{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GAOOJO6UPOM2NTKYVN2YY34W43","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":"6249a9c1c92263128091291d6740563f8b44a098104364759ca152932a213132","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T20:32:37Z","title_canon_sha256":"105ac23c3d49e28e8c9c48c8bccf10464bb72887325e94cc6d5f7475b3397d5c"},"schema_version":"1.0","source":{"id":"1301.1664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1664","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1664v1","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1664","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"GAOOJO6UPOM2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GAOOJO6UPOM2NTKY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GAOOJO6U","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:2ac4855d9fb3bcf0b9a31b836ab351e869a89349690470bd5dfde18ced324e1b","target":"graph","created_at":"2026-05-18T03:36:56Z","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":"Consider the minimum spanning tree (MST) of the complete graph with n vertices, when edges are assigned independent random weights. Endow this tree with the graph distance renormalized by n^{1/3} and with the uniform measure on its vertices. We show that the resulting space converges in distribution, as n tends to infinity, to a random measured metric space in the Gromov-Hausdorff-Prokhorov topology. We additionally show that the limit is a random binary R-tree and has Minkowski dimension 3 almost surely. In particular, its law is mutually singular with that of the Brownian continuum random tr","authors_text":"Christina Goldschmidt, Gr\\'egory Miermont, Louigi Addario-Berry, Nicolas Broutin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T20:32:37Z","title":"The scaling limit of the minimum spanning tree of the complete graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1664","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":"sha256:0cde971ab5b3a4a1ea980a4c8875ed52f3993fde1293af713fce7bdf4a760434","target":"record","created_at":"2026-05-18T03:36:56Z","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":"6249a9c1c92263128091291d6740563f8b44a098104364759ca152932a213132","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T20:32:37Z","title_canon_sha256":"105ac23c3d49e28e8c9c48c8bccf10464bb72887325e94cc6d5f7475b3397d5c"},"schema_version":"1.0","source":{"id":"1301.1664","kind":"arxiv","version":1}},"canonical_sha256":"301ce4bbd47b99a6cd58ab758c6f96e6e238490011f287273071b782ab1caa67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"301ce4bbd47b99a6cd58ab758c6f96e6e238490011f287273071b782ab1caa67","first_computed_at":"2026-05-18T03:36:56.967953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:56.967953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SRYuljW0TxZ/NUfFO/wD+0ZK+QpIh4ttHSTZm6uvQyJrYG+pEvMuavhlWL944IPeaQreh2M2vEFYD2+gGrKbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:56.968472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cde971ab5b3a4a1ea980a4c8875ed52f3993fde1293af713fce7bdf4a760434","sha256:2ac4855d9fb3bcf0b9a31b836ab351e869a89349690470bd5dfde18ced324e1b"],"state_sha256":"8e3b8dee672522714872ec1f47dc45fd05a64ad3f8594439c8fb657ad7b30af7"}