{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RMDPIDGZGDLW6GGPFDMCTPA2GS","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":"e4e895e18bac45c20f8084ab00edfd408dc157069177bee449f873ab564e52f7","cross_cats_sorted":["math.AC","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-28T20:56:35Z","title_canon_sha256":"b07ceb8dd95c0a0c5ab3e9fb1572ad6d7a2ea57a0c4eb876cae24f375441ef19"},"schema_version":"1.0","source":{"id":"1310.7623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7623","created_at":"2026-05-18T03:08:26Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7623v2","created_at":"2026-05-18T03:08:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7623","created_at":"2026-05-18T03:08:26Z"},{"alias_kind":"pith_short_12","alias_value":"RMDPIDGZGDLW","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RMDPIDGZGDLW6GGP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RMDPIDGZ","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:1ccef4b2f5c002ceeb80c82cd8339c1fbffcdf03f6cc211b08bec1fef6fffb6e","target":"graph","created_at":"2026-05-18T03:08:26Z","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"},"paper":{"abstract_excerpt":"Fix an odd prime $p$, and let $F$ be a field containing a primitive $p$th root of unity. It is known that a $p$-rigid field $F$ is characterized by the property that the Galois group $G_F(p)$ of the maximal $p$-extension $F(p)/F$ is a solvable group. We give a new characterization of $p$-rigidity which says that a field $F$ is $p$-rigid precisely when two fundamental canonical quotients of the absolute Galois groups coincide. This condition is further related to analytic $p$-adic groups and to some Galois modules. When $F$ is $p$-rigid, we also show that it is possible to solve for the roots o","authors_text":"Claudio Quadrelli, Jan Minac, Sunil K. Chebolu","cross_cats":["math.AC","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-28T20:56:35Z","title":"Detecting Fast solvability of equations via small powerful Galois groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7623","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":"sha256:89d4729e70ab7b656e67e561dec6f8232ad05d9940d18fdd162d1a38589d345e","target":"record","created_at":"2026-05-18T03:08:26Z","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":"e4e895e18bac45c20f8084ab00edfd408dc157069177bee449f873ab564e52f7","cross_cats_sorted":["math.AC","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-28T20:56:35Z","title_canon_sha256":"b07ceb8dd95c0a0c5ab3e9fb1572ad6d7a2ea57a0c4eb876cae24f375441ef19"},"schema_version":"1.0","source":{"id":"1310.7623","kind":"arxiv","version":2}},"canonical_sha256":"8b06f40cd930d76f18cf28d829bc1a34b5bde266362ae70dcd0ebe3cffe747fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b06f40cd930d76f18cf28d829bc1a34b5bde266362ae70dcd0ebe3cffe747fb","first_computed_at":"2026-05-18T03:08:26.491645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:26.491645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yGPZQxL/gAjhMTvJOOFFwgXxRJeSFKeyW78hTEPGlwRy1WNJ2v6Qjr8lGAW9gjzXwoeeqqGmyzFJTj3FnEd0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:26.492478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89d4729e70ab7b656e67e561dec6f8232ad05d9940d18fdd162d1a38589d345e","sha256:1ccef4b2f5c002ceeb80c82cd8339c1fbffcdf03f6cc211b08bec1fef6fffb6e"],"state_sha256":"e3d918815236cf3a6512c889f4c11da977e24593e8c79a8ebc2de12bc4e609e7"}