{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3GJST76FNV36N46TP4CVOGHD6F","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"24c29ec10669d9d4a1b8f75d81b9b29fa24330a4f8e1569539f94e5571b8f481","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-19T19:11:22Z","title_canon_sha256":"13a142a6dc3bcd53b5411f9442ffa0975e1267f6dc97114318574c74dee4acca"},"schema_version":"1.0","source":{"id":"1810.08655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08655","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08655v1","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08655","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"pith_short_12","alias_value":"3GJST76FNV36","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3GJST76FNV36N46T","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3GJST76F","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:ab125cffda3ba6e3a06277126acf1b13ca10da473aa64b44bb3ce8c6c85fb08d","target":"graph","created_at":"2026-05-18T00:02:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a tree $T$, the subtree polynomial of $T$ is the generating polynomial for the number of subtrees of $T$. We show that the complex roots of the subtree polynomial are contained in the disk $\\left\\{z\\in\\mathbb{C}\\colon\\ |z|\\leq 1+\\sqrt[3]{3}\\right\\}$, and that $K_{1,3}$ is the only tree whose subtree polynomial has a root on the boundary. We also prove that the closure of the collection of all real roots of subtree polynomials contains the interval $[-2,-1]$, while the intervals $(\\infty,-1-\\sqrt[3]{3})$, $[-1,0)$, and $(0,\\infty)$ are root-free.","authors_text":"Jason I. Brown, Lucas Mol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-19T19:11:22Z","title":"On the roots of the subtree polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08655","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f9e5ada7e76d0cb79566b15ccc5180e6dcfa63a04d5e4aded76ba331b60e7a9e","target":"record","created_at":"2026-05-18T00:02:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"24c29ec10669d9d4a1b8f75d81b9b29fa24330a4f8e1569539f94e5571b8f481","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-19T19:11:22Z","title_canon_sha256":"13a142a6dc3bcd53b5411f9442ffa0975e1267f6dc97114318574c74dee4acca"},"schema_version":"1.0","source":{"id":"1810.08655","kind":"arxiv","version":1}},"canonical_sha256":"d99329ffc56d77e6f3d37f055718e3f14d2771c171b1f7b94de483f171c01784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d99329ffc56d77e6f3d37f055718e3f14d2771c171b1f7b94de483f171c01784","first_computed_at":"2026-05-18T00:02:43.886813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:43.886813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vviUCFsN9FS7/ETOccrfgRdG7M+vLZx+ymn5v6nE6uecXJ4mTtm3YaiZ5K/DA9QxYfulxzaCEVjCimNpBBz2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:43.887332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9e5ada7e76d0cb79566b15ccc5180e6dcfa63a04d5e4aded76ba331b60e7a9e","sha256:ab125cffda3ba6e3a06277126acf1b13ca10da473aa64b44bb3ce8c6c85fb08d"],"state_sha256":"e76c9351d694862b7141bdb31943426b59f61e56623fed167241049a52e525d0"}