{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:K2MG53HP64QQMK7MZ7XHAOLBAH","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":"7e6560b5cdddcdab3abec5262080da12f21e4ae304885a34b75dd23bd81939d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T04:13:13Z","title_canon_sha256":"d9407f27da1fb08b7311982e65cc293bb607b27b102e4deafae1e3e68632b4f1"},"schema_version":"1.0","source":{"id":"1608.06705","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06705","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06705v3","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06705","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"K2MG53HP64QQ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"K2MG53HP64QQMK7M","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"K2MG53HP","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:c76d430b49506f86b0400e443bb909fe95378dd1c0d335e9284da1507cdf5728","target":"graph","created_at":"2026-05-18T00:38:39Z","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 $K$ be an imaginary quadratic field, and let $\\mathfrak{f}$ be a nontrivial integral ideal of $K$. Hasse and Ramachandra asked whether the ray class field of $K$ modulo $\\mathfrak{f}$ can be generated by a single value of the Weber function. We completely resolve this question when $\\mathfrak{f}=(N)$ for an integer $N>1$.","authors_text":"Dong Hwa Shin, Dong Sung Yoon, Ja Kyung Koo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T04:13:13Z","title":"On a problem of Hasse and Ramachandra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06705","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":"sha256:734653a8e9306033c417184dacf3e8260baf591ed818b30f17d32b14b2aed119","target":"record","created_at":"2026-05-18T00:38:39Z","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":"7e6560b5cdddcdab3abec5262080da12f21e4ae304885a34b75dd23bd81939d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T04:13:13Z","title_canon_sha256":"d9407f27da1fb08b7311982e65cc293bb607b27b102e4deafae1e3e68632b4f1"},"schema_version":"1.0","source":{"id":"1608.06705","kind":"arxiv","version":3}},"canonical_sha256":"56986eeceff721062beccfee70396101d20c6c4e02f5439e7111f66ca5475c1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56986eeceff721062beccfee70396101d20c6c4e02f5439e7111f66ca5475c1a","first_computed_at":"2026-05-18T00:38:39.932202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:39.932202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/slJXIsTT8Kdt6O8wrN1JzaujLunUwWXqtpuImRGxvqgUGube0bZTK4Z07I0hC0vF1T/aRmGbxQ9pS0XcAEQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:39.932738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06705","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734653a8e9306033c417184dacf3e8260baf591ed818b30f17d32b14b2aed119","sha256:c76d430b49506f86b0400e443bb909fe95378dd1c0d335e9284da1507cdf5728"],"state_sha256":"59f02c8b6bbba20e067ab5f304f855acbed8708ff2c87372245e93dc183b8f46"}