{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q62KMP4B6HJ3EFQSPYS63TZTL4","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":"67880894e6347f43bc7db909ecba5700382eedae47b3b2d461729b5f47dc1088","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-28T17:21:22Z","title_canon_sha256":"37e7453f513a88fe169a5e92c05bb0b321640f5d7e5dbad15b9638e4009108e4"},"schema_version":"1.0","source":{"id":"1704.09018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.09018","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1704.09018v2","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.09018","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"Q62KMP4B6HJ3","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q62KMP4B6HJ3EFQS","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q62KMP4B","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0013ebe8ab89ae274b3e26b68e498bbfcef111f625c12910d3ec4c103213e88a","target":"graph","created_at":"2026-05-18T00:08:16Z","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":"Given a simplicial complex whose vertices are labeled with positive integers, one can associate a vector configuration whose corresponding toric variety is the Zariski closure of a hierarchical model. We classify all the vertex-weighted simplicial complexes that give rise to unimodular vector configurations. We also provide a combinatorial characterization of their Graver bases.","authors_text":"Christopher O'Neill, Daniel Irving Bernstein","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-28T17:21:22Z","title":"Unimodular hierarchical models and their Graver bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.09018","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":"sha256:322cd8a149adee390c7dd9f7a1c409c73b753545e20daf48853e92947e38f7c9","target":"record","created_at":"2026-05-18T00:08:16Z","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":"67880894e6347f43bc7db909ecba5700382eedae47b3b2d461729b5f47dc1088","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-28T17:21:22Z","title_canon_sha256":"37e7453f513a88fe169a5e92c05bb0b321640f5d7e5dbad15b9638e4009108e4"},"schema_version":"1.0","source":{"id":"1704.09018","kind":"arxiv","version":2}},"canonical_sha256":"87b4a63f81f1d3b216127e25edcf335f00bfdc53237c57c54e8099f4436d5e75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87b4a63f81f1d3b216127e25edcf335f00bfdc53237c57c54e8099f4436d5e75","first_computed_at":"2026-05-18T00:08:16.208193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:16.208193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OG/MYuYGuqNKcxWloJIyJGvDkcjyXBX9ysu4hPk2AJBKuj4lMyabhT4V4iluCfHx/+AWfFlaNLUrx0q4JUiBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:16.208676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.09018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:322cd8a149adee390c7dd9f7a1c409c73b753545e20daf48853e92947e38f7c9","sha256:0013ebe8ab89ae274b3e26b68e498bbfcef111f625c12910d3ec4c103213e88a"],"state_sha256":"51b3c84340008d104a0d72f03c62c61ea764383e4a7f854aa4642b6a30a647e1"}