{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GAOOJO6UPOM2NTKYVN2YY34W43","short_pith_number":"pith:GAOOJO6U","schema_version":"1.0","canonical_sha256":"301ce4bbd47b99a6cd58ab758c6f96e6e238490011f287273071b782ab1caa67","source":{"kind":"arxiv","id":"1301.1664","version":1},"attestation_state":"computed","paper":{"title":"The scaling 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":"Christina Goldschmidt, Gr\\'egory Miermont, Louigi Addario-Berry, Nicolas Broutin","submitted_at":"2013-01-08T20:32:37Z","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"},"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":"1301.1664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T20:32:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"105ac23c3d49e28e8c9c48c8bccf10464bb72887325e94cc6d5f7475b3397d5c","abstract_canon_sha256":"6249a9c1c92263128091291d6740563f8b44a098104364759ca152932a213132"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:56.968472Z","signature_b64":"SRYuljW0TxZ/NUfFO/wD+0ZK+QpIh4ttHSTZm6uvQyJrYG+pEvMuavhlWL944IPeaQreh2M2vEFYD2+gGrKbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"301ce4bbd47b99a6cd58ab758c6f96e6e238490011f287273071b782ab1caa67","last_reissued_at":"2026-05-18T03:36:56.967953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:56.967953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The scaling 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":"Christina Goldschmidt, Gr\\'egory Miermont, Louigi Addario-Berry, Nicolas Broutin","submitted_at":"2013-01-08T20:32:37Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1664","kind":"arxiv","version":1},"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":"1301.1664","created_at":"2026-05-18T03:36:56.968030+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.1664v1","created_at":"2026-05-18T03:36:56.968030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1664","created_at":"2026-05-18T03:36:56.968030+00:00"},{"alias_kind":"pith_short_12","alias_value":"GAOOJO6UPOM2","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GAOOJO6UPOM2NTKY","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GAOOJO6U","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43","json":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43.json","graph_json":"https://pith.science/api/pith-number/GAOOJO6UPOM2NTKYVN2YY34W43/graph.json","events_json":"https://pith.science/api/pith-number/GAOOJO6UPOM2NTKYVN2YY34W43/events.json","paper":"https://pith.science/paper/GAOOJO6U"},"agent_actions":{"view_html":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43","download_json":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43.json","view_paper":"https://pith.science/paper/GAOOJO6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.1664&json=true","fetch_graph":"https://pith.science/api/pith-number/GAOOJO6UPOM2NTKYVN2YY34W43/graph.json","fetch_events":"https://pith.science/api/pith-number/GAOOJO6UPOM2NTKYVN2YY34W43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43/action/storage_attestation","attest_author":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43/action/author_attestation","sign_citation":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43/action/citation_signature","submit_replication":"https://pith.science/pith/GAOOJO6UPOM2NTKYVN2YY34W43/action/replication_record"}},"created_at":"2026-05-18T03:36:56.968030+00:00","updated_at":"2026-05-18T03:36:56.968030+00:00"}