{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:T4EH3MZZD2YLDODKSV7NL4EMMO","short_pith_number":"pith:T4EH3MZZ","canonical_record":{"source":{"id":"1003.5149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-03-26T14:39:52Z","cross_cats_sorted":[],"title_canon_sha256":"5274d96012ef37bc49046ab4b3328c662c90b318be35184899e67a2f568b18c6","abstract_canon_sha256":"1173cb8c0da10affd372033737c4fd3ede73034a497b11a7c56092ddc025a391"},"schema_version":"1.0"},"canonical_sha256":"9f087db3391eb0b1b86a957ed5f08c6384c9aa5d5f019e297842979ede36db85","source":{"kind":"arxiv","id":"1003.5149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5149","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5149v2","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5149","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"T4EH3MZZD2YL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T4EH3MZZD2YLDODK","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T4EH3MZZ","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:T4EH3MZZD2YLDODKSV7NL4EMMO","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-03-26T14:39:52Z","cross_cats_sorted":[],"title_canon_sha256":"5274d96012ef37bc49046ab4b3328c662c90b318be35184899e67a2f568b18c6","abstract_canon_sha256":"1173cb8c0da10affd372033737c4fd3ede73034a497b11a7c56092ddc025a391"},"schema_version":"1.0"},"canonical_sha256":"9f087db3391eb0b1b86a957ed5f08c6384c9aa5d5f019e297842979ede36db85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:27.926051Z","signature_b64":"T7HhOzkonQ9sZgVSaIPr/mCf9Y8LoPr9dGMr/sIMDeQj7mzEKDR1PvGTCoAq9xiR/e54ADwQFnUHqrGZUVaJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f087db3391eb0b1b86a957ed5f08c6384c9aa5d5f019e297842979ede36db85","last_reissued_at":"2026-05-18T04:05:27.925485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:27.925485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5149","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":"2026-05-18T04:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9o+wrzbeD7BjjKskcxchzZ6Vu7PjOCavgs+KW4q3e8+zJvPuU/+m36UaUjowUOmYbmDkAVTElRHJjrsgoB0oBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:56:52.347721Z"},"content_sha256":"811620e7398974d37f020e86084b0bae6be6c4db36933981abdbeab1649323e4","schema_version":"1.0","event_id":"sha256:811620e7398974d37f020e86084b0bae6be6c4db36933981abdbeab1649323e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:T4EH3MZZD2YLDODKSV7NL4EMMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic Automorphisms and Green Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Martin Hils","submitted_at":"2010-03-26T14:39:52Z","abstract_excerpt":"We show that the generic automorphism is axiomatisable in the green field of Poizat (once Morleyised) as well as in the bad fields which are obtained by collapsing this green field to finite Morley rank. As a corollary, we obtain \"bad pseudofinite fields\" in characteristic 0. In both cases, we give geometric axioms. In fact, a general framework is presented allowing this kind of axiomatisation. We deduce from various constructibility results for algebraic varieties in characteristic 0 that the green and bad fields fall into this framework. Finally, we give similar results for other theories ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5149","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":"2026-05-18T04:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHJFijCRGHTrMZ1d+8QgcrN/3jFgqPc6jlqGnS5ctnXSrky8cLm5fBMqudhjE6IBGS5U+HqOUw8Dhs8QBJ0kAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:56:52.348366Z"},"content_sha256":"ab60b89e41e072ebaf88f7a46f1ef3f5e4e43bb79dbe91c29bb7848ed0a79184","schema_version":"1.0","event_id":"sha256:ab60b89e41e072ebaf88f7a46f1ef3f5e4e43bb79dbe91c29bb7848ed0a79184"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4EH3MZZD2YLDODKSV7NL4EMMO/bundle.json","state_url":"https://pith.science/pith/T4EH3MZZD2YLDODKSV7NL4EMMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4EH3MZZD2YLDODKSV7NL4EMMO/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":"2026-05-27T03:56:52Z","links":{"resolver":"https://pith.science/pith/T4EH3MZZD2YLDODKSV7NL4EMMO","bundle":"https://pith.science/pith/T4EH3MZZD2YLDODKSV7NL4EMMO/bundle.json","state":"https://pith.science/pith/T4EH3MZZD2YLDODKSV7NL4EMMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4EH3MZZD2YLDODKSV7NL4EMMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T4EH3MZZD2YLDODKSV7NL4EMMO","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":"1173cb8c0da10affd372033737c4fd3ede73034a497b11a7c56092ddc025a391","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-03-26T14:39:52Z","title_canon_sha256":"5274d96012ef37bc49046ab4b3328c662c90b318be35184899e67a2f568b18c6"},"schema_version":"1.0","source":{"id":"1003.5149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5149","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5149v2","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5149","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"T4EH3MZZD2YL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T4EH3MZZD2YLDODK","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T4EH3MZZ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:ab60b89e41e072ebaf88f7a46f1ef3f5e4e43bb79dbe91c29bb7848ed0a79184","target":"graph","created_at":"2026-05-18T04:05:27Z","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 show that the generic automorphism is axiomatisable in the green field of Poizat (once Morleyised) as well as in the bad fields which are obtained by collapsing this green field to finite Morley rank. As a corollary, we obtain \"bad pseudofinite fields\" in characteristic 0. In both cases, we give geometric axioms. In fact, a general framework is presented allowing this kind of axiomatisation. We deduce from various constructibility results for algebraic varieties in characteristic 0 that the green and bad fields fall into this framework. Finally, we give similar results for other theories ob","authors_text":"Martin Hils","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-03-26T14:39:52Z","title":"Generic Automorphisms and Green Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5149","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":"sha256:811620e7398974d37f020e86084b0bae6be6c4db36933981abdbeab1649323e4","target":"record","created_at":"2026-05-18T04:05:27Z","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":"1173cb8c0da10affd372033737c4fd3ede73034a497b11a7c56092ddc025a391","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-03-26T14:39:52Z","title_canon_sha256":"5274d96012ef37bc49046ab4b3328c662c90b318be35184899e67a2f568b18c6"},"schema_version":"1.0","source":{"id":"1003.5149","kind":"arxiv","version":2}},"canonical_sha256":"9f087db3391eb0b1b86a957ed5f08c6384c9aa5d5f019e297842979ede36db85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f087db3391eb0b1b86a957ed5f08c6384c9aa5d5f019e297842979ede36db85","first_computed_at":"2026-05-18T04:05:27.925485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:27.925485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T7HhOzkonQ9sZgVSaIPr/mCf9Y8LoPr9dGMr/sIMDeQj7mzEKDR1PvGTCoAq9xiR/e54ADwQFnUHqrGZUVaJDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:27.926051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:811620e7398974d37f020e86084b0bae6be6c4db36933981abdbeab1649323e4","sha256:ab60b89e41e072ebaf88f7a46f1ef3f5e4e43bb79dbe91c29bb7848ed0a79184"],"state_sha256":"69695a1f8a75f31f8717a8459823c074f4dae0ae23efa119a00a8d1cc6a68b15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYfgYMPpQxvi1sanV7i9URcvVMJhKm4a/rZ7xog6j4cDsdTqaWel7t0fx6CzPU7zkcnYvUbt+mFNweWlgcjIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:56:52.351900Z","bundle_sha256":"e9997f3b45ea7f188b820e8514915b0b3355f1e57ba14ed2c0fff7e6a6c4d5d5"}}