{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VRGEB554TQ2NEXJRUDWTNUH3QI","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":"f0a18bf5e101b9f4b184d1e5d22556c6b491a86e1816b6b8b1b01241b4cf7970","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-05T19:39:09Z","title_canon_sha256":"0ccf8200483b02869a2a625455903d12a481f21fe07533557869d0731ac4b93e"},"schema_version":"1.0","source":{"id":"1601.00944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00944","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00944v1","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00944","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"VRGEB554TQ2N","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VRGEB554TQ2NEXJR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VRGEB554","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:7ae01f984634632a817da6ac49eaea02929ff2cf579d99f86669cfb8b814e1c1","target":"graph","created_at":"2026-05-18T01:23:21Z","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":"We show that a tree of order $n$ has at most $O(5^{n/4})$ nonisomorphic subtrees, and that this bound is best possible. We also prove an analogous result for the number of nonisomorphic rooted subtrees of a rooted tree.","authors_text":"\\'Eva Czabarka, L\\'aszl\\'o A. Sz\\'ekely, Stephan Wagner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-05T19:39:09Z","title":"On the number of nonisomorphic subtrees of a tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00944","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":"sha256:1fd041ae4d0504b203b64a9cdd4361e56ba70fc4798bb00d5caf2e1a902ff92c","target":"record","created_at":"2026-05-18T01:23:21Z","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":"f0a18bf5e101b9f4b184d1e5d22556c6b491a86e1816b6b8b1b01241b4cf7970","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-05T19:39:09Z","title_canon_sha256":"0ccf8200483b02869a2a625455903d12a481f21fe07533557869d0731ac4b93e"},"schema_version":"1.0","source":{"id":"1601.00944","kind":"arxiv","version":1}},"canonical_sha256":"ac4c40f7bc9c34d25d31a0ed36d0fb820d00ab0393a223014a587e42bfd85a8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4c40f7bc9c34d25d31a0ed36d0fb820d00ab0393a223014a587e42bfd85a8c","first_computed_at":"2026-05-18T01:23:21.242434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:21.242434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5kt6pgIYAUIgyE3OZsd/08Gist8bRmGVI6le3JNatbsUH59EZXLFd+Ws/HOJP6+IyZwGV4hfFWBXzSWQdLiWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:21.243141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fd041ae4d0504b203b64a9cdd4361e56ba70fc4798bb00d5caf2e1a902ff92c","sha256:7ae01f984634632a817da6ac49eaea02929ff2cf579d99f86669cfb8b814e1c1"],"state_sha256":"ef0647f5cc3b629417b3000bd44d2eb0aa6a71b13915291573a83fa3bbe96311"}