{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KP7DQECYKDKFQYMJG3VHH7EYH4","short_pith_number":"pith:KP7DQECY","canonical_record":{"source":{"id":"1702.01744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-06T11:47:19Z","cross_cats_sorted":[],"title_canon_sha256":"6157502c3c9883e39389e00ec9f0d987fdfb6f5a1740bb1ec7fe46807b92a464","abstract_canon_sha256":"af37714e89da1fd5acbbd5d14ace71bc22bd953138ed2369baf4de980571869f"},"schema_version":"1.0"},"canonical_sha256":"53fe38105850d458618936ea73fc983f35308aeee7670955b22ecfc39e8a3ad7","source":{"kind":"arxiv","id":"1702.01744","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01744","created_at":"2026-05-18T00:51:11Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01744v1","created_at":"2026-05-18T00:51:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01744","created_at":"2026-05-18T00:51:11Z"},{"alias_kind":"pith_short_12","alias_value":"KP7DQECYKDKF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KP7DQECYKDKFQYMJ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KP7DQECY","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KP7DQECYKDKFQYMJG3VHH7EYH4","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-06T11:47:19Z","cross_cats_sorted":[],"title_canon_sha256":"6157502c3c9883e39389e00ec9f0d987fdfb6f5a1740bb1ec7fe46807b92a464","abstract_canon_sha256":"af37714e89da1fd5acbbd5d14ace71bc22bd953138ed2369baf4de980571869f"},"schema_version":"1.0"},"canonical_sha256":"53fe38105850d458618936ea73fc983f35308aeee7670955b22ecfc39e8a3ad7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:11.385281Z","signature_b64":"ytJQNB7T75YCVeR7LcgVVd0cNxGAW7QXdeYzM7y+GGiV1nXlBRzn8o5AeLYi+g6rMQnlrhIrC23+h3QIr65hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53fe38105850d458618936ea73fc983f35308aeee7670955b22ecfc39e8a3ad7","last_reissued_at":"2026-05-18T00:51:11.384456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:11.384456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01744","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":"2026-05-18T00:51:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AgZRy/NCHLmijZWTy8rt5SJZc2Ij3nA68AgngKHrtWMbk+JeSLU6772WL1lLSPuClNnzIWC5qQGoJXuPYoYkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:24:12.971554Z"},"content_sha256":"abdca047c9d60df2f00fe0464cafc995fd8ce27c8bf801e6a86caa15c25b75d0","schema_version":"1.0","event_id":"sha256:abdca047c9d60df2f00fe0464cafc995fd8ce27c8bf801e6a86caa15c25b75d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KP7DQECYKDKFQYMJG3VHH7EYH4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A recursive algorithm for trees and forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Song Guo, Victor J. W. Guo","submitted_at":"2017-02-06T11:47:19Z","abstract_excerpt":"Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on $\\{1,2,\\ldots,n\\}$. Classical formulas for counting various trees such as rooted trees, bipartite trees, tripartite trees, plane trees, $k$-ary plane trees, $k$-edge colored trees follow immediately from our recursive relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01744","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":"2026-05-18T00:51:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"645Pj/wm12HfkXjrKISwmQiMW+FYnfmxHhRNemBkTYxfmey704xIoVGnTYyxpXizNCaU2BWFAnyCHxosAVsUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:24:12.972090Z"},"content_sha256":"b81d1598aa7a6bd4010ab8108e805c03e2f7f40db1de841aaec20ed459617d14","schema_version":"1.0","event_id":"sha256:b81d1598aa7a6bd4010ab8108e805c03e2f7f40db1de841aaec20ed459617d14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KP7DQECYKDKFQYMJG3VHH7EYH4/bundle.json","state_url":"https://pith.science/pith/KP7DQECYKDKFQYMJG3VHH7EYH4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KP7DQECYKDKFQYMJG3VHH7EYH4/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":"2026-05-26T12:24:12Z","links":{"resolver":"https://pith.science/pith/KP7DQECYKDKFQYMJG3VHH7EYH4","bundle":"https://pith.science/pith/KP7DQECYKDKFQYMJG3VHH7EYH4/bundle.json","state":"https://pith.science/pith/KP7DQECYKDKFQYMJG3VHH7EYH4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KP7DQECYKDKFQYMJG3VHH7EYH4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KP7DQECYKDKFQYMJG3VHH7EYH4","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":"af37714e89da1fd5acbbd5d14ace71bc22bd953138ed2369baf4de980571869f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-06T11:47:19Z","title_canon_sha256":"6157502c3c9883e39389e00ec9f0d987fdfb6f5a1740bb1ec7fe46807b92a464"},"schema_version":"1.0","source":{"id":"1702.01744","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01744","created_at":"2026-05-18T00:51:11Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01744v1","created_at":"2026-05-18T00:51:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01744","created_at":"2026-05-18T00:51:11Z"},{"alias_kind":"pith_short_12","alias_value":"KP7DQECYKDKF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KP7DQECYKDKFQYMJ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KP7DQECY","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:b81d1598aa7a6bd4010ab8108e805c03e2f7f40db1de841aaec20ed459617d14","target":"graph","created_at":"2026-05-18T00:51:11Z","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":"Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on $\\{1,2,\\ldots,n\\}$. Classical formulas for counting various trees such as rooted trees, bipartite trees, tripartite trees, plane trees, $k$-ary plane trees, $k$-edge colored trees follow immediately from our recursive relations.","authors_text":"Song Guo, Victor J. W. Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-06T11:47:19Z","title":"A recursive algorithm for trees and forests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01744","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:abdca047c9d60df2f00fe0464cafc995fd8ce27c8bf801e6a86caa15c25b75d0","target":"record","created_at":"2026-05-18T00:51:11Z","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":"af37714e89da1fd5acbbd5d14ace71bc22bd953138ed2369baf4de980571869f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-06T11:47:19Z","title_canon_sha256":"6157502c3c9883e39389e00ec9f0d987fdfb6f5a1740bb1ec7fe46807b92a464"},"schema_version":"1.0","source":{"id":"1702.01744","kind":"arxiv","version":1}},"canonical_sha256":"53fe38105850d458618936ea73fc983f35308aeee7670955b22ecfc39e8a3ad7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53fe38105850d458618936ea73fc983f35308aeee7670955b22ecfc39e8a3ad7","first_computed_at":"2026-05-18T00:51:11.384456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:11.384456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ytJQNB7T75YCVeR7LcgVVd0cNxGAW7QXdeYzM7y+GGiV1nXlBRzn8o5AeLYi+g6rMQnlrhIrC23+h3QIr65hAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:11.385281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01744","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abdca047c9d60df2f00fe0464cafc995fd8ce27c8bf801e6a86caa15c25b75d0","sha256:b81d1598aa7a6bd4010ab8108e805c03e2f7f40db1de841aaec20ed459617d14"],"state_sha256":"3e534489bdf151cd8853e6ebf554535d4ae1a850785b6bae9397e318590e0324"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LoaW42NJCI+8q+4cVps48HSh8xNrP3UhIEDUknSXqBC17QDlUUZVDsVvRJIWMEInGSx1LJOQ41QC1J1HATvIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:24:12.975054Z","bundle_sha256":"222943e1099d2e5c7211140e169aac130265b02ba1e7ef5e29a0b97fcb38d6fb"}}