{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:TSMTJ72X73ADSZZSQFGSXX4X2N","short_pith_number":"pith:TSMTJ72X","schema_version":"1.0","canonical_sha256":"9c9934ff57fec0396732814d2bdf97d356b0a58ce03fb06832f917a6cc741e54","source":{"kind":"arxiv","id":"math/0506610","version":1},"attestation_state":"computed","paper":{"title":"The Alternating Groups and K3 Surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. -Q. Zhang","submitted_at":"2005-06-30T02:11:57Z","abstract_excerpt":"In this note, we consider all possible extensions G of a non-trivial perfect group H acting faithfully on a K3 surface X. The pair (X, G) is proved to be uniquely determined by G if the transcendental value of G is maximum. In particular, we have G/H < Z/(2) + Z/(2), if H is the alternating group A_5 and normal in G."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0506610","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-06-30T02:11:57Z","cross_cats_sorted":[],"title_canon_sha256":"1e907c630306ede83ad9dacafad0fea0ac4865f0ef0972d970aa5e9acb516be3","abstract_canon_sha256":"033e840aaf7cfbb25167ce175f763d291398da1ab8661e39e61b2fb709e58c92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:11.576437Z","signature_b64":"5XECS7W1sgQu6Iw3hh7qs2P0enaOBeerjUsktMdz02uBz+b5wCaKG0QbNIKxvY+jKx+rgSt1J5e9RxvewfvRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c9934ff57fec0396732814d2bdf97d356b0a58ce03fb06832f917a6cc741e54","last_reissued_at":"2026-07-04T14:40:11.575978Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:11.575978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Alternating Groups and K3 Surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. -Q. Zhang","submitted_at":"2005-06-30T02:11:57Z","abstract_excerpt":"In this note, we consider all possible extensions G of a non-trivial perfect group H acting faithfully on a K3 surface X. The pair (X, G) is proved to be uniquely determined by G if the transcendental value of G is maximum. In particular, we have G/H < Z/(2) + Z/(2), if H is the alternating group A_5 and normal in G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506610","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/math/0506610/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0506610","created_at":"2026-07-04T14:40:11.576043+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506610v1","created_at":"2026-07-04T14:40:11.576043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506610","created_at":"2026-07-04T14:40:11.576043+00:00"},{"alias_kind":"pith_short_12","alias_value":"TSMTJ72X73AD","created_at":"2026-07-04T14:40:11.576043+00:00"},{"alias_kind":"pith_short_16","alias_value":"TSMTJ72X73ADSZZS","created_at":"2026-07-04T14:40:11.576043+00:00"},{"alias_kind":"pith_short_8","alias_value":"TSMTJ72X","created_at":"2026-07-04T14:40:11.576043+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N","json":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N.json","graph_json":"https://pith.science/api/pith-number/TSMTJ72X73ADSZZSQFGSXX4X2N/graph.json","events_json":"https://pith.science/api/pith-number/TSMTJ72X73ADSZZSQFGSXX4X2N/events.json","paper":"https://pith.science/paper/TSMTJ72X"},"agent_actions":{"view_html":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N","download_json":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N.json","view_paper":"https://pith.science/paper/TSMTJ72X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506610&json=true","fetch_graph":"https://pith.science/api/pith-number/TSMTJ72X73ADSZZSQFGSXX4X2N/graph.json","fetch_events":"https://pith.science/api/pith-number/TSMTJ72X73ADSZZSQFGSXX4X2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N/action/storage_attestation","attest_author":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N/action/author_attestation","sign_citation":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N/action/citation_signature","submit_replication":"https://pith.science/pith/TSMTJ72X73ADSZZSQFGSXX4X2N/action/replication_record"}},"created_at":"2026-07-04T14:40:11.576043+00:00","updated_at":"2026-07-04T14:40:11.576043+00:00"}