{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NUR7DPX4VKEFD5COEFABUBOHTR","short_pith_number":"pith:NUR7DPX4","canonical_record":{"source":{"id":"2209.00571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"6655f8653d8e3df595e6fdb78437b2247ab3adb923bedcd8b4fea8c64f1f34f2","abstract_canon_sha256":"6fbe5374f2c32ad02a48b9d713926e977f6b02816f02b7adf7ba21ce1e788b15"},"schema_version":"1.0"},"canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","source":{"kind":"arxiv","id":"2209.00571","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00571","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00571v1","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00571","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"NUR7DPX4VKEF","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_16","alias_value":"NUR7DPX4VKEFD5CO","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_8","alias_value":"NUR7DPX4","created_at":"2026-07-05T04:53:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NUR7DPX4VKEFD5COEFABUBOHTR","target":"record","payload":{"canonical_record":{"source":{"id":"2209.00571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"6655f8653d8e3df595e6fdb78437b2247ab3adb923bedcd8b4fea8c64f1f34f2","abstract_canon_sha256":"6fbe5374f2c32ad02a48b9d713926e977f6b02816f02b7adf7ba21ce1e788b15"},"schema_version":"1.0"},"canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:53:51.552741Z","signature_b64":"jyQxCx2+urUbpvmDll5ykB4Eafu1dbd3Ee2/H0QPC9Yjej3XgbGi3mi/KnXa22GDpnLsvrZGI4W7oVuAv/PjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","last_reissued_at":"2026-07-05T04:53:51.552334Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:53:51.552334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.00571","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":"2026-07-05T04:53:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8fxB6g+lX1uptz7io+GfFX5bKyGBFqwsao8C/fjQe/L/grorKRbPiZrcUYBgAb5JOuz4P6fec7WGtTqLsa6uBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:17:45.648547Z"},"content_sha256":"4c2ee315e787c1c4d279988cf5556a676387987ce981917dc49321f6562b061f","schema_version":"1.0","event_id":"sha256:4c2ee315e787c1c4d279988cf5556a676387987ce981917dc49321f6562b061f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NUR7DPX4VKEFD5COEFABUBOHTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Model-theoretic dividing lines via posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dar\\'io Garc\\'ia, Rosario Mennuni","submitted_at":"2022-09-01T16:32:19Z","abstract_excerpt":"We show that for each property $\\mathsf{P}\\in \\{\\mathsf{OP}, \\mathsf{IP}, \\mathsf{TP}_1, \\mathsf{TP}_2, \\mathsf{ATP}, \\mathsf{SOP}_3\\}$ there is a poset $\\Sigma_{\\mathsf{P}}$ such that a theory has property $\\mathsf{P}$ if and only if some model interprets a poset in which $\\Sigma_{\\mathsf{P}}$ can be embedded. We also introduce a new property $\\mathsf{SUP}$, consistent with $\\mathsf{NIP}_2$ and implying $\\mathsf{ATP}$ and $\\mathsf{SOP}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00571","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.00571/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:53:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ivNpVxGsOj1yDFZ2YtWQ2l5po5eg8fPdLMscY0FNG8m86H2zlHxVSX9uS36kZgtF1IQ8iThc04zDBiFuI54Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:17:45.649075Z"},"content_sha256":"e369e8da339b00ec7a8ec0a718b440dd0b67b0e716c68b6f40e9cac2ccb71082","schema_version":"1.0","event_id":"sha256:e369e8da339b00ec7a8ec0a718b440dd0b67b0e716c68b6f40e9cac2ccb71082"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUR7DPX4VKEFD5COEFABUBOHTR/bundle.json","state_url":"https://pith.science/pith/NUR7DPX4VKEFD5COEFABUBOHTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUR7DPX4VKEFD5COEFABUBOHTR/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":"2026-08-08T16:17:45Z","links":{"resolver":"https://pith.science/pith/NUR7DPX4VKEFD5COEFABUBOHTR","bundle":"https://pith.science/pith/NUR7DPX4VKEFD5COEFABUBOHTR/bundle.json","state":"https://pith.science/pith/NUR7DPX4VKEFD5COEFABUBOHTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUR7DPX4VKEFD5COEFABUBOHTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NUR7DPX4VKEFD5COEFABUBOHTR","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":"6fbe5374f2c32ad02a48b9d713926e977f6b02816f02b7adf7ba21ce1e788b15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","title_canon_sha256":"6655f8653d8e3df595e6fdb78437b2247ab3adb923bedcd8b4fea8c64f1f34f2"},"schema_version":"1.0","source":{"id":"2209.00571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00571","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00571v1","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00571","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"NUR7DPX4VKEF","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_16","alias_value":"NUR7DPX4VKEFD5CO","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_8","alias_value":"NUR7DPX4","created_at":"2026-07-05T04:53:51Z"}],"graph_snapshots":[{"event_id":"sha256:e369e8da339b00ec7a8ec0a718b440dd0b67b0e716c68b6f40e9cac2ccb71082","target":"graph","created_at":"2026-07-05T04:53:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.00571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for each property $\\mathsf{P}\\in \\{\\mathsf{OP}, \\mathsf{IP}, \\mathsf{TP}_1, \\mathsf{TP}_2, \\mathsf{ATP}, \\mathsf{SOP}_3\\}$ there is a poset $\\Sigma_{\\mathsf{P}}$ such that a theory has property $\\mathsf{P}$ if and only if some model interprets a poset in which $\\Sigma_{\\mathsf{P}}$ can be embedded. We also introduce a new property $\\mathsf{SUP}$, consistent with $\\mathsf{NIP}_2$ and implying $\\mathsf{ATP}$ and $\\mathsf{SOP}$.","authors_text":"Dar\\'io Garc\\'ia, Rosario Mennuni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","title":"Model-theoretic dividing lines via posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00571","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":"sha256:4c2ee315e787c1c4d279988cf5556a676387987ce981917dc49321f6562b061f","target":"record","created_at":"2026-07-05T04:53:51Z","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":"6fbe5374f2c32ad02a48b9d713926e977f6b02816f02b7adf7ba21ce1e788b15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","title_canon_sha256":"6655f8653d8e3df595e6fdb78437b2247ab3adb923bedcd8b4fea8c64f1f34f2"},"schema_version":"1.0","source":{"id":"2209.00571","kind":"arxiv","version":1}},"canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","first_computed_at":"2026-07-05T04:53:51.552334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:53:51.552334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jyQxCx2+urUbpvmDll5ykB4Eafu1dbd3Ee2/H0QPC9Yjej3XgbGi3mi/KnXa22GDpnLsvrZGI4W7oVuAv/PjBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:53:51.552741Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.00571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c2ee315e787c1c4d279988cf5556a676387987ce981917dc49321f6562b061f","sha256:e369e8da339b00ec7a8ec0a718b440dd0b67b0e716c68b6f40e9cac2ccb71082"],"state_sha256":"fb126acfae79bc74e4c24474655283f8de0cc57ed9f05e6ac1c6cebee48a603a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NOtzggBgYJrxnh+S3B7np8LFU2JotD/MvS6849oVrGnc1UwZ5xtrzj3MOZA/yNf2BwY0muNG3r2iq0gJj/6UBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:17:45.653639Z","bundle_sha256":"f8c6e615b5ecc86fd8254e3bad36f10d89b7458cc3a990324f06b69638ffda8c"}}