{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:K2FKTIGIDUIPFY4GG7MJH4BNY3","short_pith_number":"pith:K2FKTIGI","canonical_record":{"source":{"id":"math/0606189","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2006-06-08T14:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"d549b52f3d604401d9d3adaa7260e8c2f1ed59ca3ed445e359012b613264ab21","abstract_canon_sha256":"36a824f4f9d81055d07980a77d768df391dc698413e2cad2e4276babd8318f50"},"schema_version":"1.0"},"canonical_sha256":"568aa9a0c81d10f2e38637d893f02dc6c133ba2e47f1722493df81adc0781e16","source":{"kind":"arxiv","id":"math/0606189","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606189","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606189v2","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606189","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"K2FKTIGIDUIP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"K2FKTIGIDUIPFY4G","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"K2FKTIGI","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:K2FKTIGIDUIPFY4GG7MJH4BNY3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0606189","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2006-06-08T14:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"d549b52f3d604401d9d3adaa7260e8c2f1ed59ca3ed445e359012b613264ab21","abstract_canon_sha256":"36a824f4f9d81055d07980a77d768df391dc698413e2cad2e4276babd8318f50"},"schema_version":"1.0"},"canonical_sha256":"568aa9a0c81d10f2e38637d893f02dc6c133ba2e47f1722493df81adc0781e16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:02.694167Z","signature_b64":"Y0BrjBduAEafpCqiBN6fdOEvpry/8wo/TovUvcvblyPs9d9yQ++JTd4tiGL9bnth59J5RcOI+f0W4fNukEKSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"568aa9a0c81d10f2e38637d893f02dc6c133ba2e47f1722493df81adc0781e16","last_reissued_at":"2026-05-17T23:41:02.693561Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:02.693561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0606189","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":"2026-05-17T23:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"io0lBUcZejHvgsMAb7cz2Fzjo7J7BUq+2K379DXrcbeOQQvvLhNymnbv88pkzPOaxGvTwm1LxgrOMXn0d4VDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:00:11.417971Z"},"content_sha256":"c4790a70bdccba80b7a1c4b02ab4112b76ad0a7c9558ed3cd47c36aed897d854","schema_version":"1.0","event_id":"sha256:c4790a70bdccba80b7a1c4b02ab4112b76ad0a7c9558ed3cd47c36aed897d854"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:K2FKTIGIDUIPFY4GG7MJH4BNY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Groebner bases of ideals of few points in high dimensions","license":"","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"(2) Mathematical Biosciences Institute, Brandilyn Stigler (2) ((1) Department of Mathematics, Ohio University, The Ohio State University), Winfried Just (1)","submitted_at":"2006-06-08T14:26:38Z","abstract_excerpt":"A contemporary and exciting application of Groebner bases is their use in computational biology, particularly in the reverse engineering of gene regulatory networks from experimental data. In this setting, the data are typically limited to tens of points, while the number of genes or variables is potentially in the thousands. As such data sets vastly underdetermine the biological network, many models may fit the same data and reverse engineering programs often require the use of methods for choosing parsimonious models. Grobner bases have recently been employed as a selection tool for polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606189","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":"2026-05-17T23:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPiUbdL4gKVJcwmJIM+3EMBPw93B9iTuMXYUeBgdT9e10g54zkNoiT+cjaitMlDXYG/ujAYgiV4k325mqc+KCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:00:11.418577Z"},"content_sha256":"ac413015a467f9ad778758289ae1623e228ef88909769a2260ccccabaea0947e","schema_version":"1.0","event_id":"sha256:ac413015a467f9ad778758289ae1623e228ef88909769a2260ccccabaea0947e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3/bundle.json","state_url":"https://pith.science/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3/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":"2026-05-22T05:00:11Z","links":{"resolver":"https://pith.science/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3","bundle":"https://pith.science/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3/bundle.json","state":"https://pith.science/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2FKTIGIDUIPFY4GG7MJH4BNY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:K2FKTIGIDUIPFY4GG7MJH4BNY3","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":"36a824f4f9d81055d07980a77d768df391dc698413e2cad2e4276babd8318f50","cross_cats_sorted":[],"license":"","primary_cat":"math.AC","submitted_at":"2006-06-08T14:26:38Z","title_canon_sha256":"d549b52f3d604401d9d3adaa7260e8c2f1ed59ca3ed445e359012b613264ab21"},"schema_version":"1.0","source":{"id":"math/0606189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606189","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606189v2","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606189","created_at":"2026-05-17T23:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"K2FKTIGIDUIP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"K2FKTIGIDUIPFY4G","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"K2FKTIGI","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:ac413015a467f9ad778758289ae1623e228ef88909769a2260ccccabaea0947e","target":"graph","created_at":"2026-05-17T23:41:02Z","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 contemporary and exciting application of Groebner bases is their use in computational biology, particularly in the reverse engineering of gene regulatory networks from experimental data. In this setting, the data are typically limited to tens of points, while the number of genes or variables is potentially in the thousands. As such data sets vastly underdetermine the biological network, many models may fit the same data and reverse engineering programs often require the use of methods for choosing parsimonious models. Grobner bases have recently been employed as a selection tool for polynomi","authors_text":"(2) Mathematical Biosciences Institute, Brandilyn Stigler (2) ((1) Department of Mathematics, Ohio University, The Ohio State University), Winfried Just (1)","cross_cats":[],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2006-06-08T14:26:38Z","title":"Computing Groebner bases of ideals of few points in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606189","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:c4790a70bdccba80b7a1c4b02ab4112b76ad0a7c9558ed3cd47c36aed897d854","target":"record","created_at":"2026-05-17T23:41:02Z","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":"36a824f4f9d81055d07980a77d768df391dc698413e2cad2e4276babd8318f50","cross_cats_sorted":[],"license":"","primary_cat":"math.AC","submitted_at":"2006-06-08T14:26:38Z","title_canon_sha256":"d549b52f3d604401d9d3adaa7260e8c2f1ed59ca3ed445e359012b613264ab21"},"schema_version":"1.0","source":{"id":"math/0606189","kind":"arxiv","version":2}},"canonical_sha256":"568aa9a0c81d10f2e38637d893f02dc6c133ba2e47f1722493df81adc0781e16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"568aa9a0c81d10f2e38637d893f02dc6c133ba2e47f1722493df81adc0781e16","first_computed_at":"2026-05-17T23:41:02.693561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:02.693561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0BrjBduAEafpCqiBN6fdOEvpry/8wo/TovUvcvblyPs9d9yQ++JTd4tiGL9bnth59J5RcOI+f0W4fNukEKSDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:02.694167Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4790a70bdccba80b7a1c4b02ab4112b76ad0a7c9558ed3cd47c36aed897d854","sha256:ac413015a467f9ad778758289ae1623e228ef88909769a2260ccccabaea0947e"],"state_sha256":"3ae817e05bfbc611431bd8478fafa0dea44e0af74cf0ff99671064670fcefda7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/PrnWxRUBulbXgvqEXVaUtsMRJ9bV3Pt3Hq0L49NfsNZC+uhovzEzIK/Yy4n+uXuNcS56AbxHOcmJwjYW0ejAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T05:00:11.421876Z","bundle_sha256":"eb5864a9783a96860533a5ed79524297feaa86350909c5ebe42a2dbcff9d8477"}}