{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UOV6LM23HA5FTAIMJLEGGVEBFU","short_pith_number":"pith:UOV6LM23","schema_version":"1.0","canonical_sha256":"a3abe5b35b383a59810c4ac86354812d0e7d80e4a9d0a9686704ebb7c61d06c6","source":{"kind":"arxiv","id":"1808.08140","version":2},"attestation_state":"computed","paper":{"title":"Simply Generated Unrooted Plane Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Benedikt Stufler, Leon Ramzews","submitted_at":"2018-08-24T13:54:19Z","abstract_excerpt":"We study random unrooted plane trees with $n$ vertices sampled according to the weights corresponding to the vertex-degrees. Our main result shows that if the generating series of the weights has positive radius of convergence, then this model of random trees may be approximated geometrically by a Galton--Watson tree conditioned on having a large random size.\n  This implies that a variety of results for the well-studied planted case also hold for unrooted trees, including Gromov--Hausdorff--Prokhorov scaling limits, tail-bounds for the diameter, distributional graph limits, and limits for the "},"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":"1808.08140","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-24T13:54:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"11c10088613d9a38e34d8b47677a78b33645c86c3b2a067543ee8795c6c6760f","abstract_canon_sha256":"c10b8934eb6fab4ccd2b7f41b20fc370abae2cc469b3ca1b1534cf9dc253defd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:45.073977Z","signature_b64":"IDsRKHeOjREDIMg+p2gkKu5burSzbVjsTZjgFJ6dnI+8aXVgAsl0xBWZ0VG7yDerzbnzT5Xp+IrOqrxqhc/EAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3abe5b35b383a59810c4ac86354812d0e7d80e4a9d0a9686704ebb7c61d06c6","last_reissued_at":"2026-05-18T00:05:45.073280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:45.073280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simply Generated Unrooted Plane Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Benedikt Stufler, Leon Ramzews","submitted_at":"2018-08-24T13:54:19Z","abstract_excerpt":"We study random unrooted plane trees with $n$ vertices sampled according to the weights corresponding to the vertex-degrees. Our main result shows that if the generating series of the weights has positive radius of convergence, then this model of random trees may be approximated geometrically by a Galton--Watson tree conditioned on having a large random size.\n  This implies that a variety of results for the well-studied planted case also hold for unrooted trees, including Gromov--Hausdorff--Prokhorov scaling limits, tail-bounds for the diameter, distributional graph limits, and limits for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08140","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":"1808.08140","created_at":"2026-05-18T00:05:45.073412+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.08140v2","created_at":"2026-05-18T00:05:45.073412+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08140","created_at":"2026-05-18T00:05:45.073412+00:00"},{"alias_kind":"pith_short_12","alias_value":"UOV6LM23HA5F","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UOV6LM23HA5FTAIM","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UOV6LM23","created_at":"2026-05-18T12:32:56.356000+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/UOV6LM23HA5FTAIMJLEGGVEBFU","json":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU.json","graph_json":"https://pith.science/api/pith-number/UOV6LM23HA5FTAIMJLEGGVEBFU/graph.json","events_json":"https://pith.science/api/pith-number/UOV6LM23HA5FTAIMJLEGGVEBFU/events.json","paper":"https://pith.science/paper/UOV6LM23"},"agent_actions":{"view_html":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU","download_json":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU.json","view_paper":"https://pith.science/paper/UOV6LM23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.08140&json=true","fetch_graph":"https://pith.science/api/pith-number/UOV6LM23HA5FTAIMJLEGGVEBFU/graph.json","fetch_events":"https://pith.science/api/pith-number/UOV6LM23HA5FTAIMJLEGGVEBFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU/action/storage_attestation","attest_author":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU/action/author_attestation","sign_citation":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU/action/citation_signature","submit_replication":"https://pith.science/pith/UOV6LM23HA5FTAIMJLEGGVEBFU/action/replication_record"}},"created_at":"2026-05-18T00:05:45.073412+00:00","updated_at":"2026-05-18T00:05:45.073412+00:00"}