{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3UXP2RVNIWB7NYHESTYWHQWYXA","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":"be911cf08d201101cec3c5fef2d1d8db2f82d5f398b636737f800153f510e44d","cross_cats_sorted":["cs.CY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-07-30T16:58:43Z","title_canon_sha256":"ad9b8162435b28be83e625c0931a78f30740dc8d160dc2535c962eddceebd402"},"schema_version":"1.0","source":{"id":"1207.6994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6994","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6994v1","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6994","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"3UXP2RVNIWB7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3UXP2RVNIWB7NYHE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3UXP2RVN","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:d4caba235728d259eba553086bf55cfbec9c9985b4e76d4ebe91d219afc2c32f","target":"graph","created_at":"2026-05-18T01:11:21Z","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 consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are not transient and we consider various approaches to computing the probability of a given length walk.One approach is to label nodes according to both their total degree and the number of links connected to leaf nodes, and as a byproduct we compute the probability of a random node of a scale free network having such a label.","authors_text":"David Lancaster","cross_cats":["cs.CY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-07-30T16:58:43Z","title":"Random Walks between Leaves of Random Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6994","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:ba7d2b978f9ace55a46d6032b05d37515f7ae89c4040323ee86b70c21f6e7d8f","target":"record","created_at":"2026-05-18T01:11:21Z","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":"be911cf08d201101cec3c5fef2d1d8db2f82d5f398b636737f800153f510e44d","cross_cats_sorted":["cs.CY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-07-30T16:58:43Z","title_canon_sha256":"ad9b8162435b28be83e625c0931a78f30740dc8d160dc2535c962eddceebd402"},"schema_version":"1.0","source":{"id":"1207.6994","kind":"arxiv","version":1}},"canonical_sha256":"dd2efd46ad4583f6e0e494f163c2d8b80d7080bc4a08946fbd9895ee493b7e2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd2efd46ad4583f6e0e494f163c2d8b80d7080bc4a08946fbd9895ee493b7e2b","first_computed_at":"2026-05-18T01:11:21.993106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:21.993106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Po+qd5+8ZJelXP9vPYqVG9x64opaHG2rE/i4B19Qe36oOYm6adeWf2YPlRmmpwQiGi14swZGg7RJ95FJHTFlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:21.993628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba7d2b978f9ace55a46d6032b05d37515f7ae89c4040323ee86b70c21f6e7d8f","sha256:d4caba235728d259eba553086bf55cfbec9c9985b4e76d4ebe91d219afc2c32f"],"state_sha256":"054312855311c01a7a09c9e7bd258050467e7589011ebaacd2f5fa0f8d41da87"}