{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NYGWZKU6RJDDPMYMTY7DAUGHBL","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":"36a776ae252a5fd07b8f025d993f25c8db4fb27eea36539e93202f335c3d5bc6","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T20:00:02Z","title_canon_sha256":"26aa6cdace034c9d65a6912ce4bb8a0fb6a3ce5824fed1571e2ed1ecbc0d98f8"},"schema_version":"1.0","source":{"id":"1604.06098","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06098","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06098v3","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06098","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"NYGWZKU6RJDD","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"pith_short_16","alias_value":"NYGWZKU6RJDDPMYM","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"pith_short_8","alias_value":"NYGWZKU6","created_at":"2026-07-05T00:32:35Z"}],"graph_snapshots":[{"event_id":"sha256:fff21591fd0ddbe3f99587f215a4843be3c552b1d3e8f454517d14a9f3c2ae8b","target":"graph","created_at":"2026-07-05T00:32:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1604.06098/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For certain real quadratic fields $K$ with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of $K$ using a numerical method that arose in the study of complete sets of equiangular lines in $\\mathbb{C}^d$ (known in quantum information as symmetric informationally complete measurements or SICs). The construction in low dimensions suggests a general recipe for producing unit generators in infinite towers of ray class fields above arbitrary real quadratic $K$, and we summarise this in a conjecture. There are indications [19,20] that the logarithms o","authors_text":"Gary McConnell, Jon Yard, Marcus Appleby, Steven Flammia","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T20:00:02Z","title":"Generating Ray Class Fields of Real Quadratic Fields via Complex Equiangular Lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06098","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:acb39c615c38153792fec3478b5d3855b9881c90a995f5ca1119ad4da86a6bf3","target":"record","created_at":"2026-07-05T00:32:35Z","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":"36a776ae252a5fd07b8f025d993f25c8db4fb27eea36539e93202f335c3d5bc6","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T20:00:02Z","title_canon_sha256":"26aa6cdace034c9d65a6912ce4bb8a0fb6a3ce5824fed1571e2ed1ecbc0d98f8"},"schema_version":"1.0","source":{"id":"1604.06098","kind":"arxiv","version":3}},"canonical_sha256":"6e0d6caa9e8a4637b30c9e3e3050c70acb49e545a6b7b1a456be1bd061612e22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e0d6caa9e8a4637b30c9e3e3050c70acb49e545a6b7b1a456be1bd061612e22","first_computed_at":"2026-07-05T00:32:35.255056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:32:35.255056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pq5kfZrWxYwjkHsHpqAtkmhrhuFr2244nDMmsw8Q0yZ9sOK2QwnnanCFpOqYZrJl//oSAeByhJ2762uqkqU0Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T00:32:35.255530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06098","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb39c615c38153792fec3478b5d3855b9881c90a995f5ca1119ad4da86a6bf3","sha256:fff21591fd0ddbe3f99587f215a4843be3c552b1d3e8f454517d14a9f3c2ae8b"],"state_sha256":"7cc2a664da9a12ed400db5aee63e4ad916bfcef9ad5c6619cedf4501f0350d12"}