{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QYODA44KKJSLWPI2XIGQVHC23G","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":"fd55409e1ca448cf20a948df4a51794e6d5ceff36c1a12d33dd75d63959e5c6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-04T16:10:00Z","title_canon_sha256":"ff367968705b1b474abd29f73a98cc200e75768c8e3709a053f60278286913f8"},"schema_version":"1.0","source":{"id":"1110.0739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0739","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0739v2","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0739","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"QYODA44KKJSL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYODA44KKJSLWPI2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYODA44K","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:7a43095686ba33b98fde4710aa06d291edb4dce5c454f62e1149e8ec88d156f0","target":"graph","created_at":"2026-05-18T03:50:22Z","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":"We construct many nonpolytopal nonsimplicial Gorenstein* meet semi-lattices with nonnegative toric g-vector, supporting a conjecture of Stanley. These are formed as Bier spheres over the face posets of multiplexes, polytopes constructed by Bisztriczky as generalizations of simplices.","authors_text":"Eran Nevo, Louis J. Billera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-04T16:10:00Z","title":"Nonpolytopal nonsimplicial lattice spheres with nonnegative toric g-vector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0739","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":"sha256:229ff07ec491d2b6faf6ebd3aa10380386bcaae1a390e7dad48b64da23de647b","target":"record","created_at":"2026-05-18T03:50:22Z","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":"fd55409e1ca448cf20a948df4a51794e6d5ceff36c1a12d33dd75d63959e5c6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-04T16:10:00Z","title_canon_sha256":"ff367968705b1b474abd29f73a98cc200e75768c8e3709a053f60278286913f8"},"schema_version":"1.0","source":{"id":"1110.0739","kind":"arxiv","version":2}},"canonical_sha256":"861c30738a5264bb3d1aba0d0a9c5ad9a026d81c383144063342c3d98b2f67e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"861c30738a5264bb3d1aba0d0a9c5ad9a026d81c383144063342c3d98b2f67e8","first_computed_at":"2026-05-18T03:50:22.028767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:22.028767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nk9ijiPqCE2aYw/dfROM+dINCnNTY2lGmfPXppYIOfcIHuWzreEf5FIgC9uK+IhMxy39llcYM99bZk1axqMrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:22.029720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:229ff07ec491d2b6faf6ebd3aa10380386bcaae1a390e7dad48b64da23de647b","sha256:7a43095686ba33b98fde4710aa06d291edb4dce5c454f62e1149e8ec88d156f0"],"state_sha256":"f12f7374a9d4e2fed7a3710a5247ca478b8ee2132e3057f27436671a3e37b29d"}