{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MDMIWP3GFLOUPOT4J556SD5YLC","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":"f5e7736b7c145c8c99185dead06d6b332e3d15765e3e29588594a072858f0408","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.LO","submitted_at":"2025-01-07T13:54:04Z","title_canon_sha256":"785a295a2b89baf6dfb266f29081caf5817e1c7db8bb30c2ec18cb3ce77b7566"},"schema_version":"1.0","source":{"id":"2501.03789","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03789","created_at":"2026-06-09T02:08:28Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03789v4","created_at":"2026-06-09T02:08:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03789","created_at":"2026-06-09T02:08:28Z"},{"alias_kind":"pith_short_12","alias_value":"MDMIWP3GFLOU","created_at":"2026-06-09T02:08:28Z"},{"alias_kind":"pith_short_16","alias_value":"MDMIWP3GFLOUPOT4","created_at":"2026-06-09T02:08:28Z"},{"alias_kind":"pith_short_8","alias_value":"MDMIWP3G","created_at":"2026-06-09T02:08:28Z"}],"graph_snapshots":[{"event_id":"sha256:7dfb5ee39d974a6b89f8739f4bc9e9672245f5d07bee68435ce6917ada617667","target":"graph","created_at":"2026-06-09T02:08:28Z","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/2501.03789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a dichotomy for structures $A$ that are preserved by primitive actions of $S_{\\omega} = \\text{Sym}({\\mathbb N})$: such a structure primitively positively constructs all finite structures and the constraint satisfaction problem is NP-complete, or the constraint satisfaction problem for $A$ is in P. To prove our result, we study the first-order reducts of the Johnson graph $J(k)$, for $k \\geq 2$, whose automorphism group $G$ equals the action of $\\text{Sym}({\\mathbb N})$ on the set $V$ of $k$-element subsets of $\\mathbb N$. We use the fact that $J(k)$ has a finitely bounded homogeneou","authors_text":"Bertalan Bodor, Manuel Bodirsky","cross_cats":["cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.LO","submitted_at":"2025-01-07T13:54:04Z","title":"Structures preserved by primitive actions of $S_\\omega$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03789","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":"sha256:6c937231013ac7608f92a0384b47724cd0623569c72f94085dbf97a8d6ff3ce5","target":"record","created_at":"2026-06-09T02:08:28Z","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":"f5e7736b7c145c8c99185dead06d6b332e3d15765e3e29588594a072858f0408","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.LO","submitted_at":"2025-01-07T13:54:04Z","title_canon_sha256":"785a295a2b89baf6dfb266f29081caf5817e1c7db8bb30c2ec18cb3ce77b7566"},"schema_version":"1.0","source":{"id":"2501.03789","kind":"arxiv","version":4}},"canonical_sha256":"60d88b3f662add47ba7c4f7be90fb8588e851e675e5783dae986e27372cf232b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60d88b3f662add47ba7c4f7be90fb8588e851e675e5783dae986e27372cf232b","first_computed_at":"2026-06-09T02:08:28.112782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:28.112782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O6rrnmBS9SScHf9bO8l2rOwP3V4YHLy312fKACM58tSXodLKUHE22ec/NL4V2x6uVMSOef8Bf3QdP9vFSo0nAw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:28.113925Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03789","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c937231013ac7608f92a0384b47724cd0623569c72f94085dbf97a8d6ff3ce5","sha256:7dfb5ee39d974a6b89f8739f4bc9e9672245f5d07bee68435ce6917ada617667"],"state_sha256":"8c2ce1062846a64a7264913f0e5ecc987bd75cb87c9a41cbab6d5e1a6463cb05"}