{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OIE76ZSFGO5FLF4JNONMBJ2Q27","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":"b4a1263ec894a0e278905680d8e30eac9199b5310fdb44793af231e736f1f607","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-03-21T08:16:12Z","title_canon_sha256":"69d6f3f71f01c3079b64cb8051129361c1a0ed09af9bf7ecb36282af8d79e644"},"schema_version":"1.0","source":{"id":"1803.07792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07792","created_at":"2026-05-18T00:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07792v1","created_at":"2026-05-18T00:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07792","created_at":"2026-05-18T00:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"OIE76ZSFGO5F","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OIE76ZSFGO5FLF4J","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OIE76ZSF","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:434f4442366536accb8199e24c03c1c78283275e003cf7f15c04da27688a9b14","target":"graph","created_at":"2026-05-18T00:20:28Z","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":"Using the ramification theory of tame and Kaplansky fields, we show that maximal Kaplansky fields contain maximal immediate extensions of each of their subfields. Likewise, algebraically maximal Kaplansky fields contain maximal immediate algebraic extensions of each of their subfields. This study is inspired by problems that appear in henselian valued fields of rank higher than 1 when a Hensel root of a polynomial is approximated by the elements generated by a (transfinite) Newton algorithm.","authors_text":"Franz-Viktor Kuhlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-03-21T08:16:12Z","title":"Subfields of algebraically maximal Kaplansky fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07792","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:bedabb437c6e42d8667103de405432cd7e68118c8029199a8d37fd353e095e6d","target":"record","created_at":"2026-05-18T00:20:28Z","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":"b4a1263ec894a0e278905680d8e30eac9199b5310fdb44793af231e736f1f607","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-03-21T08:16:12Z","title_canon_sha256":"69d6f3f71f01c3079b64cb8051129361c1a0ed09af9bf7ecb36282af8d79e644"},"schema_version":"1.0","source":{"id":"1803.07792","kind":"arxiv","version":1}},"canonical_sha256":"7209ff664533ba5597896b9ac0a750d7f45d33cc53bcfce1094f53e767b2238a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7209ff664533ba5597896b9ac0a750d7f45d33cc53bcfce1094f53e767b2238a","first_computed_at":"2026-05-18T00:20:28.930514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:28.930514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LTwHGMYHDdm9AlXuiE36DBSQ6X1nRUZxymTz2qSFFm8Y1Cu+ZfwtdOVPaOINK9a7coukfSk32GJYNqnwC4IWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:28.931012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bedabb437c6e42d8667103de405432cd7e68118c8029199a8d37fd353e095e6d","sha256:434f4442366536accb8199e24c03c1c78283275e003cf7f15c04da27688a9b14"],"state_sha256":"b868ff9acbd08a9b2003157123b3631d9f85dc2573e1521f53e7e1d3af65a07b"}