{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3SFMF24Z6FKOAEGOYD5YAQQATT","short_pith_number":"pith:3SFMF24Z","schema_version":"1.0","canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","source":{"kind":"arxiv","id":"1605.05191","version":1},"attestation_state":"computed","paper":{"title":"Graph limits of random graphs from a subset of connected $k$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Benedikt Stufler, Emma Yu Jin, Michael Drmota","submitted_at":"2016-05-17T14:40:13Z","abstract_excerpt":"For any set $\\Omega$ of non-negative integers such that $\\{0,1\\}\\subseteq \\Omega$ and $\\{0,1\\}\\ne \\Omega$, we consider a random $\\Omega$-$k$-tree ${\\sf G}_{n,k}$ that is uniformly selected from all connected $k$-trees of $(n+k)$ vertices where the number of $(k+1)$-cliques that contain any fixed $k$-clique belongs to $\\Omega$. We prove that ${\\sf G}_{n,k}$, scaled by $(kH_{k}\\sigma_{\\Omega})/(2\\sqrt{n})$ where $H_{k}$ is the $k$-th Harmonic number and $\\sigma_{\\Omega}>0$, converges to the Continuum Random Tree $\\mathcal{T}_{{\\sf e}}$. Furthermore, we prove the local convergence of the rooted r"},"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":"1605.05191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-17T14:40:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3a4da0374b6609ab434901695a8c70abe90bf0e28bd43d37906bbcb8677500fa","abstract_canon_sha256":"0d63523568e182b117ad69c9587884d99e4e658b4142f300941589a43e6c917f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:37.142634Z","signature_b64":"E+Pux2Qvh2QTJ617dFD3jzGQdtTl0MvnuLw/4G1gFCIFl0273F67s+yryLTs3tjDvxfq56wo1pI5WKDA4mNDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","last_reissued_at":"2026-05-18T01:14:37.141863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:37.141863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph limits of random graphs from a subset of connected $k$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Benedikt Stufler, Emma Yu Jin, Michael Drmota","submitted_at":"2016-05-17T14:40:13Z","abstract_excerpt":"For any set $\\Omega$ of non-negative integers such that $\\{0,1\\}\\subseteq \\Omega$ and $\\{0,1\\}\\ne \\Omega$, we consider a random $\\Omega$-$k$-tree ${\\sf G}_{n,k}$ that is uniformly selected from all connected $k$-trees of $(n+k)$ vertices where the number of $(k+1)$-cliques that contain any fixed $k$-clique belongs to $\\Omega$. We prove that ${\\sf G}_{n,k}$, scaled by $(kH_{k}\\sigma_{\\Omega})/(2\\sqrt{n})$ where $H_{k}$ is the $k$-th Harmonic number and $\\sigma_{\\Omega}>0$, converges to the Continuum Random Tree $\\mathcal{T}_{{\\sf e}}$. Furthermore, we prove the local convergence of the rooted r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05191","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":"1605.05191","created_at":"2026-05-18T01:14:37.142001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05191v1","created_at":"2026-05-18T01:14:37.142001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05191","created_at":"2026-05-18T01:14:37.142001+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SFMF24Z6FKO","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SFMF24Z6FKOAEGO","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SFMF24Z","created_at":"2026-05-18T12:29:58.707656+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/3SFMF24Z6FKOAEGOYD5YAQQATT","json":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT.json","graph_json":"https://pith.science/api/pith-number/3SFMF24Z6FKOAEGOYD5YAQQATT/graph.json","events_json":"https://pith.science/api/pith-number/3SFMF24Z6FKOAEGOYD5YAQQATT/events.json","paper":"https://pith.science/paper/3SFMF24Z"},"agent_actions":{"view_html":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT","download_json":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT.json","view_paper":"https://pith.science/paper/3SFMF24Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05191&json=true","fetch_graph":"https://pith.science/api/pith-number/3SFMF24Z6FKOAEGOYD5YAQQATT/graph.json","fetch_events":"https://pith.science/api/pith-number/3SFMF24Z6FKOAEGOYD5YAQQATT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/action/storage_attestation","attest_author":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/action/author_attestation","sign_citation":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/action/citation_signature","submit_replication":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/action/replication_record"}},"created_at":"2026-05-18T01:14:37.142001+00:00","updated_at":"2026-05-18T01:14:37.142001+00:00"}