{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SHOPRP5EC2PURGAXFAFGMJ7OT4","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":"b3ce3997965f29638a0e953ee781a460eb2ecef556dc168168955f4851f6689a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-16T22:29:12Z","title_canon_sha256":"31e6ca5d1369262dc0d0730bfccc076c85535057dc979ee2533ddebf78044a20"},"schema_version":"1.0","source":{"id":"2501.09865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09865","created_at":"2026-07-05T10:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09865v1","created_at":"2026-07-05T10:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09865","created_at":"2026-07-05T10:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"SHOPRP5EC2PU","created_at":"2026-07-05T10:02:12Z"},{"alias_kind":"pith_short_16","alias_value":"SHOPRP5EC2PURGAX","created_at":"2026-07-05T10:02:12Z"},{"alias_kind":"pith_short_8","alias_value":"SHOPRP5E","created_at":"2026-07-05T10:02:12Z"}],"graph_snapshots":[{"event_id":"sha256:fd83390bc0551de0b0773436da050d7ccf5351e5ff636501c25a823d8597afd2","target":"graph","created_at":"2026-07-05T10:02:12Z","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/2501.09865/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a prime number $\\ell$ and an extension of number fields $K/F$, we prove new lower bounds on the $\\ell$-rank of the ideal class group of $K$ based on prime ramification in $K/F$. Unlike related results from the literature, our bound is supported on prime ideals in $F$ over which at least one (rather than each) prime in $K$ has ramification index divisible by $\\ell$. This bound holds with a proviso on the Galois group of the normal closure of $K/F$, which is satisfied by towers of Galois extensions, intermediate fields in nilpotent extensions, and intermediate fields in dihedral extensions o","authors_text":"Daniel E. Martin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-16T22:29:12Z","title":"Lower bounds on the $\\ell$-rank of ideal class groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09865","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":"sha256:9d09ea4c5355bec2995ba1a03b5eec0950bfabf033982be81be8226277ff6027","target":"record","created_at":"2026-07-05T10:02:12Z","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":"b3ce3997965f29638a0e953ee781a460eb2ecef556dc168168955f4851f6689a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-16T22:29:12Z","title_canon_sha256":"31e6ca5d1369262dc0d0730bfccc076c85535057dc979ee2533ddebf78044a20"},"schema_version":"1.0","source":{"id":"2501.09865","kind":"arxiv","version":1}},"canonical_sha256":"91dcf8bfa4169f489817280a6627ee9f333a9f7b09cefa501e558a262deef462","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91dcf8bfa4169f489817280a6627ee9f333a9f7b09cefa501e558a262deef462","first_computed_at":"2026-07-05T10:02:12.498447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:12.498447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMYpIv+79q2H+sHnqOi3Y/igBAVeD2UcVUte+MxaAMwlgC6LeOxyZth5l0InarQ1Xab+SEFb+hpCpu5ksatgBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:12.498831Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.09865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d09ea4c5355bec2995ba1a03b5eec0950bfabf033982be81be8226277ff6027","sha256:fd83390bc0551de0b0773436da050d7ccf5351e5ff636501c25a823d8597afd2"],"state_sha256":"7692b0283df8196dac5611242100ddafe440a6d3dbac1acf459be7ca5f7c5a2d"}