{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UC4E6D573YLJR3US7VXIOTLUL2","short_pith_number":"pith:UC4E6D57","canonical_record":{"source":{"id":"1508.06039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-25T06:22:08Z","cross_cats_sorted":[],"title_canon_sha256":"bb0df2213aea3a8a07192feb7c805ab80f0e537e8d9769c8b0378e796d253b69","abstract_canon_sha256":"a36a4c406d755740c0f11d639d7a17d97743b4c99b87473a01f07df6a6070e99"},"schema_version":"1.0"},"canonical_sha256":"a0b84f0fbfde1698ee92fd6e874d745eb344692b9b92e6185de239426013c099","source":{"kind":"arxiv","id":"1508.06039","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06039","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06039v2","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06039","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"UC4E6D573YLJ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UC4E6D573YLJR3US","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UC4E6D57","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UC4E6D573YLJR3US7VXIOTLUL2","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-25T06:22:08Z","cross_cats_sorted":[],"title_canon_sha256":"bb0df2213aea3a8a07192feb7c805ab80f0e537e8d9769c8b0378e796d253b69","abstract_canon_sha256":"a36a4c406d755740c0f11d639d7a17d97743b4c99b87473a01f07df6a6070e99"},"schema_version":"1.0"},"canonical_sha256":"a0b84f0fbfde1698ee92fd6e874d745eb344692b9b92e6185de239426013c099","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:49.725426Z","signature_b64":"rNH7sbCCb087X4KinXbur60MebeIlna3UxyzY6Q+MiRNPWBt2SIdqCqawFbbKW/lmKmwsAFcJlWGxky0lL47Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0b84f0fbfde1698ee92fd6e874d745eb344692b9b92e6185de239426013c099","last_reissued_at":"2026-05-18T00:46:49.724734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:49.724734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06039","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":"2026-05-18T00:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uCXqMYIjarO1FZReKTs0ABEL60gIF7XLQidoOOFPuS2aGA1dC2AYvjdQlUciILZ5HbPsZAya7sZp1EVwzTkGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:55:25.867821Z"},"content_sha256":"3904ff89fba3b8ffab5b031a5c4a16be7ddd8a230bf3ddfefb901b0c6ac493f7","schema_version":"1.0","event_id":"sha256:3904ff89fba3b8ffab5b031a5c4a16be7ddd8a230bf3ddfefb901b0c6ac493f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UC4E6D573YLJR3US7VXIOTLUL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple structures axiomatized by almost sure theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ove Ahlman","submitted_at":"2015-08-25T06:22:08Z","abstract_excerpt":"In this article we give a classification of the binary, simple, $\\omega$-categorical structures with SU-rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as $\\omega$-stability or strong minimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06039","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":"2026-05-18T00:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8KPmIpixvjxXqWFkuYFXqUaPGs/hAynH05YcbqrPqFAp28DJvQdXn36cOhNuqNMjN8BbBaPZ0XVeqhW4MJ+FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:55:25.868395Z"},"content_sha256":"f4b5eda9a40258b7927db102f292748e72617c4299c70e06fbfe8d95b20d6e83","schema_version":"1.0","event_id":"sha256:f4b5eda9a40258b7927db102f292748e72617c4299c70e06fbfe8d95b20d6e83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UC4E6D573YLJR3US7VXIOTLUL2/bundle.json","state_url":"https://pith.science/pith/UC4E6D573YLJR3US7VXIOTLUL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UC4E6D573YLJR3US7VXIOTLUL2/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":"2026-06-24T21:55:25Z","links":{"resolver":"https://pith.science/pith/UC4E6D573YLJR3US7VXIOTLUL2","bundle":"https://pith.science/pith/UC4E6D573YLJR3US7VXIOTLUL2/bundle.json","state":"https://pith.science/pith/UC4E6D573YLJR3US7VXIOTLUL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UC4E6D573YLJR3US7VXIOTLUL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UC4E6D573YLJR3US7VXIOTLUL2","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":"a36a4c406d755740c0f11d639d7a17d97743b4c99b87473a01f07df6a6070e99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-25T06:22:08Z","title_canon_sha256":"bb0df2213aea3a8a07192feb7c805ab80f0e537e8d9769c8b0378e796d253b69"},"schema_version":"1.0","source":{"id":"1508.06039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06039","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06039v2","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06039","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"UC4E6D573YLJ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UC4E6D573YLJR3US","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UC4E6D57","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:f4b5eda9a40258b7927db102f292748e72617c4299c70e06fbfe8d95b20d6e83","target":"graph","created_at":"2026-05-18T00:46:49Z","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 article we give a classification of the binary, simple, $\\omega$-categorical structures with SU-rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as $\\omega$-stability or strong minimal","authors_text":"Ove Ahlman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-25T06:22:08Z","title":"Simple structures axiomatized by almost sure theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06039","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":"sha256:3904ff89fba3b8ffab5b031a5c4a16be7ddd8a230bf3ddfefb901b0c6ac493f7","target":"record","created_at":"2026-05-18T00:46:49Z","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":"a36a4c406d755740c0f11d639d7a17d97743b4c99b87473a01f07df6a6070e99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-25T06:22:08Z","title_canon_sha256":"bb0df2213aea3a8a07192feb7c805ab80f0e537e8d9769c8b0378e796d253b69"},"schema_version":"1.0","source":{"id":"1508.06039","kind":"arxiv","version":2}},"canonical_sha256":"a0b84f0fbfde1698ee92fd6e874d745eb344692b9b92e6185de239426013c099","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0b84f0fbfde1698ee92fd6e874d745eb344692b9b92e6185de239426013c099","first_computed_at":"2026-05-18T00:46:49.724734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:49.724734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rNH7sbCCb087X4KinXbur60MebeIlna3UxyzY6Q+MiRNPWBt2SIdqCqawFbbKW/lmKmwsAFcJlWGxky0lL47Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:49.725426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3904ff89fba3b8ffab5b031a5c4a16be7ddd8a230bf3ddfefb901b0c6ac493f7","sha256:f4b5eda9a40258b7927db102f292748e72617c4299c70e06fbfe8d95b20d6e83"],"state_sha256":"07bd4b3b65c2bb8e6a397d10eb8bc9b6ef2657098c11cd6b96bccd7357b8e262"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVthaWlktl1sxcd/MFFWecYwjzAvDOMn9uO0RUKbIJ4iZPKT7DHo8Ll8VTb8HBDETYt2V+WXy/zSKs7rNudnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:55:25.870597Z","bundle_sha256":"39fbb615a425625b8516b31a56eb1741aeecd92d4d56547320b186734ff4e539"}}