{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5GA5EGTEUZPXRE6ILJU6Z3S5WK","short_pith_number":"pith:5GA5EGTE","canonical_record":{"source":{"id":"1503.04368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-15T00:56:52Z","cross_cats_sorted":[],"title_canon_sha256":"94eaa06d12ebc5fda41b7875848e56de48c5f48bd05714c863ac3988ba4a13b2","abstract_canon_sha256":"86dd6c607ef49dd145dc4d3d11992b25cd25d9cce0d265b81a059854da875371"},"schema_version":"1.0"},"canonical_sha256":"e981d21a64a65f7893c85a69ecee5db2b25eea4f329a11662006fad8eabf0ed2","source":{"kind":"arxiv","id":"1503.04368","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04368","created_at":"2026-05-18T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04368v2","created_at":"2026-05-18T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04368","created_at":"2026-05-18T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"5GA5EGTEUZPX","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GA5EGTEUZPXRE6I","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GA5EGTE","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5GA5EGTEUZPXRE6ILJU6Z3S5WK","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-15T00:56:52Z","cross_cats_sorted":[],"title_canon_sha256":"94eaa06d12ebc5fda41b7875848e56de48c5f48bd05714c863ac3988ba4a13b2","abstract_canon_sha256":"86dd6c607ef49dd145dc4d3d11992b25cd25d9cce0d265b81a059854da875371"},"schema_version":"1.0"},"canonical_sha256":"e981d21a64a65f7893c85a69ecee5db2b25eea4f329a11662006fad8eabf0ed2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:07.745979Z","signature_b64":"dal7woaVQ9zEbGYO7spS/HnkRePqNpICGiv0xPix+atUjxbYc3Ol5x2t9P7lw/X5088do2BNSBn57XEbPAY8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e981d21a64a65f7893c85a69ecee5db2b25eea4f329a11662006fad8eabf0ed2","last_reissued_at":"2026-05-18T02:19:07.745281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:07.745281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04368","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXkCIsZOHUCDrwgfMnaJpvxLl+sOqmADWuchblVA0aRbNteywXI6RvRnnKyLYzusPn8Zjc4pCLHk7Gbi5N2uCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:51:49.035935Z"},"content_sha256":"072497ec9ed7f7e3db9ff615bea97b85ad3c3a8a29754f31fddc18f587246ab1","schema_version":"1.0","event_id":"sha256:072497ec9ed7f7e3db9ff615bea97b85ad3c3a8a29754f31fddc18f587246ab1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5GA5EGTEUZPXRE6ILJU6Z3S5WK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian-by-Central Galois Groups of Fields II: Definability of Inertia/Decomposition Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adam Topaz","submitted_at":"2015-03-15T00:56:52Z","abstract_excerpt":"This paper explores some first-order properties of commuting-liftable pairs in pro-$\\ell$ abelian-by-central Galois groups of fields. The main focus of the paper is to prove that minimized inertia and decomposition groups of many valuations are first-order definable using a predicate for the collection of commuting-liftable pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04368","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6CWO5iZtDISNVN/wXCM+c5K++shhK1kaJbXyuGhkfeCMGibJyknSOn5Kgd4XLsf9F6ADywLFGfzu/HVo4rgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:51:49.036302Z"},"content_sha256":"f2ed217ab2f787b2e0cbda45a1108548ee21895a5e00c4e8011fbab24a0dee99","schema_version":"1.0","event_id":"sha256:f2ed217ab2f787b2e0cbda45a1108548ee21895a5e00c4e8011fbab24a0dee99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK/bundle.json","state_url":"https://pith.science/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T09:51:49Z","links":{"resolver":"https://pith.science/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK","bundle":"https://pith.science/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK/bundle.json","state":"https://pith.science/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GA5EGTEUZPXRE6ILJU6Z3S5WK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5GA5EGTEUZPXRE6ILJU6Z3S5WK","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":"86dd6c607ef49dd145dc4d3d11992b25cd25d9cce0d265b81a059854da875371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-15T00:56:52Z","title_canon_sha256":"94eaa06d12ebc5fda41b7875848e56de48c5f48bd05714c863ac3988ba4a13b2"},"schema_version":"1.0","source":{"id":"1503.04368","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04368","created_at":"2026-05-18T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04368v2","created_at":"2026-05-18T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04368","created_at":"2026-05-18T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"5GA5EGTEUZPX","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GA5EGTEUZPXRE6I","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GA5EGTE","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:f2ed217ab2f787b2e0cbda45a1108548ee21895a5e00c4e8011fbab24a0dee99","target":"graph","created_at":"2026-05-18T02:19:07Z","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":"This paper explores some first-order properties of commuting-liftable pairs in pro-$\\ell$ abelian-by-central Galois groups of fields. The main focus of the paper is to prove that minimized inertia and decomposition groups of many valuations are first-order definable using a predicate for the collection of commuting-liftable pairs.","authors_text":"Adam Topaz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-15T00:56:52Z","title":"Abelian-by-Central Galois Groups of Fields II: Definability of Inertia/Decomposition Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04368","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":"sha256:072497ec9ed7f7e3db9ff615bea97b85ad3c3a8a29754f31fddc18f587246ab1","target":"record","created_at":"2026-05-18T02:19:07Z","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":"86dd6c607ef49dd145dc4d3d11992b25cd25d9cce0d265b81a059854da875371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-15T00:56:52Z","title_canon_sha256":"94eaa06d12ebc5fda41b7875848e56de48c5f48bd05714c863ac3988ba4a13b2"},"schema_version":"1.0","source":{"id":"1503.04368","kind":"arxiv","version":2}},"canonical_sha256":"e981d21a64a65f7893c85a69ecee5db2b25eea4f329a11662006fad8eabf0ed2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e981d21a64a65f7893c85a69ecee5db2b25eea4f329a11662006fad8eabf0ed2","first_computed_at":"2026-05-18T02:19:07.745281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:07.745281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dal7woaVQ9zEbGYO7spS/HnkRePqNpICGiv0xPix+atUjxbYc3Ol5x2t9P7lw/X5088do2BNSBn57XEbPAY8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:07.745979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04368","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:072497ec9ed7f7e3db9ff615bea97b85ad3c3a8a29754f31fddc18f587246ab1","sha256:f2ed217ab2f787b2e0cbda45a1108548ee21895a5e00c4e8011fbab24a0dee99"],"state_sha256":"6e07a5c28819ce63cf2ba00c001184120a40287059bfd6f735b85c3efadb9226"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jij7JcZaDpl5oJXUem7r1tI8WSqNf5Q9ykq5+BKRuqAblB1VnEbr+cCpqkLU9W5YEPrleEH/d9UDFpNvO+1HDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:51:49.038305Z","bundle_sha256":"6a6b27e5d7f24b10383e96961c7f91ee2fb7990ae089447f70c8970abfca69a9"}}