{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HEX4GTK3LIF5UJ4TLQHHUXIGOJ","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":"5b3809c1de8e6faf1b174e8a1499e098261ada2ddb5a57732a91605374b9c0bb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2020-11-28T15:55:17Z","title_canon_sha256":"bff4499705a522aca8300f38781c97773216a198c96a6832e590699f54ed6691"},"schema_version":"1.0","source":{"id":"2011.14154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.14154","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"2011.14154v1","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.14154","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"HEX4GTK3LIF5","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_16","alias_value":"HEX4GTK3LIF5UJ4T","created_at":"2026-07-05T01:55:17Z"},{"alias_kind":"pith_short_8","alias_value":"HEX4GTK3","created_at":"2026-07-05T01:55:17Z"}],"graph_snapshots":[{"event_id":"sha256:ad464394da4e19a165605110b6c2c34183a57caae4436eac6d0a0b022de96fe4","target":"graph","created_at":"2026-07-05T01:55:17Z","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/2011.14154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Property $\\mathcal{O}$ for an arbitrary complex, Fano manifold $X$, is a statement about the eigenvalues of the linear operator obtained from the quantum multiplication of the anticanonical class of $X$. Conjecture $\\mathcal{O}$ is a conjecture that Property $\\mathcal{O}$ holds for any Fano variety. Pasquier listed the smooth non-homogeneous horospherical varieties of Picard rank 1 into five classes. Conjecture $\\mathcal{O}$ has already been shown to hold for the odd symplectic Grassmannians which is one of these classes. We will show that Conjecture $\\mathcal{O}$ holds for two more classes an","authors_text":"Garrett Fowler, Lela Bones, Lisa Schneider, Ryan M. Shifler","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2020-11-28T15:55:17Z","title":"Conjecture $\\mathcal{O}$ holds for some Horospherical Varieties of Picard Rank 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.14154","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:f123dba73cc7ef07d365e7c38ea48db607bb898b5ae7b18659695fca608c4699","target":"record","created_at":"2026-07-05T01:55:17Z","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":"5b3809c1de8e6faf1b174e8a1499e098261ada2ddb5a57732a91605374b9c0bb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2020-11-28T15:55:17Z","title_canon_sha256":"bff4499705a522aca8300f38781c97773216a198c96a6832e590699f54ed6691"},"schema_version":"1.0","source":{"id":"2011.14154","kind":"arxiv","version":1}},"canonical_sha256":"392fc34d5b5a0bda27935c0e7a5d06725c4b7dac1bb9c2758b68b20468f4a834","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"392fc34d5b5a0bda27935c0e7a5d06725c4b7dac1bb9c2758b68b20468f4a834","first_computed_at":"2026-07-05T01:55:17.878188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:55:17.878188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eaxgyiWFs2d/e3rn9rlryWWeolWZm+FDKVwmL9r6OqJWUzo3EHrkTLTmbq8hq1vKsgXntG6DCrawR+XLFB83Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:55:17.878661Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.14154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f123dba73cc7ef07d365e7c38ea48db607bb898b5ae7b18659695fca608c4699","sha256:ad464394da4e19a165605110b6c2c34183a57caae4436eac6d0a0b022de96fe4"],"state_sha256":"a2d4cca5c8d22b6746ca72ed9df5974fa8b7bb799864691bee8a3ab56c6e56ad"}