:2dc285e643b8069f8407aad5e23990fbbd9740c4b35bdcd45deabf25a83ff8f8"],"state_sha256":"9756ff10fe2fa2042492332d796b92115e099793524aabdb986d2577c99ca9a6"}