{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:G5HLEIYS6QIL6XLKJ4QHMASHYE","short_pith_number":"pith:G5HLEIYS","schema_version":"1.0","canonical_sha256":"374eb22312f410bf5d6a4f20760247c1377326528f8049142dba89e059b68d75","source":{"kind":"arxiv","id":"1301.1667","version":2},"attestation_state":"computed","paper":{"title":"The local weak limit of the minimum spanning tree of the complete graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Louigi Addario-Berry","submitted_at":"2013-01-08T20:36:32Z","abstract_excerpt":"Assign i.i.d. standard exponential edge weights to the edges of the complete graph K_n, and let M_n be the resulting minimum spanning tree. We show that M_n converges in the local weak sense (also called Aldous-Steele or Benjamini-Schramm convergence), to a random infinite tree M. The tree M may be viewed as the component containing the root in the wired minimum spanning forest of the Poisson-weighted infinite tree (PWIT). We describe a Markov process construction of M starting from the invasion percolation cluster on the PWIT. We then show that M has cubic volume growth, up to lower order flu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.1667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T20:36:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"64ef8be96908f2dc845be7f0cc76747a21524a2cb46eed021057747ab879c2da","abstract_canon_sha256":"1d1d69f918fc6416cfc69482e56fdda9c27b178088a6b42ee04d1410cb773df3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:35.875243Z","signature_b64":"rVP52RVj6T34u20FC2/jZGVTf+vRGbAraMv//3EK9aiWDMDn+44hqWU0jo2YyFl8wWxjVd6WDJATRca0oZxYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"374eb22312f410bf5d6a4f20760247c1377326528f8049142dba89e059b68d75","last_reissued_at":"2026-05-18T03:36:35.874525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:35.874525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The local weak limit of the minimum spanning tree of the complete graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Louigi Addario-Berry","submitted_at":"2013-01-08T20:36:32Z","abstract_excerpt":"Assign i.i.d. standard exponential edge weights to the edges of the complete graph K_n, and let M_n be the resulting minimum spanning tree. We show that M_n converges in the local weak sense (also called Aldous-Steele or Benjamini-Schramm convergence), to a random infinite tree M. The tree M may be viewed as the component containing the root in the wired minimum spanning forest of the Poisson-weighted infinite tree (PWIT). We describe a Markov process construction of M starting from the invasion percolation cluster on the PWIT. We then show that M has cubic volume growth, up to lower order flu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1667","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.1667","created_at":"2026-05-18T03:36:35.874640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.1667v2","created_at":"2026-05-18T03:36:35.874640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1667","created_at":"2026-05-18T03:36:35.874640+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5HLEIYS6QIL","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5HLEIYS6QIL6XLK","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5HLEIYS","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2410.16836","citing_title":"Local limits of random spanning trees in random environment","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2605.01444","citing_title":"From second moments to pairwise negative correlation: applications to minimal and uniform spanning trees","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE","json":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE.json","graph_json":"https://pith.science/api/pith-number/G5HLEIYS6QIL6XLKJ4QHMASHYE/graph.json","events_json":"https://pith.science/api/pith-number/G5HLEIYS6QIL6XLKJ4QHMASHYE/events.json","paper":"https://pith.science/paper/G5HLEIYS"},"agent_actions":{"view_html":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE","download_json":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE.json","view_paper":"https://pith.science/paper/G5HLEIYS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.1667&json=true","fetch_graph":"https://pith.science/api/pith-number/G5HLEIYS6QIL6XLKJ4QHMASHYE/graph.json","fetch_events":"https://pith.science/api/pith-number/G5HLEIYS6QIL6XLKJ4QHMASHYE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE/action/storage_attestation","attest_author":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE/action/author_attestation","sign_citation":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE/action/citation_signature","submit_replication":"https://pith.science/pith/G5HLEIYS6QIL6XLKJ4QHMASHYE/action/replication_record"}},"created_at":"2026-05-18T03:36:35.874640+00:00","updated_at":"2026-05-18T03:36:35.874640+00:00"}