{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3GJST76FNV36N46TP4CVOGHD6F","short_pith_number":"pith:3GJST76F","canonical_record":{"source":{"id":"1810.08655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-19T19:11:22Z","cross_cats_sorted":[],"title_canon_sha256":"13a142a6dc3bcd53b5411f9442ffa0975e1267f6dc97114318574c74dee4acca","abstract_canon_sha256":"24c29ec10669d9d4a1b8f75d81b9b29fa24330a4f8e1569539f94e5571b8f481"},"schema_version":"1.0"},"canonical_sha256":"d99329ffc56d77e6f3d37f055718e3f14d2771c171b1f7b94de483f171c01784","source":{"kind":"arxiv","id":"1810.08655","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3GJST76FNV36N46TP4CVOGHD6F","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-19T19:11:22Z","cross_cats_sorted":[],"title_canon_sha256":"13a142a6dc3bcd53b5411f9442ffa0975e1267f6dc97114318574c74dee4acca","abstract_canon_sha256":"24c29ec10669d9d4a1b8f75d81b9b29fa24330a4f8e1569539f94e5571b8f481"},"schema_version":"1.0"},"canonical_sha256":"d99329ffc56d77e6f3d37f055718e3f14d2771c171b1f7b94de483f171c01784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:43.887332Z","signature_b64":"vviUCFsN9FS7/ETOccrfgRdG7M+vLZx+ymn5v6nE6uecXJ4mTtm3YaiZ5K/DA9QxYfulxzaCEVjCimNpBBz2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d99329ffc56d77e6f3d37f055718e3f14d2771c171b1f7b94de483f171c01784","last_reissued_at":"2026-05-18T00:02:43.886813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:43.886813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08655","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkafV3aLSSGcNtCmsXHK0LIVoyKV/ciXeyTffK5w5AwsojA3ucg8Pz6B44WRd4u+L689zreN3RZMfKC9al1lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:01:15.737976Z"},"content_sha256":"f9e5ada7e76d0cb79566b15ccc5180e6dcfa63a04d5e4aded76ba331b60e7a9e","schema_version":"1.0","event_id":"sha256:f9e5ada7e76d0cb79566b15ccc5180e6dcfa63a04d5e4aded76ba331b60e7a9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3GJST76FNV36N46TP4CVOGHD6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the roots of the subtree polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jason I. Brown, Lucas Mol","submitted_at":"2018-10-19T19:11:22Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08655","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PdhHCjemV78T4zJv7/x9hD3CiomAsdeWZJRzUkeMUUZdz9A77VmFA3xWODcd2HIniTB36+op79hBoit8PMx4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:01:15.738482Z"},"content_sha256":"ab125cffda3ba6e3a06277126acf1b13ca10da473aa64b44bb3ce8c6c85fb08d","schema_version":"1.0","event_id":"sha256:ab125cffda3ba6e3a06277126acf1b13ca10da473aa64b44bb3ce8c6c85fb08d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GJST76FNV36N46TP4CVOGHD6F/bundle.json","state_url":"https://pith.science/pith/3GJST76FNV36N46TP4CVOGHD6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GJST76FNV36N46TP4CVOGHD6F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T07:01:15Z","links":{"resolver":"https://pith.science/pith/3GJST76FNV36N46TP4CVOGHD6F","bundle":"https://pith.science/pith/3GJST76FNV36N46TP4CVOGHD6F/bundle.json","state":"https://pith.science/pith/3GJST76FNV36N46TP4CVOGHD6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GJST76FNV36N46TP4CVOGHD6F/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3aMt089iuL0bH0awJAN7+bfR/OhtLgLgWs92+UxOStS06rZjieVuy3JVXJ6+cZXe8tYGrYdDC/5EHK02G6ZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:01:15.740940Z","bundle_sha256":"5389f839d7fb21c34e300583cbff0b6da8f7d5efb20619bee3f1c4bd1b8b8d91"}}