{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WYEDUSJI6OC6LSXMSY55RGQHYM","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":"19e8bbe8431cd006806dc53b9f8cc90e70b9744dc721253710f7abdd9f7fe765","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-15T09:26:38Z","title_canon_sha256":"cbadbc87d7d152861f4cd0e6a4995ba8816d1d22024a51666839fccbd1dd1593"},"schema_version":"1.0","source":{"id":"1712.06502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06502","created_at":"2026-05-18T00:25:28Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06502v2","created_at":"2026-05-18T00:25:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06502","created_at":"2026-05-18T00:25:28Z"},{"alias_kind":"pith_short_12","alias_value":"WYEDUSJI6OC6","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WYEDUSJI6OC6LSXM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WYEDUSJI","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:73e103adf7add16d647e38d058d6575bc74f8533eaaa77f03c1675d9b8d83fd0","target":"graph","created_at":"2026-05-18T00:25:28Z","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":"We show that the field $\\mathbb{Q}(x,y)$, generated by two singular moduli~$x$ and~$y$, is generated by their sum ${x+y}$, unless~$x$ and~$y$ are conjugate over~$\\mathbb{Q}$, in which case ${x+y}$ generates a subfield of degree at most~$2$. We obtain a similar result for the product of two singular moduli.","authors_text":"Antonin Riffaut, Bernadette Faye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-15T09:26:38Z","title":"Fields generated by sums and products of singular moduli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06502","kind":"arxiv","version":2},"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":"sha256:8de1f12a35084ed76e2d2a9695afd6b57b3be0e287f453b68d4cbb497e7d5e7e","target":"record","created_at":"2026-05-18T00:25:28Z","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":"19e8bbe8431cd006806dc53b9f8cc90e70b9744dc721253710f7abdd9f7fe765","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-15T09:26:38Z","title_canon_sha256":"cbadbc87d7d152861f4cd0e6a4995ba8816d1d22024a51666839fccbd1dd1593"},"schema_version":"1.0","source":{"id":"1712.06502","kind":"arxiv","version":2}},"canonical_sha256":"b6083a4928f385e5caec963bd89a07c31f8c0a99246877a0e08fbd0989559de4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6083a4928f385e5caec963bd89a07c31f8c0a99246877a0e08fbd0989559de4","first_computed_at":"2026-05-18T00:25:28.581262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:28.581262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGIK7PvgRaO4dtuqQX8z+CdhdjCs8UFGEnMUgZcK5O8RBsJLPXC5Ly4Q31EE/vMCoNQWurTtoNh0O7N+GwuKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:28.582046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8de1f12a35084ed76e2d2a9695afd6b57b3be0e287f453b68d4cbb497e7d5e7e","sha256:73e103adf7add16d647e38d058d6575bc74f8533eaaa77f03c1675d9b8d83fd0"],"state_sha256":"59717b01fcec2744696f052baf219b818840b3bd555f9b40cedb58a11bd2f462"}