{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ODUB6XV3LN6VUW26PO22UWLUFW","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":"55a07a411e9631a4ab8f09313c5b76bb28eba76c97f3f82e001d77416c7971e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-11T01:18:16Z","title_canon_sha256":"b2bce7688e7789742fb8a2e4ec4f61f8b46cf4b50fed0c1941a805d2c9dec5d9"},"schema_version":"1.0","source":{"id":"1610.03150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03150","created_at":"2026-05-18T00:26:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03150v2","created_at":"2026-05-18T00:26:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03150","created_at":"2026-05-18T00:26:57Z"},{"alias_kind":"pith_short_12","alias_value":"ODUB6XV3LN6V","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODUB6XV3LN6VUW26","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODUB6XV3","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:2babbf63d13e5d6510edbb0ac9c816ccc3523e291115fb546242b99cb0863876","target":"graph","created_at":"2026-05-18T00:26:57Z","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":"In this paper we develop three different subjects. We study and prove alternative versions of Hrushovski's \"Stabilizer Theorem\", we generalize part of the basic theory of definably amenable NIP groups to NTP2 theories, and finally, we use all this machinery to study groups with f-generic types definable in bounded PRC fields.","authors_text":"Alf Onshuus, Pierre Simon, Samaria Montenegro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-11T01:18:16Z","title":"Stabilizers, groups with f-generics in NTP2 and PRC fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03150","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:c84b83ea2a4c939477e524e6ccb76682e8b2b9549e114ce89c9bf7f95d177546","target":"record","created_at":"2026-05-18T00:26:57Z","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":"55a07a411e9631a4ab8f09313c5b76bb28eba76c97f3f82e001d77416c7971e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-11T01:18:16Z","title_canon_sha256":"b2bce7688e7789742fb8a2e4ec4f61f8b46cf4b50fed0c1941a805d2c9dec5d9"},"schema_version":"1.0","source":{"id":"1610.03150","kind":"arxiv","version":2}},"canonical_sha256":"70e81f5ebb5b7d5a5b5e7bb5aa59742d830dac685088e302d92fd9ba1178f22a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70e81f5ebb5b7d5a5b5e7bb5aa59742d830dac685088e302d92fd9ba1178f22a","first_computed_at":"2026-05-18T00:26:57.774846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:57.774846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L0WMuzNNWtzQvZn5Gqpj4NSPylhF0/2NdekZTH1Q4FM7d6deIeVUDkJZ80zoB8qgbQG1ynUpFK02ZQIJrU5SBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:57.775470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c84b83ea2a4c939477e524e6ccb76682e8b2b9549e114ce89c9bf7f95d177546","sha256:2babbf63d13e5d6510edbb0ac9c816ccc3523e291115fb546242b99cb0863876"],"state_sha256":"58ce284186e0426519d7ba08ffbf12a7da538fdb1f53d3185b8deadbd23e0b82"}