{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5AKL4PG57AN7MZ2HBXSY336VMY","short_pith_number":"pith:5AKL4PG5","canonical_record":{"source":{"id":"2302.11921","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-23T10:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"c54d062591fa0f348fc9989f976330533bc63759c73d8185df84714bd717f04d","abstract_canon_sha256":"0fd2a2acc1c4bf2d62759cabee99f8a5cdd683dd587ab924a57b5efea1d552a3"},"schema_version":"1.0"},"canonical_sha256":"e814be3cddf81bf667470de58defd56606448e1f005517e66acd1baf544f034d","source":{"kind":"arxiv","id":"2302.11921","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.11921","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"arxiv_version","alias_value":"2302.11921v5","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11921","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"pith_short_12","alias_value":"5AKL4PG57AN7","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"pith_short_16","alias_value":"5AKL4PG57AN7MZ2H","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"pith_short_8","alias_value":"5AKL4PG5","created_at":"2026-07-05T08:07:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5AKL4PG57AN7MZ2HBXSY336VMY","target":"record","payload":{"canonical_record":{"source":{"id":"2302.11921","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-23T10:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"c54d062591fa0f348fc9989f976330533bc63759c73d8185df84714bd717f04d","abstract_canon_sha256":"0fd2a2acc1c4bf2d62759cabee99f8a5cdd683dd587ab924a57b5efea1d552a3"},"schema_version":"1.0"},"canonical_sha256":"e814be3cddf81bf667470de58defd56606448e1f005517e66acd1baf544f034d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:07:26.910511Z","signature_b64":"qfURqz9n/9fn18csd0aQOoAqvjkUm9xovO5vHbwHrnfHhCJxhw9jJrBQOW68NlU+dTxG/BK+7CKDOv9l9S32Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e814be3cddf81bf667470de58defd56606448e1f005517e66acd1baf544f034d","last_reissued_at":"2026-07-05T08:07:26.910107Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:07:26.910107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.11921","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:07:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+VVkD11EOjPqX9qAL9E4Dtovc2vbiSL1V/yAu/oDQw7hpBOYmOfAifnf4y+j5enUzp4DezFWePm149BodV0wDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:29:35.177331Z"},"content_sha256":"9a7f07b1723da8ca416498cfca8d915b295d83dd49b14adc5bbbd84126b51586","schema_version":"1.0","event_id":"sha256:9a7f07b1723da8ca416498cfca8d915b295d83dd49b14adc5bbbd84126b51586"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5AKL4PG57AN7MZ2HBXSY336VMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Endomorphisms of varieties and Bott vanishing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Burt Totaro, Tatsuro Kawakami","submitted_at":"2023-02-23T10:57:07Z","abstract_excerpt":"We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. The classification results in characteristic zero are due to Amerik-Rovinsky-Van de Ven, Hwang-Mok, Paranjape-Srinivas, Beauville, and Shao-Zhong. Our method also bounds the degree of morphisms into a given var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11921","kind":"arxiv","version":5},"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/2302.11921/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":"2026-07-05T08:07:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TLfXyxzexvOTmCvz5WsIqNUUJkHH45PAjdKxvfRsSQHjd22X8Lz+ZTIqK/TONGA3sK18ZENkIWbQ1/FAjis9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:29:35.177974Z"},"content_sha256":"d0e4c6b2096deff0825822c64e07a594b9cd0216d49c5d11be285eecf3218d76","schema_version":"1.0","event_id":"sha256:d0e4c6b2096deff0825822c64e07a594b9cd0216d49c5d11be285eecf3218d76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5AKL4PG57AN7MZ2HBXSY336VMY/bundle.json","state_url":"https://pith.science/pith/5AKL4PG57AN7MZ2HBXSY336VMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5AKL4PG57AN7MZ2HBXSY336VMY/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":"2026-08-11T17:29:35Z","links":{"resolver":"https://pith.science/pith/5AKL4PG57AN7MZ2HBXSY336VMY","bundle":"https://pith.science/pith/5AKL4PG57AN7MZ2HBXSY336VMY/bundle.json","state":"https://pith.science/pith/5AKL4PG57AN7MZ2HBXSY336VMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5AKL4PG57AN7MZ2HBXSY336VMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5AKL4PG57AN7MZ2HBXSY336VMY","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":"0fd2a2acc1c4bf2d62759cabee99f8a5cdd683dd587ab924a57b5efea1d552a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-23T10:57:07Z","title_canon_sha256":"c54d062591fa0f348fc9989f976330533bc63759c73d8185df84714bd717f04d"},"schema_version":"1.0","source":{"id":"2302.11921","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.11921","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"arxiv_version","alias_value":"2302.11921v5","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11921","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"pith_short_12","alias_value":"5AKL4PG57AN7","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"pith_short_16","alias_value":"5AKL4PG57AN7MZ2H","created_at":"2026-07-05T08:07:26Z"},{"alias_kind":"pith_short_8","alias_value":"5AKL4PG5","created_at":"2026-07-05T08:07:26Z"}],"graph_snapshots":[{"event_id":"sha256:d0e4c6b2096deff0825822c64e07a594b9cd0216d49c5d11be285eecf3218d76","target":"graph","created_at":"2026-07-05T08:07:26Z","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/2302.11921/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. The classification results in characteristic zero are due to Amerik-Rovinsky-Van de Ven, Hwang-Mok, Paranjape-Srinivas, Beauville, and Shao-Zhong. Our method also bounds the degree of morphisms into a given var","authors_text":"Burt Totaro, Tatsuro Kawakami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-23T10:57:07Z","title":"Endomorphisms of varieties and Bott vanishing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11921","kind":"arxiv","version":5},"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":"sha256:9a7f07b1723da8ca416498cfca8d915b295d83dd49b14adc5bbbd84126b51586","target":"record","created_at":"2026-07-05T08:07:26Z","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":"0fd2a2acc1c4bf2d62759cabee99f8a5cdd683dd587ab924a57b5efea1d552a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-23T10:57:07Z","title_canon_sha256":"c54d062591fa0f348fc9989f976330533bc63759c73d8185df84714bd717f04d"},"schema_version":"1.0","source":{"id":"2302.11921","kind":"arxiv","version":5}},"canonical_sha256":"e814be3cddf81bf667470de58defd56606448e1f005517e66acd1baf544f034d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e814be3cddf81bf667470de58defd56606448e1f005517e66acd1baf544f034d","first_computed_at":"2026-07-05T08:07:26.910107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:07:26.910107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qfURqz9n/9fn18csd0aQOoAqvjkUm9xovO5vHbwHrnfHhCJxhw9jJrBQOW68NlU+dTxG/BK+7CKDOv9l9S32Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:07:26.910511Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.11921","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a7f07b1723da8ca416498cfca8d915b295d83dd49b14adc5bbbd84126b51586","sha256:d0e4c6b2096deff0825822c64e07a594b9cd0216d49c5d11be285eecf3218d76"],"state_sha256":"504f78dda9fe017d2c36b05c4f8ab75ba52609acdb1b682697cc0ba2f3a30126"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u7OmwE3RpJzEy2Fro7Ti2nq5MDWi/Dme6lAIHo40BZyZkQjgf7BavaVNpahybpNgvGOHuiOjDS5DWb8biNVxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T17:29:35.184036Z","bundle_sha256":"b353ff0bec6a0835d5d2123e92c6ece3561c6b73f537277754c18dad017e8c48"}}