{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F4HZYHX4RLSRBMQHXW43B5E3NO","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":"9d3640905cab73b831fe7e0e6076892151e6eab22d9321d6d1ba8afbb3de2cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-15T15:10:40Z","title_canon_sha256":"1f15c0726d4dbeb3270b451a33306e26cca0eb1fce513b9589d7a1d45d661820"},"schema_version":"1.0","source":{"id":"1912.07054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.07054","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1912.07054v2","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.07054","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"F4HZYHX4RLSR","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"F4HZYHX4RLSRBMQH","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"F4HZYHX4","created_at":"2026-07-05T04:14:21Z"}],"graph_snapshots":[{"event_id":"sha256:102aa8ff05de2c3d8b48404b9f5af489791e0cc0e39946cf1bf9f867f254b002","target":"graph","created_at":"2026-07-05T04:14:21Z","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/1912.07054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $m>1$ and $\\mathfrak{d} \\neq 0$ be integers such that $v_{p}(\\mathfrak{d}) \\neq m$ for any prime $p$. We construct a matrix $A(\\mathfrak{d})$ of size $(m-1) \\times (m-1)$ depending on only of $\\mathfrak{d}$ with the following property: For any tame $\\mathbb{Z}/m\\mathbb{Z}$-number field $K$ of discriminant $\\mathfrak{d}$ the matrix $A(\\mathfrak{d})$ represents the Gram matrix of the integral trace zero form of $K$. In particular, we have that the integral trace zero form of tame cyclic number fields is determined by the degree and discriminant of the field. Furthermore, if in addition to th","authors_text":"Guillermo Mantilla-Soler, Wilmar Bola\\~nos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-15T15:10:40Z","title":"The Shape of cyclic number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.07054","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":"sha256:3145ff6356fb638e972308aaa44efaa6b9f86ae95e97fa4aa4d2ef2e73eeed35","target":"record","created_at":"2026-07-05T04:14:21Z","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":"9d3640905cab73b831fe7e0e6076892151e6eab22d9321d6d1ba8afbb3de2cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-15T15:10:40Z","title_canon_sha256":"1f15c0726d4dbeb3270b451a33306e26cca0eb1fce513b9589d7a1d45d661820"},"schema_version":"1.0","source":{"id":"1912.07054","kind":"arxiv","version":2}},"canonical_sha256":"2f0f9c1efc8ae510b207bdb9b0f49b6b8d74737513155f0b9b34f9cefb928367","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f0f9c1efc8ae510b207bdb9b0f49b6b8d74737513155f0b9b34f9cefb928367","first_computed_at":"2026-07-05T04:14:21.986137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:14:21.986137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ro9meiSn2INVfNFD3vRCD0R0D5XDWu1ucr64INwsTTLOQRdRYzZG1XZ7MYHzc7Ypy4pIpSt32YXgq1PADnEiAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:14:21.986484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.07054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3145ff6356fb638e972308aaa44efaa6b9f86ae95e97fa4aa4d2ef2e73eeed35","sha256:102aa8ff05de2c3d8b48404b9f5af489791e0cc0e39946cf1bf9f867f254b002"],"state_sha256":"fbb088aa130581f7b0cb958c61fbc2beff9e50cb2171da7d8da32e4032a50875"}