{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:TDJLC564ZP3A2DSSR3T3UE7JYZ","short_pith_number":"pith:TDJLC564","canonical_record":{"source":{"id":"math/9906006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-06-01T22:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"c1c5acb9a9054c91fbfc7110303ae7a8ebea346e0a5547bb516bd3d23ec63421","abstract_canon_sha256":"1ca98c1aa76f231dc0b9a6fe761d7e502dca1c1623a852b1ceebab38c1d126b9"},"schema_version":"1.0"},"canonical_sha256":"98d2b177dccbf60d0e528ee7ba13e9c67bf2c9db96d883c24c2901717384a204","source":{"kind":"arxiv","id":"math/9906006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9906006","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/9906006v1","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9906006","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"TDJLC564ZP3A","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"TDJLC564ZP3A2DSS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"TDJLC564","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:TDJLC564ZP3A2DSSR3T3UE7JYZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/9906006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-06-01T22:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"c1c5acb9a9054c91fbfc7110303ae7a8ebea346e0a5547bb516bd3d23ec63421","abstract_canon_sha256":"1ca98c1aa76f231dc0b9a6fe761d7e502dca1c1623a852b1ceebab38c1d126b9"},"schema_version":"1.0"},"canonical_sha256":"98d2b177dccbf60d0e528ee7ba13e9c67bf2c9db96d883c24c2901717384a204","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:57.471550Z","signature_b64":"12MEuu6HD/n8Ok17wiSQpaBsYAhhxzmClDVTo7oZnL917hoCpwx1dRwmkNPiLzHBOspdgjsHlnYV70L03TjJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98d2b177dccbf60d0e528ee7ba13e9c67bf2c9db96d883c24c2901717384a204","last_reissued_at":"2026-05-18T00:12:57.471028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:57.471028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9906006","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":"2026-05-18T00:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0A4q0wzrmVLjZa3psYVGhw2rEueAyMELtE8jmP8y1G1jsEviL3VB224a/tCXmR4WMNxGTNViXf+ishOuESLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:27:22.690153Z"},"content_sha256":"e9d40a86b526e8345fbf605fddf0ba065947bcfdcfb1ff0976307aae5368cc3a","schema_version":"1.0","event_id":"sha256:e9d40a86b526e8345fbf605fddf0ba065947bcfdcfb1ff0976307aae5368cc3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:TDJLC564ZP3A2DSSR3T3UE7JYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Vorontsov's theorem on K3 surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. -Q. Zhang, K. Oguiso","submitted_at":"1999-06-01T22:11:08Z","abstract_excerpt":"Let X be a K3 surface with the Neron-Severi lattice S_X and transcendental lattice T_X. Nukulin considered the kernel H_X of the natural representation Aut(X) ---> O(S_X) and proved that H_{X} is a finite cyclic group with phi(h(X))) | t(X) and acts faithfully on the space H^{2,0}(X) = C omega_{X}, where h(X) = ord(H_X), t(X) = rank T_X and phi(.) is the Euler function. Consider the extremal case where phi(h(X)) = t(X). In the situation where T_{X} is unimodular, Kondo has determined the list of t(X), as well as the actual realizations, and showed that t(X) alone uniquely determines the isomor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9906006","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":""},"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":"2026-05-18T00:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMOdav3A9kKV1fyyVUBYZI0IgGqlFmBmtEM1bg0nf7OSIJBbqtgbvHway3cZfrUNtfCw3mjKCtWKtLy2T4ZXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:27:22.690519Z"},"content_sha256":"df1663494ddee5cbb613831216f7be077c42e083fd678e596d007f382aef6a1e","schema_version":"1.0","event_id":"sha256:df1663494ddee5cbb613831216f7be077c42e083fd678e596d007f382aef6a1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ/bundle.json","state_url":"https://pith.science/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ/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":"2026-06-27T20:27:22Z","links":{"resolver":"https://pith.science/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ","bundle":"https://pith.science/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ/bundle.json","state":"https://pith.science/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDJLC564ZP3A2DSSR3T3UE7JYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:TDJLC564ZP3A2DSSR3T3UE7JYZ","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":"1ca98c1aa76f231dc0b9a6fe761d7e502dca1c1623a852b1ceebab38c1d126b9","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-06-01T22:11:08Z","title_canon_sha256":"c1c5acb9a9054c91fbfc7110303ae7a8ebea346e0a5547bb516bd3d23ec63421"},"schema_version":"1.0","source":{"id":"math/9906006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9906006","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/9906006v1","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9906006","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"TDJLC564ZP3A","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"TDJLC564ZP3A2DSS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"TDJLC564","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:df1663494ddee5cbb613831216f7be077c42e083fd678e596d007f382aef6a1e","target":"graph","created_at":"2026-05-18T00:12:57Z","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"},"paper":{"abstract_excerpt":"Let X be a K3 surface with the Neron-Severi lattice S_X and transcendental lattice T_X. Nukulin considered the kernel H_X of the natural representation Aut(X) ---> O(S_X) and proved that H_{X} is a finite cyclic group with phi(h(X))) | t(X) and acts faithfully on the space H^{2,0}(X) = C omega_{X}, where h(X) = ord(H_X), t(X) = rank T_X and phi(.) is the Euler function. Consider the extremal case where phi(h(X)) = t(X). In the situation where T_{X} is unimodular, Kondo has determined the list of t(X), as well as the actual realizations, and showed that t(X) alone uniquely determines the isomor","authors_text":"D. -Q. Zhang, K. Oguiso","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1999-06-01T22:11:08Z","title":"On Vorontsov's theorem on K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9906006","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:e9d40a86b526e8345fbf605fddf0ba065947bcfdcfb1ff0976307aae5368cc3a","target":"record","created_at":"2026-05-18T00:12:57Z","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":"1ca98c1aa76f231dc0b9a6fe761d7e502dca1c1623a852b1ceebab38c1d126b9","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-06-01T22:11:08Z","title_canon_sha256":"c1c5acb9a9054c91fbfc7110303ae7a8ebea346e0a5547bb516bd3d23ec63421"},"schema_version":"1.0","source":{"id":"math/9906006","kind":"arxiv","version":1}},"canonical_sha256":"98d2b177dccbf60d0e528ee7ba13e9c67bf2c9db96d883c24c2901717384a204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98d2b177dccbf60d0e528ee7ba13e9c67bf2c9db96d883c24c2901717384a204","first_computed_at":"2026-05-18T00:12:57.471028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:57.471028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"12MEuu6HD/n8Ok17wiSQpaBsYAhhxzmClDVTo7oZnL917hoCpwx1dRwmkNPiLzHBOspdgjsHlnYV70L03TjJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:57.471550Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9906006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d40a86b526e8345fbf605fddf0ba065947bcfdcfb1ff0976307aae5368cc3a","sha256:df1663494ddee5cbb613831216f7be077c42e083fd678e596d007f382aef6a1e"],"state_sha256":"2ee853526f92bc0aebacd77334823005a016b2b2a464bd4060c44eb91ef52d5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01ugqXJsZP6HcntHLP7kYW17wcSH92ClSwkO5PuvmbXas3RpdpUt59AdFwC+HXCP/BanUiVxt8W9Vtz/HcVyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:27:22.692446Z","bundle_sha256":"059877bc810f5f528ddba188ea6fc34b1eff7c15f8b101b40e1c5c8b12a5e772"}}