{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LYSEXAWYWEVB765P3SMNUPOROV","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":"c9bd22ea3030ab05c9d50e292893be8b4265de66374e5afe272d5ae01c6a3e44","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-02T19:43:52Z","title_canon_sha256":"8695cbc4767221c7c69d42f0bc178d69354cdd0c492ac5343914ff150b63646c"},"schema_version":"1.0","source":{"id":"1208.0583","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0583","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0583v5","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0583","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"LYSEXAWYWEVB","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LYSEXAWYWEVB765P","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LYSEXAWY","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:f3b9727b8fbc800c8d8fa902356135098a2689482528f2818163f64656d5560c","target":"graph","created_at":"2026-05-18T02:23:35Z","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":"Let $n$ denote either a positive integer or $\\infty$, let $\\ell$ be a fixed prime and let $K$ be a field of characteristic different from $\\ell$. In the presence of sufficiently many roots of unity in $K$, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal $\\ell^n$-abelian Galois group of $K$ using the maximal $\\ell^N$-abelian-by-central Galois group of $K$, whenever $N$ is sufficiently large relative to $n$.","authors_text":"Adam Topaz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-02T19:43:52Z","title":"Commuting-Liftable Subgroups of Galois Groups II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0583","kind":"arxiv","version":5},"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":"sha256:0fba69c31940682dcdce45037af407c0d1506d29814c8c1b45f30d91cc36e8f2","target":"record","created_at":"2026-05-18T02:23:35Z","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":"c9bd22ea3030ab05c9d50e292893be8b4265de66374e5afe272d5ae01c6a3e44","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-02T19:43:52Z","title_canon_sha256":"8695cbc4767221c7c69d42f0bc178d69354cdd0c492ac5343914ff150b63646c"},"schema_version":"1.0","source":{"id":"1208.0583","kind":"arxiv","version":5}},"canonical_sha256":"5e244b82d8b12a1ffbafdc98da3dd175654feb0205d5059a26e8afd71d8fcb01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e244b82d8b12a1ffbafdc98da3dd175654feb0205d5059a26e8afd71d8fcb01","first_computed_at":"2026-05-18T02:23:35.788330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:35.788330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wMdfKyKUwH6gvkqmS5BkaTJKb6KwWw9z3iMOBQBfpidepM8DJJHLPLweZERtjdzF2y/GR/qERNxYI0EfghKiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:35.789091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0583","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fba69c31940682dcdce45037af407c0d1506d29814c8c1b45f30d91cc36e8f2","sha256:f3b9727b8fbc800c8d8fa902356135098a2689482528f2818163f64656d5560c"],"state_sha256":"90b48497c6ad219710d4e5709d0b7f7e52b3e13ca5706f28a442a9e97ab6ce08"}