{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CGWWAUGQ7YLBHD3QS4GZVAS5C3","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":"4bef2da65bb1553df53116e2e776a3ef71ceb96bd6d736b7dde7cc768c2f02f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-19T14:00:03Z","title_canon_sha256":"7ca44b7e13c5f3658cb5754c1a2159a8e0166121d649320e2fc4b9899da92c3e"},"schema_version":"1.0","source":{"id":"2506.16325","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.16325","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"arxiv_version","alias_value":"2506.16325v3","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.16325","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_12","alias_value":"CGWWAUGQ7YLB","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_16","alias_value":"CGWWAUGQ7YLBHD3Q","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_8","alias_value":"CGWWAUGQ","created_at":"2026-06-26T00:15:22Z"}],"graph_snapshots":[{"event_id":"sha256:2cf6dd18601938f9a85ff05f05d7cf3a02944e00c1c10ef25b0dabd9c8fda53b","target":"graph","created_at":"2026-06-26T00:15:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.16325/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that some important classes of weak Fano $3$-folds of Picard rank $2$ do not satisfy Bott vanishing. Using this we show that any smooth projective $3$-fold $X$ of Picard rank $2$ with $-K_X$ nef which is the image of a projective toric variety is toric. This proves a special case of a conjecture by Ochetta-Wisniewski, extending a corresponding previous work for Fano $3$-folds. We also show that a weak Fano $3$-fold of Picard rank $2$ having an int-amplified endomorphism is toric. This proves a special case of a conjecture by Fakhrudding, Meng, Zhang and Zhong, extending corresponding p","authors_text":"Supravat Sarkar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-19T14:00:03Z","title":"Images of toric variety and amplified endomorphism of weak Fano threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16325","kind":"arxiv","version":3},"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":"sha256:7aa1d74842832014af0044165cdda5b1ce703ec0f3b1118999e770130756b2d4","target":"record","created_at":"2026-06-26T00:15:22Z","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":"4bef2da65bb1553df53116e2e776a3ef71ceb96bd6d736b7dde7cc768c2f02f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-19T14:00:03Z","title_canon_sha256":"7ca44b7e13c5f3658cb5754c1a2159a8e0166121d649320e2fc4b9899da92c3e"},"schema_version":"1.0","source":{"id":"2506.16325","kind":"arxiv","version":3}},"canonical_sha256":"11ad6050d0fe16138f70970d9a825d16ee09d58364c3abe26384edc5af324a15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11ad6050d0fe16138f70970d9a825d16ee09d58364c3abe26384edc5af324a15","first_computed_at":"2026-06-26T00:15:22.188578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T00:15:22.188578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fkjlGnv7KPMsg8Dy7EQ+JqMrPKcx6jnDEQYmavr7fqJblsUgVZ+wuLIEUTi61z/tgLpMFM8Q8qlbnxCAY9dIDw==","signature_status":"signed_v1","signed_at":"2026-06-26T00:15:22.189156Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.16325","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa1d74842832014af0044165cdda5b1ce703ec0f3b1118999e770130756b2d4","sha256:2cf6dd18601938f9a85ff05f05d7cf3a02944e00c1c10ef25b0dabd9c8fda53b"],"state_sha256":"5fc481ef4bedbe3491829acc067fa33f9757db75b202844a43b0889347334ea9"}