{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:G5LCDSJ3IIXHFKGZSNLB7PQMTF","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":"f7fffd46c741d1fad87179600bc34a801b47eb3dafdb00a014d7fa58c090759a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-12T11:09:34Z","title_canon_sha256":"6ea148e32d51affc2eade3b5f122870192704a6b92524e6fd7b5540958240359"},"schema_version":"1.0","source":{"id":"2409.07941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.07941","created_at":"2026-07-05T09:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"2409.07941v1","created_at":"2026-07-05T09:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.07941","created_at":"2026-07-05T09:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"G5LCDSJ3IIXH","created_at":"2026-07-05T09:06:17Z"},{"alias_kind":"pith_short_16","alias_value":"G5LCDSJ3IIXHFKGZ","created_at":"2026-07-05T09:06:17Z"},{"alias_kind":"pith_short_8","alias_value":"G5LCDSJ3","created_at":"2026-07-05T09:06:17Z"}],"graph_snapshots":[{"event_id":"sha256:21b36cdb379d7520f10950a8ca716916aaac5f2dcdad1e5a1da134e04ccb0f2a","target":"graph","created_at":"2026-07-05T09:06:17Z","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/2409.07941/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is universal. We also construct an example illustrating that the positive-definiteness condition is necessary.","authors_text":"Anna R\\r{u}\\v{z}i\\v{c}kov\\'a, Emma P\\v{e}chou\\v{c}kov\\'a, Mat\\v{e}j Dole\\v{z}\\'alek, Mikul\\'a\\v{s} Zindulka (Charles University), Om Prakash, Ond\\v{r}ej Chwiedziuk, Simona Hlavinkov\\'a, Zden\\v{e}k Pezlar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-12T11:09:34Z","title":"No proper generalized quadratic forms are universal over quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.07941","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:e7cf8c3b148d91dbb9469f469d6f75742a93a68166f6377e13bdaec3d5ada64a","target":"record","created_at":"2026-07-05T09:06:17Z","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":"f7fffd46c741d1fad87179600bc34a801b47eb3dafdb00a014d7fa58c090759a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-12T11:09:34Z","title_canon_sha256":"6ea148e32d51affc2eade3b5f122870192704a6b92524e6fd7b5540958240359"},"schema_version":"1.0","source":{"id":"2409.07941","kind":"arxiv","version":1}},"canonical_sha256":"375621c93b422e72a8d993561fbe0c994756f1748d22739394d30aa53fa6a151","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"375621c93b422e72a8d993561fbe0c994756f1748d22739394d30aa53fa6a151","first_computed_at":"2026-07-05T09:06:17.653219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:06:17.653219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EUaLUgyBv6Aw9b+fb8/Xx15PPZqdRnUuYl6fWOce1ZKAhMtkoY3mngf89ZQPCUT3q91HGLGXhq+HfLwSf6MwBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:06:17.653628Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.07941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7cf8c3b148d91dbb9469f469d6f75742a93a68166f6377e13bdaec3d5ada64a","sha256:21b36cdb379d7520f10950a8ca716916aaac5f2dcdad1e5a1da134e04ccb0f2a"],"state_sha256":"d9b8bfc47f18182d769101e20fc0ae9465906a8caf48293cb59544cd2aeb3c2d"}