{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MXYBPJWTNLD4JDJL3SXGID7SEC","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":"28733a0422316fb0117d8fa213f2a1fb84543cc4d27d9d1267adb5bef49dcb36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-05T18:35:09Z","title_canon_sha256":"23a223b2cf5b922f53a9d6e8926e7d3aa51dd6410f1c29a7c806b9302dc0ab12"},"schema_version":"1.0","source":{"id":"1711.01635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01635","created_at":"2026-05-18T00:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01635v1","created_at":"2026-05-18T00:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01635","created_at":"2026-05-18T00:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"MXYBPJWTNLD4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MXYBPJWTNLD4JDJL","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MXYBPJWT","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:963e115a3a25bd06af5ae7197e39bb748fc6f45dd6adeaf88a3cda92e23603c5","target":"graph","created_at":"2026-05-18T00:07:11Z","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":"D. Wilson~\\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational ","authors_text":"A. Gaudilliere, C. Melot, F. Castell, L. Avena","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-05T18:35:09Z","title":"Random Forests and Networks Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01635","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":"sha256:8d4982ee4274188a6c8f88d3b3f8549e7a303fa4df3f1bf27fc2c97406cb3bbb","target":"record","created_at":"2026-05-18T00:07:11Z","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":"28733a0422316fb0117d8fa213f2a1fb84543cc4d27d9d1267adb5bef49dcb36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-05T18:35:09Z","title_canon_sha256":"23a223b2cf5b922f53a9d6e8926e7d3aa51dd6410f1c29a7c806b9302dc0ab12"},"schema_version":"1.0","source":{"id":"1711.01635","kind":"arxiv","version":1}},"canonical_sha256":"65f017a6d36ac7c48d2bdcae640ff220b419b9daf876028cce3cb2837a8a6cfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65f017a6d36ac7c48d2bdcae640ff220b419b9daf876028cce3cb2837a8a6cfa","first_computed_at":"2026-05-18T00:07:11.631584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:11.631584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O/W3XoW1j0GXkYcrkClXchcLQS4DNOtea5C3Dfr2m6nArDcUurCPBMFWO2PIUWMHn0HWi0MXu15JWKfttky8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:11.632198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d4982ee4274188a6c8f88d3b3f8549e7a303fa4df3f1bf27fc2c97406cb3bbb","sha256:963e115a3a25bd06af5ae7197e39bb748fc6f45dd6adeaf88a3cda92e23603c5"],"state_sha256":"e22f6c085241b85ef4f07b2d6e18286be3e564ea9c6374890c3bf15e781ccfe0"}