{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Q4TMKDCFGIMOILOC4HWJXJOZ2T","short_pith_number":"pith:Q4TMKDCF","schema_version":"1.0","canonical_sha256":"8726c50c453218e42dc2e1ec9ba5d9d4cb87b9d33490e19aab5084b9027343a3","source":{"kind":"arxiv","id":"1506.01091","version":1},"attestation_state":"computed","paper":{"title":"Recovering a tree from the lengths of subtrees spanned by a randomly chosen sequence of leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Daniel Lanoue, Steven N. Evans","submitted_at":"2015-06-03T00:29:38Z","abstract_excerpt":"Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \\le k \\le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, \"Can $T$ be identified (up to isomorphism) by the joint probability distribution of the random vector $(W_2, \\ldots, W_n)$?\" We show that if $T$ is known {\\em a priori} to belong to one of various families of edge-weighted trees, then the answer is, \"Yes.\" These families include the edge-weighted trees with edge-weights in general position, the ultrametric edge-weighted "},"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":"1506.01091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-03T00:29:38Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"013d41f7d0e6322fc537df827fe6218062277283e0530b425738e6f4c75f12b0","abstract_canon_sha256":"56af882f0f104d903301df980c4de5d59bcd6a82733f1d57dbcc5722f02a211f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:26.423095Z","signature_b64":"/ejDcnXPCMAorc5guxkMMOdm+OlgWBVXdOgpBnALFPeVXwU22E9DTwzgB4UnqTrCdZOCr3DiPxP2lY9Md1UPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8726c50c453218e42dc2e1ec9ba5d9d4cb87b9d33490e19aab5084b9027343a3","last_reissued_at":"2026-05-18T01:58:26.422641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:26.422641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recovering a tree from the lengths of subtrees spanned by a randomly chosen sequence of leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Daniel Lanoue, Steven N. Evans","submitted_at":"2015-06-03T00:29:38Z","abstract_excerpt":"Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \\le k \\le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, \"Can $T$ be identified (up to isomorphism) by the joint probability distribution of the random vector $(W_2, \\ldots, W_n)$?\" We show that if $T$ is known {\\em a priori} to belong to one of various families of edge-weighted trees, then the answer is, \"Yes.\" These families include the edge-weighted trees with edge-weights in general position, the ultrametric edge-weighted "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01091","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":"1506.01091","created_at":"2026-05-18T01:58:26.422717+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01091v1","created_at":"2026-05-18T01:58:26.422717+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01091","created_at":"2026-05-18T01:58:26.422717+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q4TMKDCFGIMO","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q4TMKDCFGIMOILOC","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q4TMKDCF","created_at":"2026-05-18T12:29:37.295048+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/Q4TMKDCFGIMOILOC4HWJXJOZ2T","json":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T.json","graph_json":"https://pith.science/api/pith-number/Q4TMKDCFGIMOILOC4HWJXJOZ2T/graph.json","events_json":"https://pith.science/api/pith-number/Q4TMKDCFGIMOILOC4HWJXJOZ2T/events.json","paper":"https://pith.science/paper/Q4TMKDCF"},"agent_actions":{"view_html":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T","download_json":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T.json","view_paper":"https://pith.science/paper/Q4TMKDCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01091&json=true","fetch_graph":"https://pith.science/api/pith-number/Q4TMKDCFGIMOILOC4HWJXJOZ2T/graph.json","fetch_events":"https://pith.science/api/pith-number/Q4TMKDCFGIMOILOC4HWJXJOZ2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T/action/storage_attestation","attest_author":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T/action/author_attestation","sign_citation":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T/action/citation_signature","submit_replication":"https://pith.science/pith/Q4TMKDCFGIMOILOC4HWJXJOZ2T/action/replication_record"}},"created_at":"2026-05-18T01:58:26.422717+00:00","updated_at":"2026-05-18T01:58:26.422717+00:00"}