{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:BCUZVU2C7ZV7NDLELEFU6V3YRI","short_pith_number":"pith:BCUZVU2C","canonical_record":{"source":{"id":"q-bio/0405001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-bio.QM","submitted_at":"2004-05-01T22:11:23Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"7b325ae80ce34962c4d06c97a25f8af6da436cc5047098e52881c46303da2369","abstract_canon_sha256":"2787b85d0be40c231b9b58ef03bf419cb5bcfbc8eb5dffc37d08ce214f16d5fa"},"schema_version":"1.0"},"canonical_sha256":"08a99ad342fe6bf68d64590b4f57788a0bb13d31a89dfe8be35cba4d0e76a834","source":{"kind":"arxiv","id":"q-bio/0405001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-bio/0405001","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0405001v2","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0405001","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"BCUZVU2C7ZV7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"BCUZVU2C7ZV7NDLE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"BCUZVU2C","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:BCUZVU2C7ZV7NDLELEFU6V3YRI","target":"record","payload":{"canonical_record":{"source":{"id":"q-bio/0405001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-bio.QM","submitted_at":"2004-05-01T22:11:23Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"7b325ae80ce34962c4d06c97a25f8af6da436cc5047098e52881c46303da2369","abstract_canon_sha256":"2787b85d0be40c231b9b58ef03bf419cb5bcfbc8eb5dffc37d08ce214f16d5fa"},"schema_version":"1.0"},"canonical_sha256":"08a99ad342fe6bf68d64590b4f57788a0bb13d31a89dfe8be35cba4d0e76a834","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:35.200865Z","signature_b64":"VWb6WL8L2BtWjGiXEG8PjnIFGZq+BTreOUMbgwsKqLcB2pz/AmYqFyGKm12nBW1zsztM6G1zp1YzcX/FfSJjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08a99ad342fe6bf68d64590b4f57788a0bb13d31a89dfe8be35cba4d0e76a834","last_reissued_at":"2026-05-18T04:08:35.200282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:35.200282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-bio/0405001","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5JKKcu80EFr9KnZWIGldTuAvOz0lvCxgkXZ8Kx0nuEhA8zAatWswk9QF8qU6r1yEQFLIQRy1y7m6vmvKw6E+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:39:56.613829Z"},"content_sha256":"db764211a5f2769d95f5f89046c3aad15d27dee261bdc9ab5b97bef12c26872b","schema_version":"1.0","event_id":"sha256:db764211a5f2769d95f5f89046c3aad15d27dee261bdc9ab5b97bef12c26872b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:BCUZVU2C7ZV7NDLELEFU6V3YRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resultants in Genetic Linkage Analysis","license":"","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"q-bio.QM","authors_text":"Bernd Sturmfels, Ingileif B. Hallgrimsdottir","submitted_at":"2004-05-01T22:11:23Z","abstract_excerpt":"Statistical models for genetic linkage analysis of k-locus diseases are k-dimensional subvarieties of a (3^k-1)-dimensional probability simplex. We determine the algebraic invariants of these models with general characteristics for k=1, in particular we recover, and generalize, the Hardy-Weinberg curve. For k = 2, the invariants are presented as determinants of 32x32-matrices of linear forms in 9 unknowns, a suitable format for computations with numerical data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0405001","kind":"arxiv","version":2},"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":"2026-05-18T04:08:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XD6aLU1YdKf8NJT5tkvTt7jj1CCBNc9SsIM6fgJNhGKKjOTzAVV4edSQVHpksS26+o/sFkKzPXt1YFmEYiSVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:39:56.614286Z"},"content_sha256":"b2d305e474c282315ce8f5f179a5e28d9de023726db7693a759ae6d529bcbdaf","schema_version":"1.0","event_id":"sha256:b2d305e474c282315ce8f5f179a5e28d9de023726db7693a759ae6d529bcbdaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI/bundle.json","state_url":"https://pith.science/