{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:7RHZTG3A76JWA6TLEIC2OKQ4XN","short_pith_number":"pith:7RHZTG3A","canonical_record":{"source":{"id":"2012.00441","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-12-01T12:26:54Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"9555eb836ee705ff2f8c93e5736e9c3a247d0028e851f73b57de8d019958921c","abstract_canon_sha256":"a4ac822970e798f4f04e031ddb8165814ec317b8f0a8d6b0c8447b39c107c2e0"},"schema_version":"1.0"},"canonical_sha256":"fc4f999b60ff93607a6b2205a72a1cbb6b7cb016e1e746e484da5c3d055450c6","source":{"kind":"arxiv","id":"2012.00441","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.00441","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"2012.00441v3","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.00441","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"7RHZTG3A76JW","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"pith_short_16","alias_value":"7RHZTG3A76JWA6TL","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"pith_short_8","alias_value":"7RHZTG3A","created_at":"2026-07-05T03:51:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:7RHZTG3A76JWA6TLEIC2OKQ4XN","target":"record","payload":{"canonical_record":{"source":{"id":"2012.00441","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-12-01T12:26:54Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"9555eb836ee705ff2f8c93e5736e9c3a247d0028e851f73b57de8d019958921c","abstract_canon_sha256":"a4ac822970e798f4f04e031ddb8165814ec317b8f0a8d6b0c8447b39c107c2e0"},"schema_version":"1.0"},"canonical_sha256":"fc4f999b60ff93607a6b2205a72a1cbb6b7cb016e1e746e484da5c3d055450c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:51:41.286192Z","signature_b64":"0+aFB8/qvv5Z8lwd/5EUpkuB9cJzQgwr8A21tYIomXmq9v5A8Y5j6A2aiH+ZQkDLoN/DXDQLkE63H9i0ff4ZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc4f999b60ff93607a6b2205a72a1cbb6b7cb016e1e746e484da5c3d055450c6","last_reissued_at":"2026-07-05T03:51:41.285508Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:51:41.285508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.00441","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFr7sfXWweFsK549Nk1rect2ExDSjg9Gcyw+VCTKF7wHtIuOxVsUF5Mo8ge+U24Rxoi0BeVC3+vthyo7IniVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:12:07.458535Z"},"content_sha256":"e928acece81d462ae6563d0066089c0ab150464f4513f1e9e9b726155b3353ac","schema_version":"1.0","event_id":"sha256:e928acece81d462ae6563d0066089c0ab150464f4513f1e9e9b726155b3353ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:7RHZTG3A76JWA6TLEIC2OKQ4XN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic approximation and the decomposition theorem for K\\\"ahler Calabi-Yau varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Benjamin Bakker, Christian Lehn, Henri Guenancia","submitted_at":"2020-12-01T12:26:54Z","abstract_excerpt":"We extend the decomposition theorem for numerically $K$-trivial varieties with log terminal singularities to the K\\\"ahler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus completing the numerically $K$-trivial case of a conjecture of Campana and Peternell."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.00441","kind":"arxiv","version":3},"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/2012.00441/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":"2026-07-05T03:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2i8R2A57ClBQDDK49uVEaPP1KKawlSHRNBxg+PmIS4nxQMeKsN7ap5YJR/qT14RAOHa7WFfWL9jDCnyt5u7XBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:12:07.459043Z"},"content_sha256":"826e47b7f991a5360f7550144267e4168f53150f0c347eb42c132540c94db443","schema_version":"1.0","event_id":"sha256:826e47b7f991a5360f7550144267e4168f53150f0c347eb42c132540c94db443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN/bundle.json","state_url":"https://pith.science/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN/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":"2026-08-05T00:12:07Z","links":{"resolver":"https://pith.science/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN","bundle":"https://pith.science/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN/bundle.json","state":"https://pith.science/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RHZTG3A76JWA6TLEIC2OKQ4XN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7RHZTG3A76JWA6TLEIC2OKQ4XN","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":"a4ac822970e798f4f04e031ddb8165814ec317b8f0a8d6b0c8447b39c107c2e0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-12-01T12:26:54Z","title_canon_sha256":"9555eb836ee705ff2f8c93e5736e9c3a247d0028e851f73b57de8d019958921c"},"schema_version":"1.0","source":{"id":"2012.00441","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.00441","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"2012.00441v3","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.00441","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"7RHZTG3A76JW","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"pith_short_16","alias_value":"7RHZTG3A76JWA6TL","created_at":"2026-07-05T03:51:41Z"},{"alias_kind":"pith_short_8","alias_value":"7RHZTG3A","created_at":"2026-07-05T03:51:41Z"}],"graph_snapshots":[{"event_id":"sha256:826e47b7f991a5360f7550144267e4168f53150f0c347eb42c132540c94db443","target":"graph","created_at":"2026-07-05T03:51:41Z","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/2012.00441/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the decomposition theorem for numerically $K$-trivial varieties with log terminal singularities to the K\\\"ahler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus completing the numerically $K$-trivial case of a conjecture of Campana and Peternell.","authors_text":"Benjamin Bakker, Christian Lehn, Henri Guenancia","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-12-01T12:26:54Z","title":"Algebraic approximation and the decomposition theorem for K\\\"ahler Calabi-Yau varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.00441","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:e928acece81d462ae6563d0066089c0ab150464f4513f1e9e9b726155b3353ac","target":"record","created_at":"2026-07-05T03:51:41Z","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":"a4ac822970e798f4f04e031ddb8165814ec317b8f0a8d6b0c8447b39c107c2e0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-12-01T12:26:54Z","title_canon_sha256":"9555eb836ee705ff2f8c93e5736e9c3a247d0028e851f73b57de8d019958921c"},"schema_version":"1.0","source":{"id":"2012.00441","kind":"arxiv","version":3}},"canonical_sha256":"fc4f999b60ff93607a6b2205a72a1cbb6b7cb016e1e746e484da5c3d055450c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4f999b60ff93607a6b2205a72a1cbb6b7cb016e1e746e484da5c3d055450c6","first_computed_at":"2026-07-05T03:51:41.285508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:51:41.285508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0+aFB8/qvv5Z8lwd/5EUpkuB9cJzQgwr8A21tYIomXmq9v5A8Y5j6A2aiH+ZQkDLoN/DXDQLkE63H9i0ff4ZCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:51:41.286192Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.00441","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e928acece81d462ae6563d0066089c0ab150464f4513f1e9e9b726155b3353ac","sha256:826e47b7f991a5360f7550144267e4168f53150f0c347eb42c132540c94db443"],"state_sha256":"f98e243782c9c09258984c30afb84d709cca4612b736d2486aefbd24a8b0ac7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zW0DNM1DpIwjY3NM4ULm6VXdHf/j5cl0qQW5ZsY/0VUEBVFO1L0Yf9cUfNgtweoKVZoRErNZyYZeduVNaOZtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:12:07.462841Z","bundle_sha256":"76da7dfd550c35ef92b50c1c26f5d81312a379cc56b967c6f203cc8d151c1039"}}