{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LOWTFT7UH75W5LTVJ2GBXY7MK7","short_pith_number":"pith:LOWTFT7U","canonical_record":{"source":{"id":"2303.09894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-03-17T11:15:02Z","cross_cats_sorted":[],"title_canon_sha256":"18fc81bea458fb2f3736ecdf4aba2148e5b60e1f71f38e21747321dede85975c","abstract_canon_sha256":"f117a92038003884c91d0806a76519ac74f4828682f58d073fd4d0c7dd930600"},"schema_version":"1.0"},"canonical_sha256":"5bad32cff43ffb6eae754e8c1be3ec57d4214cfa39d63496c618b29fae310253","source":{"kind":"arxiv","id":"2303.09894","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.09894","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"arxiv_version","alias_value":"2303.09894v1","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.09894","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"pith_short_12","alias_value":"LOWTFT7UH75W","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"pith_short_16","alias_value":"LOWTFT7UH75W5LTV","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"pith_short_8","alias_value":"LOWTFT7U","created_at":"2026-07-05T05:52:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LOWTFT7UH75W5LTVJ2GBXY7MK7","target":"record","payload":{"canonical_record":{"source":{"id":"2303.09894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-03-17T11:15:02Z","cross_cats_sorted":[],"title_canon_sha256":"18fc81bea458fb2f3736ecdf4aba2148e5b60e1f71f38e21747321dede85975c","abstract_canon_sha256":"f117a92038003884c91d0806a76519ac74f4828682f58d073fd4d0c7dd930600"},"schema_version":"1.0"},"canonical_sha256":"5bad32cff43ffb6eae754e8c1be3ec57d4214cfa39d63496c618b29fae310253","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:52:11.969304Z","signature_b64":"dw0DhNwlukixeZbVceU2IPBeNFXlzW4vptGKgPVl0lB6CRuD+sAX4pSSrS32EUt2zwR/fv9wDr/VB8RndFaXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bad32cff43ffb6eae754e8c1be3ec57d4214cfa39d63496c618b29fae310253","last_reissued_at":"2026-07-05T05:52:11.968810Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:52:11.968810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.09894","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:52:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stcsN2xUFzAYU7z1uWQKJ1lN8/waLJQstOGKwjZKGZDneaZg8lvHSQ0H0Qbv3Yot66jEZqh0eY3P0VChdlAhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T03:12:09.997109Z"},"content_sha256":"27db0c9971b04f8955c2c25ad36bb58a64568c15f09dbe24d81bbb212140bb56","schema_version":"1.0","event_id":"sha256:27db0c9971b04f8955c2c25ad36bb58a64568c15f09dbe24d81bbb212140bb56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LOWTFT7UH75W5LTVJ2GBXY7MK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Varieties in positive characteristic with numerically flat log cotangent bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sho Ejiri, Shou Yoshikawa","submitted_at":"2023-03-17T11:15:02Z","abstract_excerpt":"In this paper, we prove that a smooth projective globally $F$-split variety with numerically flat tangent bundle is an \\'etale quotient of an ordinary abelian variety. We also show its logarithmic analog, which contains a characterization of toric varieties. We further prove that, without assumption of global $F$-splitting, a smooth projective separably rationally connected variety of arbitrary characteristic with numerically flat log cotangent bundle is a toric variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09894","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.09894/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:52:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6cDRNk54VlCC4nXVfyBVc2aJ2f2ogW28L90SOT+Hu8e+PZrI0buqpZyz9AdajT/q0B7BW1+92QeB+1422gkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T03:12:09.997646Z"},"content_sha256":"81398297d7926e3a9d3d91b6f018b7967a30ccc079b40d5f4dc385e20091e274","schema_version":"1.0","event_id":"sha256:81398297d7926e3a9d3d91b6f018b7967a30ccc079b40d5f4dc385e20091e274"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7/bundle.json","state_url":"https://pith.science/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T03:12:10Z","links":{"resolver":"https://pith.science/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7","bundle":"https://pith.science/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7/bundle.json","state":"https://pith.science/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOWTFT7UH75W5LTVJ2GBXY7MK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LOWTFT7UH75W5LTVJ2GBXY7MK7","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":"f117a92038003884c91d0806a76519ac74f4828682f58d073fd4d0c7dd930600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-03-17T11:15:02Z","title_canon_sha256":"18fc81bea458fb2f3736ecdf4aba2148e5b60e1f71f38e21747321dede85975c"},"schema_version":"1.0","source":{"id":"2303.09894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.09894","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"arxiv_version","alias_value":"2303.09894v1","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.09894","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"pith_short_12","alias_value":"LOWTFT7UH75W","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"pith_short_16","alias_value":"LOWTFT7UH75W5LTV","created_at":"2026-07-05T05:52:11Z"},{"alias_kind":"pith_short_8","alias_value":"LOWTFT7U","created_at":"2026-07-05T05:52:11Z"}],"graph_snapshots":[{"event_id":"sha256:81398297d7926e3a9d3d91b6f018b7967a30ccc079b40d5f4dc385e20091e274","target":"graph","created_at":"2026-07-05T05:52:11Z","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/2303.09894/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that a smooth projective globally $F$-split variety with numerically flat tangent bundle is an \\'etale quotient of an ordinary abelian variety. We also show its logarithmic analog, which contains a characterization of toric varieties. We further prove that, without assumption of global $F$-splitting, a smooth projective separably rationally connected variety of arbitrary characteristic with numerically flat log cotangent bundle is a toric variety.","authors_text":"Sho Ejiri, Shou Yoshikawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-03-17T11:15:02Z","title":"Varieties in positive characteristic with numerically flat log cotangent bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09894","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":"sha256:27db0c9971b04f8955c2c25ad36bb58a64568c15f09dbe24d81bbb212140bb56","target":"record","created_at":"2026-07-05T05:52:11Z","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":"f117a92038003884c91d0806a76519ac74f4828682f58d073fd4d0c7dd930600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-03-17T11:15:02Z","title_canon_sha256":"18fc81bea458fb2f3736ecdf4aba2148e5b60e1f71f38e21747321dede85975c"},"schema_version":"1.0","source":{"id":"2303.09894","kind":"arxiv","version":1}},"canonical_sha256":"5bad32cff43ffb6eae754e8c1be3ec57d4214cfa39d63496c618b29fae310253","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bad32cff43ffb6eae754e8c1be3ec57d4214cfa39d63496c618b29fae310253","first_computed_at":"2026-07-05T05:52:11.968810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:52:11.968810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dw0DhNwlukixeZbVceU2IPBeNFXlzW4vptGKgPVl0lB6CRuD+sAX4pSSrS32EUt2zwR/fv9wDr/VB8RndFaXCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:52:11.969304Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.09894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27db0c9971b04f8955c2c25ad36bb58a64568c15f09dbe24d81bbb212140bb56","sha256:81398297d7926e3a9d3d91b6f018b7967a30ccc079b40d5f4dc385e20091e274"],"state_sha256":"37eda0333ef524f653324e61290c1f50ccdb6fb7772e2594b6e2c9dcf17c35b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5eY8GrE28KnyFy2zYLy0NMmxX8v+HmaIxTRm6ZqbPmrljK6XOKF3SIYoJSW/OCRP5bQhiayTf2tMCdFX1hAoDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T03:12:10.002378Z","bundle_sha256":"2b42e825423e28a8dd5266db366d87327985c2379a78d8145eaddb3f25e8007e"}}