{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:W6E7GYOS6SFM45XEZIK7LPRFX2","short_pith_number":"pith:W6E7GYOS","canonical_record":{"source":{"id":"1603.08598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-29T00:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"21cf6ad951edae0b903b1b54c6d7f69cea10d9d0bc61d3b25e8570ec5f84ca3e","abstract_canon_sha256":"2a14ca7e3689ed2a96d6705d6b8a45e8ab934a2d13a6fcceb53796611b30eaf2"},"schema_version":"1.0"},"canonical_sha256":"b789f361d2f48ace76e4ca15f5be25be971abd7f7a578e12cbf4b25aa0a65a78","source":{"kind":"arxiv","id":"1603.08598","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08598","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08598v1","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08598","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"W6E7GYOS6SFM","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W6E7GYOS6SFM45XE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W6E7GYOS","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:W6E7GYOS6SFM45XEZIK7LPRFX2","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-29T00:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"21cf6ad951edae0b903b1b54c6d7f69cea10d9d0bc61d3b25e8570ec5f84ca3e","abstract_canon_sha256":"2a14ca7e3689ed2a96d6705d6b8a45e8ab934a2d13a6fcceb53796611b30eaf2"},"schema_version":"1.0"},"canonical_sha256":"b789f361d2f48ace76e4ca15f5be25be971abd7f7a578e12cbf4b25aa0a65a78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:05.912578Z","signature_b64":"AhOQrTaSOwPGo4xdyMFCOVyA8RFXLZf1lhb77AfF+atwzfTfyUn/tkyutwrrNBGD+S0lrIqRiWSVUIhJWSzxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b789f361d2f48ace76e4ca15f5be25be971abd7f7a578e12cbf4b25aa0a65a78","last_reissued_at":"2026-05-18T01:18:05.911839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:05.911839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08598","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u77BU79ovKjnkiM6vzdwokLNlwzh3ZNs0EMWmIBLdJPan/Y0cUNcdfjAJWqWZy7Qgx9DY+FHtLTIdlWsmGTUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:28:42.476813Z"},"content_sha256":"c55b7b14cd573f0c8729b8eb41bbd445f31fabcff37004c4650978288cb6427d","schema_version":"1.0","event_id":"sha256:c55b7b14cd573f0c8729b8eb41bbd445f31fabcff37004c4650978288cb6427d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:W6E7GYOS6SFM45XEZIK7LPRFX2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Model Completeness for Henselian Fields with finite ramification valued in a $Z$-Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Angus Macintyre, Jamshid Derakhshan","submitted_at":"2016-03-29T00:38:02Z","abstract_excerpt":"We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a $Z$-group, is model-complete in the language of rings if the theory of its residue field is model-complete in the language of rings. We apply this to prove that every infinite algebraic extension of the field of $p$-adic numbers $\\Bbb Q_p$ with finite ramification is model-complete in the language of rings. For this, we give a necessary and sufficient condition for model-completeness of the theory of a perfect pseudo-algebraically closed field with pro-cyclic absolu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08598","kind":"arxiv","version":1},"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":"2026-05-18T01:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iBcaohr31LTEFbqgV04Bz5T7raj+y47aQTn5x7nPLfXG3vBe7KFg37V+jgLlZK9O1cPOQSnUW2AE+xPpeSUCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:28:42.477258Z"},"content_sha256":"30750fe1ebf7040d4fe07a61687e6b51c6cafafedc40190f905343187294959e","schema_version":"1.0","event_id":"sha256:30750fe1ebf7040d4fe07a61687e6b51c6cafafedc40190f905343187294959e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6E7GYOS6SFM45XEZIK7LPRFX2/bundle.json","state_url":"https://pith.science/pith/W6E7GYOS6SFM45XEZIK7LPRFX2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6E7GYOS6SFM45XEZIK7LPRFX2/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":"2026-05-27T08:28:42Z","links":{"resolver":"https://pith.science/pith/W6E7GYOS6SFM45XEZIK7LPRFX2","bundle":"https://pith.science/pith/W6E7GYOS6SFM45XEZIK7LPRFX2/bundle.json","state":"https://pith.science/pith/W6E7GYOS6SFM45XEZIK7LPRFX2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6E7GYOS6SFM45XEZIK7LPRFX2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W6E7GYOS6SFM45XEZIK7LPRFX2","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":"2a14ca7e3689ed2a96d6705d6b8a45e8ab934a2d13a6fcceb53796611b30eaf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-29T00:38:02Z","title_canon_sha256":"21cf6ad951edae0b903b1b54c6d7f69cea10d9d0bc61d3b25e8570ec5f84ca3e"},"schema_version":"1.0","source":{"id":"1603.08598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08598","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08598v1","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08598","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"W6E7GYOS6SFM","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W6E7GYOS6SFM45XE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W6E7GYOS","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:30750fe1ebf7040d4fe07a61687e6b51c6cafafedc40190f905343187294959e","target":"graph","created_at":"2026-05-18T01:18:05Z","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":"We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a $Z$-group, is model-complete in the language of rings if the theory of its residue field is model-complete in the language of rings. We apply this to prove that every infinite algebraic extension of the field of $p$-adic numbers $\\Bbb Q_p$ with finite ramification is model-complete in the language of rings. For this, we give a necessary and sufficient condition for model-completeness of the theory of a perfect pseudo-algebraically closed field with pro-cyclic absolu","authors_text":"Angus Macintyre, Jamshid Derakhshan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-29T00:38:02Z","title":"Model Completeness for Henselian Fields with finite ramification valued in a $Z$-Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08598","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:c55b7b14cd573f0c8729b8eb41bbd445f31fabcff37004c4650978288cb6427d","target":"record","created_at":"2026-05-18T01:18:05Z","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":"2a14ca7e3689ed2a96d6705d6b8a45e8ab934a2d13a6fcceb53796611b30eaf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-29T00:38:02Z","title_canon_sha256":"21cf6ad951edae0b903b1b54c6d7f69cea10d9d0bc61d3b25e8570ec5f84ca3e"},"schema_version":"1.0","source":{"id":"1603.08598","kind":"arxiv","version":1}},"canonical_sha256":"b789f361d2f48ace76e4ca15f5be25be971abd7f7a578e12cbf4b25aa0a65a78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b789f361d2f48ace76e4ca15f5be25be971abd7f7a578e12cbf4b25aa0a65a78","first_computed_at":"2026-05-18T01:18:05.911839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:05.911839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AhOQrTaSOwPGo4xdyMFCOVyA8RFXLZf1lhb77AfF+atwzfTfyUn/tkyutwrrNBGD+S0lrIqRiWSVUIhJWSzxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:05.912578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c55b7b14cd573f0c8729b8eb41bbd445f31fabcff37004c4650978288cb6427d","sha256:30750fe1ebf7040d4fe07a61687e6b51c6cafafedc40190f905343187294959e"],"state_sha256":"b77378d5b104e77fce0f447a2b05b80037d9dfa9207327fa56382b9467d4962e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4X2tui40PuCDo3z1TOJKU1vcPvqRXVbDUR7eSwYLVQmm2RKaSry85Un8JtvkU3ItEezxhklvH8hsQZQ/v+reCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:28:42.479612Z","bundle_sha256":"578e4d740decfae50a1b626c85ce263abd026ef76d64d72ddaa2ede9571af0eb"}}