{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YOGBGJYPOFLL72GGRZ6V5HCPS6","short_pith_number":"pith:YOGBGJYP","canonical_record":{"source":{"id":"1103.0206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-01T16:19:07Z","cross_cats_sorted":[],"title_canon_sha256":"e141e848c86faf559c65ccb6e02fb00de63599e139627679733de6943b6894e7","abstract_canon_sha256":"508c756d5bcbb3de4147a64931bc0f50a5ddd67ba39327ef19db46bf02e7eb54"},"schema_version":"1.0"},"canonical_sha256":"c38c13270f7156bfe8c68e7d5e9c4f979ad5637619fde289a6f5892547fdc49d","source":{"kind":"arxiv","id":"1103.0206","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0206","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0206v1","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0206","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"YOGBGJYPOFLL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YOGBGJYPOFLL72GG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YOGBGJYP","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YOGBGJYPOFLL72GGRZ6V5HCPS6","target":"record","payload":{"canonical_record":{"source":{"id":"1103.0206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-01T16:19:07Z","cross_cats_sorted":[],"title_canon_sha256":"e141e848c86faf559c65ccb6e02fb00de63599e139627679733de6943b6894e7","abstract_canon_sha256":"508c756d5bcbb3de4147a64931bc0f50a5ddd67ba39327ef19db46bf02e7eb54"},"schema_version":"1.0"},"canonical_sha256":"c38c13270f7156bfe8c68e7d5e9c4f979ad5637619fde289a6f5892547fdc49d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:59.227088Z","signature_b64":"EXZFosD/3n424XHgm/AYq/9b/YDE9tpoxrPl0553Jc3QXOPPNEAqfeszynEJgEsiNFd5crUGY4Z4K0+p2C13Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c38c13270f7156bfe8c68e7d5e9c4f979ad5637619fde289a6f5892547fdc49d","last_reissued_at":"2026-05-18T03:48:59.226492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:59.226492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.0206","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":"2026-05-18T03:48:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xuZffxd1NhkFP1amE+9xtOwqFc9PoOpMXYispvpf5OsxDKArVDoJoACXJp6NbK6wPDOIWEfJh1+bzbjBhCHyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:13:28.521583Z"},"content_sha256":"ee95ed4883042d1dd4589770e64e72b44b0d2ee76d60eed47b7bfd5354dcca58","schema_version":"1.0","event_id":"sha256:ee95ed4883042d1dd4589770e64e72b44b0d2ee76d60eed47b7bfd5354dcca58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YOGBGJYPOFLL72GGRZ6V5HCPS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adding linear orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pierre Simon, Saharon Shelah","submitted_at":"2011-03-01T16:19:07Z","abstract_excerpt":"We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an \\omega-stable NDOP theory for which every expansion by a linear order interprets bounded arithmetic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0206","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":"2026-05-18T03:48:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtM/lI/bf+OM7A038iG7H2ufHdVaF45MmXa5FifMsjuRD/4NpF3fMBrDzjf0LJiGpuIdSMINbvC5/oakBn1TCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:13:28.522336Z"},"content_sha256":"bd78c9d901fd94ebfde6fac9f9617c5544ddb9b58add4244bdab0f272eed6edc","schema_version":"1.0","event_id":"sha256:bd78c9d901fd94ebfde6fac9f9617c5544ddb9b58add4244bdab0f272eed6edc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6/bundle.json","state_url":"https://pith.science/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6/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":"2026-06-10T10:13:28Z","links":{"resolver":"https://pith.science/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6","bundle":"https://pith.science/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6/bundle.json","state":"https://pith.science/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOGBGJYPOFLL72GGRZ6V5HCPS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YOGBGJYPOFLL72GGRZ6V5HCPS6","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":"508c756d5bcbb3de4147a64931bc0f50a5ddd67ba39327ef19db46bf02e7eb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-01T16:19:07Z","title_canon_sha256":"e141e848c86faf559c65ccb6e02fb00de63599e139627679733de6943b6894e7"},"schema_version":"1.0","source":{"id":"1103.0206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0206","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0206v1","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0206","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"YOGBGJYPOFLL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YOGBGJYPOFLL72GG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YOGBGJYP","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:bd78c9d901fd94ebfde6fac9f9617c5544ddb9b58add4244bdab0f272eed6edc","target":"graph","created_at":"2026-05-18T03:48:59Z","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 address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an \\omega-stable NDOP theory for which every expansion by a linear order interprets bounded arithmetic.","authors_text":"Pierre Simon, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-01T16:19:07Z","title":"Adding linear orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0206","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:ee95ed4883042d1dd4589770e64e72b44b0d2ee76d60eed47b7bfd5354dcca58","target":"record","created_at":"2026-05-18T03:48:59Z","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":"508c756d5bcbb3de4147a64931bc0f50a5ddd67ba39327ef19db46bf02e7eb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-01T16:19:07Z","title_canon_sha256":"e141e848c86faf559c65ccb6e02fb00de63599e139627679733de6943b6894e7"},"schema_version":"1.0","source":{"id":"1103.0206","kind":"arxiv","version":1}},"canonical_sha256":"c38c13270f7156bfe8c68e7d5e9c4f979ad5637619fde289a6f5892547fdc49d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c38c13270f7156bfe8c68e7d5e9c4f979ad5637619fde289a6f5892547fdc49d","first_computed_at":"2026-05-18T03:48:59.226492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:59.226492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EXZFosD/3n424XHgm/AYq/9b/YDE9tpoxrPl0553Jc3QXOPPNEAqfeszynEJgEsiNFd5crUGY4Z4K0+p2C13Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:59.227088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee95ed4883042d1dd4589770e64e72b44b0d2ee76d60eed47b7bfd5354dcca58","sha256:bd78c9d901fd94ebfde6fac9f9617c5544ddb9b58add4244bdab0f272eed6edc"],"state_sha256":"0f891da7aae61d5ae24faedf5debed19ef83de28be7aab6726d297c46ce1b4fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4BT9RvlNZQAv92nwpUy0S0HYS1qTXnbMBQQBTyVEQOpUgj8hsVL3dl1nFVSlUm2QgmjM+KptRX17mc6J4hn+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:13:28.526916Z","bundle_sha256":"4f1283923bf55dd55e98e42820932e3057e1ae3100aa6f0ddd99ce5217c842d4"}}