{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7B2RQZBH3C5YISMD77OCR2I76F","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":"73f923cec31ba76614b97da920bae2ffb216acb9cafb6fbb67dbdeefca083cb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-01-31T11:03:29Z","title_canon_sha256":"ee2bcf55e01e0715a25aea837bae8d34a84ae14d60581682431c590bae27df2d"},"schema_version":"1.0","source":{"id":"2001.11768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11768","created_at":"2026-07-05T00:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11768v1","created_at":"2026-07-05T00:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11768","created_at":"2026-07-05T00:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"7B2RQZBH3C5Y","created_at":"2026-07-05T00:37:33Z"},{"alias_kind":"pith_short_16","alias_value":"7B2RQZBH3C5YISMD","created_at":"2026-07-05T00:37:33Z"},{"alias_kind":"pith_short_8","alias_value":"7B2RQZBH","created_at":"2026-07-05T00:37:33Z"}],"graph_snapshots":[{"event_id":"sha256:c69e82e297fe75a9a18b8ff53a8a57825feefd5c507db5fe48b478f7edd4970c","target":"graph","created_at":"2026-07-05T00:37:33Z","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/2001.11768/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an algebraic number field $K$ and a prime number $p$, let $\\widetilde{K}/K$ be the maximal multiple $\\mathbb{Z}_p$-extension. Greenberg's generalized conjecture (GGC) predicts that the Galois group of the maximal unramified abelian pro-$p$ extension of $\\widetilde{K}$ is pseudo-null over the completed group ring $\\mathbb{Z}_p[\\![\\mathop{\\mathrm{Gal}}\\nolimits(\\widetilde{K}/K)]\\!]$. We show that GGC holds for some imaginary quartic fields containing imaginary quadratic fields and some prime numbers.","authors_text":"Naoya Takahashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-01-31T11:03:29Z","title":"On Greenberg's generalized conjecture for imaginary quartic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11768","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:f43d3a8b58e6232fd44fd0c094a28f91abbae0ba6f77db2e1a15faab00047f86","target":"record","created_at":"2026-07-05T00:37:33Z","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":"73f923cec31ba76614b97da920bae2ffb216acb9cafb6fbb67dbdeefca083cb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-01-31T11:03:29Z","title_canon_sha256":"ee2bcf55e01e0715a25aea837bae8d34a84ae14d60581682431c590bae27df2d"},"schema_version":"1.0","source":{"id":"2001.11768","kind":"arxiv","version":1}},"canonical_sha256":"f875186427d8bb844983ffdc28e91ff1468a50c1e121c8141aa78e2b86915234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f875186427d8bb844983ffdc28e91ff1468a50c1e121c8141aa78e2b86915234","first_computed_at":"2026-07-05T00:37:33.714389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:33.714389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4u7w3/JLH8GgZqBugCfjepBc2w6pTnrqxaa00AfOm2Cwd9JFt5M8/+4zqYotRqQGS975odH9nGrHkflRnkiADA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:33.714746Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.11768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f43d3a8b58e6232fd44fd0c094a28f91abbae0ba6f77db2e1a15faab00047f86","sha256:c69e82e297fe75a9a18b8ff53a8a57825feefd5c507db5fe48b478f7edd4970c"],"state_sha256":"9d07972cd3b58133912d6dec9fe6bd1349df7f25640603aca71697fa1be77f84"}