{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:L4275FK2OYHBYAGJNVB3ZFO6E5","short_pith_number":"pith:L4275FK2","canonical_record":{"source":{"id":"2206.08512","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-06-17T02:20:17Z","cross_cats_sorted":[],"title_canon_sha256":"7db3df88b0cb1976eb100e6b7afde56d5ccd0b95f4c869cf94626472bc94c587","abstract_canon_sha256":"634ab4713c4867e07fc3fa8f4f389595a9cfe33f5ba0a7b7d505f9841578f2d2"},"schema_version":"1.0"},"canonical_sha256":"5f35fe955a760e1c00c96d43bc95de2772b90252f5d46bc449847de94721aad2","source":{"kind":"arxiv","id":"2206.08512","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08512","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08512v4","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08512","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"L4275FK2OYHB","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4275FK2OYHBYAGJ","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4275FK2","created_at":"2026-07-05T06:20:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:L4275FK2OYHBYAGJNVB3ZFO6E5","target":"record","payload":{"canonical_record":{"source":{"id":"2206.08512","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-06-17T02:20:17Z","cross_cats_sorted":[],"title_canon_sha256":"7db3df88b0cb1976eb100e6b7afde56d5ccd0b95f4c869cf94626472bc94c587","abstract_canon_sha256":"634ab4713c4867e07fc3fa8f4f389595a9cfe33f5ba0a7b7d505f9841578f2d2"},"schema_version":"1.0"},"canonical_sha256":"5f35fe955a760e1c00c96d43bc95de2772b90252f5d46bc449847de94721aad2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:20:35.724706Z","signature_b64":"Rjh8XEfiP6Bn4mxeOynICoZ9RVX/uk6T4wFQfi1cMdN0IU02Lt+lDmdPoOMjkWOlWv03ufrpqHmEkQqxpQnWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f35fe955a760e1c00c96d43bc95de2772b90252f5d46bc449847de94721aad2","last_reissued_at":"2026-07-05T06:20:35.724198Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:20:35.724198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.08512","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nEoOx62dvI3noMemkazSZroUBR1EnuNyuZGxK+bBYP/BtJE0lNv/ru/9PV9QoSnqp6VnqSZDahqJnc6BVsNiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:55:11.226834Z"},"content_sha256":"2aea5e16d11a7eb25912fc37440ff069dfb12a5dff9c0bb56eb5ecac4d1e74f7","schema_version":"1.0","event_id":"sha256:2aea5e16d11a7eb25912fc37440ff069dfb12a5dff9c0bb56eb5ecac4d1e74f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:L4275FK2OYHBYAGJNVB3ZFO6E5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On NSOP$_2$ Theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Scott Mutchnik","submitted_at":"2022-06-17T02:20:17Z","abstract_excerpt":"Answering a question of D\\v{z}amonja and Shelah, we show that every NSOP$_2$ theory is NSOP$_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08512","kind":"arxiv","version":4},"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/2206.08512/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":"2026-07-05T06:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jPeUBys0vit37auNJrPYJbZnz9wJ3DCh5s6T1xJi/1imz/Vv1wAOifMHlf+TrqEkG6+i5XIoFLx6GzSddmVvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:55:11.227346Z"},"content_sha256":"8b9a993e9ae73f9776e3f99d5c0e780bc0c67df59595ffccdc5db55d9e806408","schema_version":"1.0","event_id":"sha256:8b9a993e9ae73f9776e3f99d5c0e780bc0c67df59595ffccdc5db55d9e806408"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L4275FK2OYHBYAGJNVB3ZFO6E5/bundle.json","state_url":"https://pith.science/pith/L4275FK2OYHBYAGJNVB3ZFO6E5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L4275FK2OYHBYAGJNVB3ZFO6E5/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":"2026-08-08T22:55:11Z","links":{"resolver":"https://pith.science/pith/L4275FK2OYHBYAGJNVB3ZFO6E5","bundle":"https://pith.science/pith/L4275FK2OYHBYAGJNVB3ZFO6E5/bundle.json","state":"https://pith.science/pith/L4275FK2OYHBYAGJNVB3ZFO6E5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L4275FK2OYHBYAGJNVB3ZFO6E5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:L4275FK2OYHBYAGJNVB3ZFO6E5","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":"634ab4713c4867e07fc3fa8f4f389595a9cfe33f5ba0a7b7d505f9841578f2d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-06-17T02:20:17Z","title_canon_sha256":"7db3df88b0cb1976eb100e6b7afde56d5ccd0b95f4c869cf94626472bc94c587"},"schema_version":"1.0","source":{"id":"2206.08512","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08512","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08512v4","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08512","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"L4275FK2OYHB","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4275FK2OYHBYAGJ","created_at":"2026-07-05T06:20:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4275FK2","created_at":"2026-07-05T06:20:35Z"}],"graph_snapshots":[{"event_id":"sha256:8b9a993e9ae73f9776e3f99d5c0e780bc0c67df59595ffccdc5db55d9e806408","target":"graph","created_at":"2026-07-05T06:20:35Z","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/2206.08512/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Answering a question of D\\v{z}amonja and Shelah, we show that every NSOP$_2$ theory is NSOP$_1$.","authors_text":"Scott Mutchnik","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-06-17T02:20:17Z","title":"On NSOP$_2$ Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08512","kind":"arxiv","version":4},"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":"sha256:2aea5e16d11a7eb25912fc37440ff069dfb12a5dff9c0bb56eb5ecac4d1e74f7","target":"record","created_at":"2026-07-05T06:20:35Z","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":"634ab4713c4867e07fc3fa8f4f389595a9cfe33f5ba0a7b7d505f9841578f2d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-06-17T02:20:17Z","title_canon_sha256":"7db3df88b0cb1976eb100e6b7afde56d5ccd0b95f4c869cf94626472bc94c587"},"schema_version":"1.0","source":{"id":"2206.08512","kind":"arxiv","version":4}},"canonical_sha256":"5f35fe955a760e1c00c96d43bc95de2772b90252f5d46bc449847de94721aad2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f35fe955a760e1c00c96d43bc95de2772b90252f5d46bc449847de94721aad2","first_computed_at":"2026-07-05T06:20:35.724198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:20:35.724198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rjh8XEfiP6Bn4mxeOynICoZ9RVX/uk6T4wFQfi1cMdN0IU02Lt+lDmdPoOMjkWOlWv03ufrpqHmEkQqxpQnWAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:20:35.724706Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.08512","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aea5e16d11a7eb25912fc37440ff069dfb12a5dff9c0bb56eb5ecac4d1e74f7","sha256:8b9a993e9ae73f9776e3f99d5c0e780bc0c67df59595ffccdc5db55d9e806408"],"state_sha256":"0cb09442ae5712a894f0045ba6054b0398a79a851ee2952c5a1e45c782c17965"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTgSDrxN5X1ZLsAnYKjYvuwHjIjUHJPP1rjKt6jr+U6ZGBcVIVRlo+UvpZG0d3p9HtDQDEXIhwl9MPL1RYWKAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:55:11.232559Z","bundle_sha256":"fe8b00a4510493708b3deee6de3eda61601973b615e2d5d45f4ba95d01408dad"}}