{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:I52BVVQDHY35RTCWXULF5NMYZW","short_pith_number":"pith:I52BVVQD","schema_version":"1.0","canonical_sha256":"47741ad6033e37d8cc56bd165eb598cd85e6b4726309e9cc1ce9df5a0653629e","source":{"kind":"arxiv","id":"cs/0605019","version":1},"attestation_state":"computed","paper":{"title":"The Distribution of Patterns in Random Trees","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fr\\'ed\\'eric Chyzak (INRIA Rocquencourt), Gerard Kok, Michael Drmota, Thomas Klausner","submitted_at":"2006-05-05T09:31:01Z","abstract_excerpt":"Let $T\\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to infinity of the number of occurrences of $M$ as an induced subtree is asymptotically normal with mean value and variance asymptotically equivalent to $\\mu n$ and $\\sigma^2n$, respectively, where the constants $\\mu>0$ and $\\sigma\\ge 0$ are computable."},"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":"cs/0605019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.DM","submitted_at":"2006-05-05T09:31:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fe1179f2355a791550d4a2e469bcce29d328655ef0566d69b88dadfe96754ed2","abstract_canon_sha256":"3fcac9bbd59146d6d3e187970d87adaebc883d48fa540aaf71fc2b707dea21c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:54.786112Z","signature_b64":"WEfomTuE9L6ZXkZ4gdDo43gj+R7J2Hf7tV488qLRqs1rJmNQpf9qsbMfbC7a4B/e1UvBZoCI/El+6ViJcRD0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47741ad6033e37d8cc56bd165eb598cd85e6b4726309e9cc1ce9df5a0653629e","last_reissued_at":"2026-05-18T01:08:54.785431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:54.785431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Distribution of Patterns in Random Trees","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fr\\'ed\\'eric Chyzak (INRIA Rocquencourt), Gerard Kok, Michael Drmota, Thomas Klausner","submitted_at":"2006-05-05T09:31:01Z","abstract_excerpt":"Let $T\\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to infinity of the number of occurrences of $M$ as an induced subtree is asymptotically normal with mean value and variance asymptotically equivalent to $\\mu n$ and $\\sigma^2n$, respectively, where the constants $\\mu>0$ and $\\sigma\\ge 0$ are computable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0605019","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":"cs/0605019","created_at":"2026-05-18T01:08:54.785554+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0605019v1","created_at":"2026-05-18T01:08:54.785554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0605019","created_at":"2026-05-18T01:08:54.785554+00:00"},{"alias_kind":"pith_short_12","alias_value":"I52BVVQDHY35","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"I52BVVQDHY35RTCW","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"I52BVVQD","created_at":"2026-05-18T12:25:53.939244+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/I52BVVQDHY35RTCWXULF5NMYZW","json":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW.json","graph_json":"https://pith.science/api/pith-number/I52BVVQDHY35RTCWXULF5NMYZW/graph.json","events_json":"https://pith.science/api/pith-number/I52BVVQDHY35RTCWXULF5NMYZW/events.json","paper":"https://pith.science/paper/I52BVVQD"},"agent_actions":{"view_html":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW","download_json":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW.json","view_paper":"https://pith.science/paper/I52BVVQD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0605019&json=true","fetch_graph":"https://pith.science/api/pith-number/I52BVVQDHY35RTCWXULF5NMYZW/graph.json","fetch_events":"https://pith.science/api/pith-number/I52BVVQDHY35RTCWXULF5NMYZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW/action/storage_attestation","attest_author":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW/action/author_attestation","sign_citation":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW/action/citation_signature","submit_replication":"https://pith.science/pith/I52BVVQDHY35RTCWXULF5NMYZW/action/replication_record"}},"created_at":"2026-05-18T01:08:54.785554+00:00","updated_at":"2026-05-18T01:08:54.785554+00:00"}