{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:O6F7TM6UH2WMRSHAY6QDS2NWGZ","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":"040c310b8423ac55f006fc72cd15a2c29880d98263cda4a5d63dabcefe44408c","cross_cats_sorted":["q-bio.PE"],"license":"","primary_cat":"math.CO","submitted_at":"2006-09-10T07:12:10Z","title_canon_sha256":"0fe3ba0811e715c7524d69555b67ea30a73a387fc05d53b1973563f4169a76eb"},"schema_version":"1.0","source":{"id":"math/0609264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609264","created_at":"2026-05-18T04:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609264v2","created_at":"2026-05-18T04:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609264","created_at":"2026-05-18T04:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"O6F7TM6UH2WM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6F7TM6UH2WMRSHA","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6F7TM6U","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:529f043c93149549d7f192204ded253a65f62d556bc13c1bc2a00882ec634200","target":"graph","created_at":"2026-05-18T04:40:35Z","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":"A pedigree is a directed graph in which each vertex (except the founder vertices) has two parents. The main result in this paper is a construction of an infinite family of counter examples to a reconstruction problem on pedigrees, thus negatively answering a question of Steel and Hein. Some positive reconstruction results are also presented. The problem of counting distinct (mutually non-isomorphic) pedigrees is considered. The known lower and upper bounds on the number of pedigrees are improved upon, and their relevance to pedigree reconstruction from DNA sequence data is discussed. It is sho","authors_text":"Bhalchandra D. Thatte","cross_cats":["q-bio.PE"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2006-09-10T07:12:10Z","title":"Combinatorics of pedigrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609264","kind":"arxiv","version":2},"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":"sha256:2fbeeb9bcd9690927cedf79fa0ea791df7ea4329a67bbfe07e54595190e5db0e","target":"record","created_at":"2026-05-18T04:40:35Z","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":"040c310b8423ac55f006fc72cd15a2c29880d98263cda4a5d63dabcefe44408c","cross_cats_sorted":["q-bio.PE"],"license":"","primary_cat":"math.CO","submitted_at":"2006-09-10T07:12:10Z","title_canon_sha256":"0fe3ba0811e715c7524d69555b67ea30a73a387fc05d53b1973563f4169a76eb"},"schema_version":"1.0","source":{"id":"math/0609264","kind":"arxiv","version":2}},"canonical_sha256":"778bf9b3d43eacc8c8e0c7a03969b63641543988f2fe392e1becb1a1389c9ada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778bf9b3d43eacc8c8e0c7a03969b63641543988f2fe392e1becb1a1389c9ada","first_computed_at":"2026-05-18T04:40:35.342220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:35.342220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7tE6s3uc8JNUaCKNOymVO5q3izqxcnoFcEVtCgiY68oqjflkY9a4jH4TEheQr6zrfAVaDnmwetMo1GjlRZnCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:35.342727Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fbeeb9bcd9690927cedf79fa0ea791df7ea4329a67bbfe07e54595190e5db0e","sha256:529f043c93149549d7f192204ded253a65f62d556bc13c1bc2a00882ec634200"],"state_sha256":"94ac02720fa75560e8f14441350d304989b55ae1cfeec1f858bc99ac0333263f"}