{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZSNRPBBAVFIJ73ETYMMQKAUVPF","short_pith_number":"pith:ZSNRPBBA","canonical_record":{"source":{"id":"2505.21145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-27T12:56:27Z","cross_cats_sorted":[],"title_canon_sha256":"7c54938485c7c7a5e0b427fa0fee17ce34ad13866cef16bcc8a93f3f5e71f1ee","abstract_canon_sha256":"dbd00541988bc7b1c7075bd2e85b31c19f5db79be6c972e767c1899923636ae4"},"schema_version":"1.0"},"canonical_sha256":"cc9b178420a9509fec93c319050295797ffa398449853ec9bee766a0cdc0c06b","source":{"kind":"arxiv","id":"2505.21145","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21145","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21145v1","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21145","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZSNRPBBAVFIJ","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"pith_short_16","alias_value":"ZSNRPBBAVFIJ73ET","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"pith_short_8","alias_value":"ZSNRPBBA","created_at":"2026-07-05T11:10:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZSNRPBBAVFIJ73ETYMMQKAUVPF","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-27T12:56:27Z","cross_cats_sorted":[],"title_canon_sha256":"7c54938485c7c7a5e0b427fa0fee17ce34ad13866cef16bcc8a93f3f5e71f1ee","abstract_canon_sha256":"dbd00541988bc7b1c7075bd2e85b31c19f5db79be6c972e767c1899923636ae4"},"schema_version":"1.0"},"canonical_sha256":"cc9b178420a9509fec93c319050295797ffa398449853ec9bee766a0cdc0c06b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:24.456926Z","signature_b64":"85nSBl/kMaOGonW2DeXa7NPsFga47tR6j772XkAg7sKPa/02gNK+3ncWWbK5zmyaEjhQaLgAA4fSJHkyeOOgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc9b178420a9509fec93c319050295797ffa398449853ec9bee766a0cdc0c06b","last_reissued_at":"2026-07-05T11:10:24.456489Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:24.456489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21145","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":"2026-07-05T11:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EeiRFV+yrnDoTlEZ0J3Giu4eHqP6kfZO8UX8Px4zYRTI2N7/o7kWx5G/WD+eXynmKdCJzX5vfdpVwRIibe7IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:18:03.431085Z"},"content_sha256":"84d85b6d0ca76c65bc087e0ed5c47c7a7588ab08c1c185d67b798677f0749765","schema_version":"1.0","event_id":"sha256:84d85b6d0ca76c65bc087e0ed5c47c7a7588ab08c1c185d67b798677f0749765"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZSNRPBBAVFIJ73ETYMMQKAUVPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On endomorphisms of varieties which are injective on open subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Takumi Asano","submitted_at":"2025-05-27T12:56:27Z","abstract_excerpt":"We consider conditions under which endomorphisms of varieties become automorphisms. For example, there is a remarkable theorem, called Ax-Grothendieck theorem, which states that any injective endomorphism of a variety is bijective. Over an algebraically closed field of characteristic zero, bijectivity of endomorphisms of varieties implies that the endomorphisms are automorphisms, thus Ax-Grothendieck theorem gives one of the conditions we considering. There is also a conjecture, called Miyanishi conjecture, which claims that for any endomorphism of a variety over an algebraically closed field "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21145","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/2505.21145/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":"2026-07-05T11:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WvMKyoWJqcslWxni4hqpeunCijxR+Wbu2Gdm/C+5yg8JRLLT34xrJICYMa8tgH7Do8Z3tLJdht5aEVTB8tiBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:18:03.432011Z"},"content_sha256":"89dceb792e97b6924d3df960f8f12e671cb426d5944c2e5d275dc4c778a0120d","schema_version":"1.0","event_id":"sha256:89dceb792e97b6924d3df960f8f12e671cb426d5944c2e5d275dc4c778a0120d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF/bundle.json","state_url":"https://pith.science/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF/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":"2026-08-08T00:18:03Z","links":{"resolver":"https://pith.science/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF","bundle":"https://pith.science/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF/bundle.json","state":"https://pith.science/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSNRPBBAVFIJ73ETYMMQKAUVPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZSNRPBBAVFIJ73ETYMMQKAUVPF","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":"dbd00541988bc7b1c7075bd2e85b31c19f5db79be6c972e767c1899923636ae4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-27T12:56:27Z","title_canon_sha256":"7c54938485c7c7a5e0b427fa0fee17ce34ad13866cef16bcc8a93f3f5e71f1ee"},"schema_version":"1.0","source":{"id":"2505.21145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21145","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21145v1","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21145","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZSNRPBBAVFIJ","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"pith_short_16","alias_value":"ZSNRPBBAVFIJ73ET","created_at":"2026-07-05T11:10:24Z"},{"alias_kind":"pith_short_8","alias_value":"ZSNRPBBA","created_at":"2026-07-05T11:10:24Z"}],"graph_snapshots":[{"event_id":"sha256:89dceb792e97b6924d3df960f8f12e671cb426d5944c2e5d275dc4c778a0120d","target":"graph","created_at":"2026-07-05T11:10:24Z","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/2505.21145/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider conditions under which endomorphisms of varieties become automorphisms. For example, there is a remarkable theorem, called Ax-Grothendieck theorem, which states that any injective endomorphism of a variety is bijective. Over an algebraically closed field of characteristic zero, bijectivity of endomorphisms of varieties implies that the endomorphisms are automorphisms, thus Ax-Grothendieck theorem gives one of the conditions we considering. There is also a conjecture, called Miyanishi conjecture, which claims that for any endomorphism of a variety over an algebraically closed field ","authors_text":"Takumi Asano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-27T12:56:27Z","title":"On endomorphisms of varieties which are injective on open subsets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21145","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":"sha256:84d85b6d0ca76c65bc087e0ed5c47c7a7588ab08c1c185d67b798677f0749765","target":"record","created_at":"2026-07-05T11:10:24Z","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":"dbd00541988bc7b1c7075bd2e85b31c19f5db79be6c972e767c1899923636ae4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-27T12:56:27Z","title_canon_sha256":"7c54938485c7c7a5e0b427fa0fee17ce34ad13866cef16bcc8a93f3f5e71f1ee"},"schema_version":"1.0","source":{"id":"2505.21145","kind":"arxiv","version":1}},"canonical_sha256":"cc9b178420a9509fec93c319050295797ffa398449853ec9bee766a0cdc0c06b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc9b178420a9509fec93c319050295797ffa398449853ec9bee766a0cdc0c06b","first_computed_at":"2026-07-05T11:10:24.456489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:24.456489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"85nSBl/kMaOGonW2DeXa7NPsFga47tR6j772XkAg7sKPa/02gNK+3ncWWbK5zmyaEjhQaLgAA4fSJHkyeOOgDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:24.456926Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84d85b6d0ca76c65bc087e0ed5c47c7a7588ab08c1c185d67b798677f0749765","sha256:89dceb792e97b6924d3df960f8f12e671cb426d5944c2e5d275dc4c778a0120d"],"state_sha256":"2a75d50536517bcc2c3535bf47856c39a1e227a0e1420ac9c79645e637056fde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n/JMYh3p1zl6Mtdtn48N1IGLUiNKC4iT2rfot5WECCBNw9Zg7dUxx++OC1qVumWkECKPF7eNcDDaNFjSsVmaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T00:18:03.439648Z","bundle_sha256":"923a28e145523d9c15b1b18d34f9e6a806737fba9506cd6ad93d44b72430d921"}}