{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7I54RKGHYEE4NIDAQ4Y76GSFCH","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":"9b0053a273c94432b21416709d8b7ff3116c4778e984648dc54f1556756e3ab6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-23T15:58:22Z","title_canon_sha256":"3439c536ea0a9047d15d2949ab8b029257041fc1a0c40f76b2f653545566c980"},"schema_version":"1.0","source":{"id":"1001.4165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4165","created_at":"2026-07-04T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4165v1","created_at":"2026-07-04T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4165","created_at":"2026-07-04T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"7I54RKGHYEE4","created_at":"2026-07-04T23:52:29Z"},{"alias_kind":"pith_short_16","alias_value":"7I54RKGHYEE4NIDA","created_at":"2026-07-04T23:52:29Z"},{"alias_kind":"pith_short_8","alias_value":"7I54RKGH","created_at":"2026-07-04T23:52:29Z"}],"graph_snapshots":[{"event_id":"sha256:5898297f7a1e82effc3e7b5b51d974ecb4f8944544ff3cfef2c60ac9212e263c","target":"graph","created_at":"2026-07-04T23:52:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1001.4165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given arbitrary integers $k$ and $d$ with $0 \\leq 2k \\leq d$, we construct a Gorenstein Fano polytope $\\Pc \\subset \\RR^d$ of dimension $d$ such that (i) its Ehrhart polynomial $i(\\Pc, n)$ possesses $d$ distinct roots; (ii) $i(\\Pc, n)$ possesses exactly $2k$ imaginary roots; (iii) $i(\\Pc, n)$ possesses exactly $d - 2k$ real roots; (iv) the real part of each of the imaginary roots is equal to $- 1 / 2$; (v) all of the real roots belong to the open interval $(-1, 0)$.","authors_text":"Akihiro Higashitani, Hidefumi Ohsugi, Takayuki Hibi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-23T15:58:22Z","title":"Roots of Ehrhart polynomials of Gorenstein Fano polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4165","kind":"arxiv","version":1},"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":"sha256:3bcd09e6d67d7e6761173ee9e3edcf4ae1801d2a5135044e96327cf69068b755","target":"record","created_at":"2026-07-04T23:52:29Z","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":"9b0053a273c94432b21416709d8b7ff3116c4778e984648dc54f1556756e3ab6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-23T15:58:22Z","title_canon_sha256":"3439c536ea0a9047d15d2949ab8b029257041fc1a0c40f76b2f653545566c980"},"schema_version":"1.0","source":{"id":"1001.4165","kind":"arxiv","version":1}},"canonical_sha256":"fa3bc8a8c7c109c6a0608731ff1a4511fd638b1d6af034258b6f8dcf3c4e3a8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa3bc8a8c7c109c6a0608731ff1a4511fd638b1d6af034258b6f8dcf3c4e3a8a","first_computed_at":"2026-07-04T23:52:29.999531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:29.999531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4IXG6S685ZksoDTl0Xsm2iAWd3W2yKVtTeA+zDdfiM0lvMpsNqJ5a5LZjvf0yDhZtZFG/oqlhdrwWSOKXHVLAw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:29.999919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bcd09e6d67d7e6761173ee9e3edcf4ae1801d2a5135044e96327cf69068b755","sha256:5898297f7a1e82effc3e7b5b51d974ecb4f8944544ff3cfef2c60ac9212e263c"],"state_sha256":"c7698e8fe4090f179a6ff7af317dc4410b5c0372ec3e88b268b9924d0b9848fe"}