{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TXJBR4HTAFGTSAYLD2X4X23IPU","short_pith_number":"pith:TXJBR4HT","canonical_record":{"source":{"id":"1409.1608","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-04T20:57:06Z","cross_cats_sorted":[],"title_canon_sha256":"fee6bdf507d0051609461f7327456ba4372fd09fdc6739d9979849fce3ff1c50","abstract_canon_sha256":"435f04d5b828fa2a37e77545db82663ac3391168777781cd7198227f9feb06df"},"schema_version":"1.0"},"canonical_sha256":"9dd218f0f3014d39030b1eafcbeb687d3aef6a54d7d5a324c462d7c9f91f7079","source":{"kind":"arxiv","id":"1409.1608","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1608","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1608v2","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1608","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"TXJBR4HTAFGT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TXJBR4HTAFGTSAYL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TXJBR4HT","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TXJBR4HTAFGTSAYLD2X4X23IPU","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1608","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-04T20:57:06Z","cross_cats_sorted":[],"title_canon_sha256":"fee6bdf507d0051609461f7327456ba4372fd09fdc6739d9979849fce3ff1c50","abstract_canon_sha256":"435f04d5b828fa2a37e77545db82663ac3391168777781cd7198227f9feb06df"},"schema_version":"1.0"},"canonical_sha256":"9dd218f0f3014d39030b1eafcbeb687d3aef6a54d7d5a324c462d7c9f91f7079","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:12.230450Z","signature_b64":"c3m/ygi0EuPoJq5bWziQKv4AnF1gRGsZOZ2PA8+0M0R20mrrjurERLzgvtlpPsYWNha9zU6vRiXeKhHhoB6xAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dd218f0f3014d39030b1eafcbeb687d3aef6a54d7d5a324c462d7c9f91f7079","last_reissued_at":"2026-05-17T23:53:12.229737Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:12.229737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1608","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":"2026-05-17T23:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q0XM9O7uTodli+JmrQsqPL6O37eGoQJw+AXmXegw3AYy0uleHmCZkLXfUm3Qy9a2xX8rT5pZuqZW68RS3bC4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T00:05:39.425881Z"},"content_sha256":"47b010806c72946bbc267c39279b870d088efdec08926724e527c82d2bcb344e","schema_version":"1.0","event_id":"sha256:47b010806c72946bbc267c39279b870d088efdec08926724e527c82d2bcb344e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TXJBR4HTAFGTSAYLD2X4X23IPU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computable Axiomatizability of Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Peter Sinclair","submitted_at":"2014-09-04T20:57:06Z","abstract_excerpt":"The goal of this paper is to generalise Alex Rennet's proof of the non-axiomatizability of the class of pseudo-o-minimal structures. Rennet showed that if L is an expansion of the language of ordered fields and K is the class of pseudo-o-minimal L-structures (L-structures elementarily equivalent to an ultraproduct of o-minimal structures) then K is not computably axiomatizable. We give a general version of this theorem, and apply it to several classes of topological structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1608","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":"2026-05-17T23:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5v93ygSSh7RoEvaKdQtjxmov1qimGr91oQqBw3yJJVcWvAGM48++GvTWs94dFHAITg4UYpHohhxeI4IrYjtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T00:05:39.426224Z"},"content_sha256":"ad3eb65832ea719550ff38c59ed007e9a2477ec603b2e7655cbc00d54484eb98","schema_version":"1.0","event_id":"sha256:ad3eb65832ea719550ff38c59ed007e9a2477ec603b2e7655cbc00d54484eb98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXJBR4HTAFGTSAYLD2X4X23IPU/bundle.json","state_url":"https://pith.science/pith/TXJBR4HTAFGTSAYLD2X4X23IPU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXJBR4HTAFGTSAYLD2X4X23IPU/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":"2026-07-20T00:05:39Z","links":{"resolver":"https://pith.science/pith/TXJBR4HTAFGTSAYLD2X4X23IPU","bundle":"https://pith.science/pith/TXJBR4HTAFGTSAYLD2X4X23IPU/bundle.json","state":"https://pith.science/pith/TXJBR4HTAFGTSAYLD2X4X23IPU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXJBR4HTAFGTSAYLD2X4X23IPU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TXJBR4HTAFGTSAYLD2X4X23IPU","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":"435f04d5b828fa2a37e77545db82663ac3391168777781cd7198227f9feb06df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-04T20:57:06Z","title_canon_sha256":"fee6bdf507d0051609461f7327456ba4372fd09fdc6739d9979849fce3ff1c50"},"schema_version":"1.0","source":{"id":"1409.1608","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1608","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1608v2","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1608","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"TXJBR4HTAFGT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TXJBR4HTAFGTSAYL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TXJBR4HT","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:ad3eb65832ea719550ff38c59ed007e9a2477ec603b2e7655cbc00d54484eb98","target":"graph","created_at":"2026-05-17T23:53:12Z","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":"The goal of this paper is to generalise Alex Rennet's proof of the non-axiomatizability of the class of pseudo-o-minimal structures. Rennet showed that if L is an expansion of the language of ordered fields and K is the class of pseudo-o-minimal L-structures (L-structures elementarily equivalent to an ultraproduct of o-minimal structures) then K is not computably axiomatizable. We give a general version of this theorem, and apply it to several classes of topological structures.","authors_text":"Peter Sinclair","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-04T20:57:06Z","title":"Computable Axiomatizability of Elementary Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1608","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":"sha256:47b010806c72946bbc267c39279b870d088efdec08926724e527c82d2bcb344e","target":"record","created_at":"2026-05-17T23:53:12Z","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":"435f04d5b828fa2a37e77545db82663ac3391168777781cd7198227f9feb06df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-04T20:57:06Z","title_canon_sha256":"fee6bdf507d0051609461f7327456ba4372fd09fdc6739d9979849fce3ff1c50"},"schema_version":"1.0","source":{"id":"1409.1608","kind":"arxiv","version":2}},"canonical_sha256":"9dd218f0f3014d39030b1eafcbeb687d3aef6a54d7d5a324c462d7c9f91f7079","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dd218f0f3014d39030b1eafcbeb687d3aef6a54d7d5a324c462d7c9f91f7079","first_computed_at":"2026-05-17T23:53:12.229737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:12.229737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c3m/ygi0EuPoJq5bWziQKv4AnF1gRGsZOZ2PA8+0M0R20mrrjurERLzgvtlpPsYWNha9zU6vRiXeKhHhoB6xAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:12.230450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1608","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47b010806c72946bbc267c39279b870d088efdec08926724e527c82d2bcb344e","sha256:ad3eb65832ea719550ff38c59ed007e9a2477ec603b2e7655cbc00d54484eb98"],"state_sha256":"2f4969a4c4ff1f7b46313a2434dd94d9b7268963d440d4015ce22835fd1a2cfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b7boyoXqfSS/Bb991kS0ml9wAPQTLOweQ49BhL6MihDxNS34gO3VFyDj63vG5HeiAX+PsfOsEzaBhOiv/zMwCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-20T00:05:39.428336Z","bundle_sha256":"7732595bff8cc85a429bd6141ee7da61b67c0c4adbc8d7f98814d8e3d67ef0c4"}}