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI/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":"2026-06-08T14:39:56Z","links":{"resolver":"https://pith.science/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI","bundle":"https://pith.science/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI/bundle.json","state":"https://pith.science/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BCUZVU2C7ZV7NDLELEFU6V3YRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:BCUZVU2C7ZV7NDLELEFU6V3YRI","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":"2787b85d0be40c231b9b58ef03bf419cb5bcfbc8eb5dffc37d08ce214f16d5fa","cross_cats_sorted":["math.ST","stat.TH"],"license":"","primary_cat":"q-bio.QM","submitted_at":"2004-05-01T22:11:23Z","title_canon_sha256":"7b325ae80ce34962c4d06c97a25f8af6da436cc5047098e52881c46303da2369"},"schema_version":"1.0","source":{"id":"q-bio/0405001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-bio/0405001","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0405001v2","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0405001","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"BCUZVU2C7ZV7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"BCUZVU2C7ZV7NDLE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"BCUZVU2C","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:b2d305e474c282315ce8f5f179a5e28d9de023726db7693a759ae6d529bcbdaf","target":"graph","created_at":"2026-05-18T04:08:35Z","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":"Statistical models for genetic linkage analysis of k-locus diseases are k-dimensional subvarieties of a (3^k-1)-dimensional probability simplex. We determine the algebraic invariants of these models with general characteristics for k=1, in particular we recover, and generalize, the Hardy-Weinberg curve. For k = 2, the invariants are presented as determinants of 32x32-matrices of linear forms in 9 unknowns, a suitable format for computations with numerical data.","authors_text":"Bernd Sturmfels, Ingileif B. Hallgrimsdottir","cross_cats":["math.ST","stat.TH"],"headline":"","license":"","primary_cat":"q-bio.QM","submitted_at":"2004-05-01T22:11:23Z","title":"Resultants in Genetic Linkage Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0405001","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:db764211a5f2769d95f5f89046c3aad15d27dee261bdc9ab5b97bef12c26872b","target":"record","created_at":"2026-05-18T04:08:35Z","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":"2787b85d0be40c231b9b58ef03bf419cb5bcfbc8eb5dffc37d08ce214f16d5fa","cross_cats_sorted":["math.ST","stat.TH"],"license":"","primary_cat":"q-bio.QM","submitted_at":"2004-05-01T22:11:23Z","title_canon_sha256":"7b325ae80ce34962c4d06c97a25f8af6da436cc5047098e52881c46303da2369"},"schema_version":"1.0","source":{"id":"q-bio/0405001","kind":"arxiv","version":2}},"canonical_sha256":"08a99ad342fe6bf68d64590b4f57788a0bb13d31a89dfe8be35cba4d0e76a834","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08a99ad342fe6bf68d64590b4f57788a0bb13d31a89dfe8be35cba4d0e76a834","first_computed_at":"2026-05-18T04:08:35.200282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:35.200282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VWb6WL8L2BtWjGiXEG8PjnIFGZq+BTreOUMbgwsKqLcB2pz/AmYqFyGKm12nBW1zsztM6G1zp1YzcX/FfSJjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:35.200865Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-bio/0405001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db764211a5f2769d95f5f89046c3aad15d27dee261bdc9ab5b97bef12c26872b","sha256:b2d305e474c282315ce8f5f179a5e28d9de023726db7693a759ae6d529bcbdaf"],"state_sha256":"40c968c125abe9314267dc32fa87fb204c0324237b1c64f662421ea8405661f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HU5qIA5oJ5H3vFwy/ziKw+0lxqCw/szigWIVNxl0v3ummZLp6tal39y0vCnWBWHDs67qcvfdR/A0WjcfK3deAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:39:56.616209Z","bundle_sha256":"e7812cc51204799d9b8fb2fe59993b5a0891d0f5a62b3c61849998cd4bdfde2d"}}