{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AYE4MAXDCGSCJZECPB5HFSMJYT","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":"2172e18bec01ac6bb487e8b9d2ce41c7634c75806ef95ee127af1fcb5bdbd825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-09T22:20:47Z","title_canon_sha256":"45670717d324d50802ecc990f7aaa79900027fa98b466435a2f486bb9fa57f2e"},"schema_version":"1.0","source":{"id":"1008.1602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1602","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1602v1","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1602","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"AYE4MAXDCGSC","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AYE4MAXDCGSCJZEC","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AYE4MAXD","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:8ea22342598743e9447f8eec28848fab6a973bfa78788e52f3043861a581e2d7","target":"graph","created_at":"2026-05-18T04:42:23Z","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":"The space of Siegel cuspforms of degree $2$ of weight $3$ with respect to the congruence subgroup $\\G_2(2,4,8)$ was studied by van Geemen and van Straten in Math. computation. {\\bf 61} (1993). They showed the space is generated by six-tuple products of Igusa $\\th$-constants, and all of them are Hecke eigenforms. They gave conjecture on the explicit description of the Andrianov $L$-functions. In J. Number Theory. {\\bf 125} (2007), we proved some conjectures by showing that some products are obtained by the Yoshida lift, a construction of Siegel eigenforms. But, other products are not obtained b","authors_text":"Takeo Okazaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-09T22:20:47Z","title":"L-functions of $S_3(\\G_2(2,4,8))$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1602","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":"sha256:082dbca98aaa82a91a124e61dc69ddb93acd8046a949e171ff85308bb9251e1c","target":"record","created_at":"2026-05-18T04:42:23Z","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":"2172e18bec01ac6bb487e8b9d2ce41c7634c75806ef95ee127af1fcb5bdbd825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-09T22:20:47Z","title_canon_sha256":"45670717d324d50802ecc990f7aaa79900027fa98b466435a2f486bb9fa57f2e"},"schema_version":"1.0","source":{"id":"1008.1602","kind":"arxiv","version":1}},"canonical_sha256":"0609c602e311a424e482787a72c989c4d0201ae3afe4582c5671a388746fe4b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0609c602e311a424e482787a72c989c4d0201ae3afe4582c5671a388746fe4b8","first_computed_at":"2026-05-18T04:42:23.727801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:23.727801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G44lU9dwUpBjcQ8SV1SgN0AWR+27Ane3nPahLDf3+L3ETn0AYLBq9dnkwVqwnvtGZziyoDk6n5A9Pw0kc7NrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:23.728397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:082dbca98aaa82a91a124e61dc69ddb93acd8046a949e171ff85308bb9251e1c","sha256:8ea22342598743e9447f8eec28848fab6a973bfa78788e52f3043861a581e2d7"],"state_sha256":"f05d8092f7e9e624697f8378879da67344090c61580f9a2c06aa1efff1efe96c"}