{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TLNEHJ4SLGPLIP4OIEKQZAT4FD","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":"4310ce64f3bd66da20ad011ff7663661315eef689c8701fa785e6f9b654a047a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-26T15:42:11Z","title_canon_sha256":"046ef7e5cc43c2f2df8ed006003d84090a6775b678a1d0dbd0220a5554237f89"},"schema_version":"1.0","source":{"id":"1206.6028","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6028","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6028v4","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6028","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"pith_short_12","alias_value":"TLNEHJ4SLGPL","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TLNEHJ4SLGPLIP4O","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TLNEHJ4S","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:2b508b97f330616d057114511078b28f17449ae24fe6416b6e784e797fed80ee","target":"graph","created_at":"2026-05-18T02:50:32Z","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":"Assume a complete superstable theory is superstable, and let P be a class of regular types, typically closed under automorphisms of the monster and non-orthogonality. We define the notion of P-NDOP and prove the existence of P-decompositions and derive an analog of Sh401 for superstable theories with P-NDOP. In this context, we also find a sufficient condition on P-decompositions that imply non-isomorphic models. For this, we investigate natural structures on the types in P\\intersect S(M) modulo non-orthogonality.","authors_text":"Michael C. Laskowski, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-26T15:42:11Z","title":"P-NDOP and P-decompositions of aleph_epsilon-saturated models of superstable theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6028","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:c00ef9ba330e615ef770bc939392652d55c3b555cdb8ff1e9e1285fb16a45df0","target":"record","created_at":"2026-05-18T02:50:32Z","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":"4310ce64f3bd66da20ad011ff7663661315eef689c8701fa785e6f9b654a047a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-26T15:42:11Z","title_canon_sha256":"046ef7e5cc43c2f2df8ed006003d84090a6775b678a1d0dbd0220a5554237f89"},"schema_version":"1.0","source":{"id":"1206.6028","kind":"arxiv","version":4}},"canonical_sha256":"9ada43a792599eb43f8e41150c827c28ee09ff59ef611ce30b93dca56905c0c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ada43a792599eb43f8e41150c827c28ee09ff59ef611ce30b93dca56905c0c6","first_computed_at":"2026-05-18T02:50:32.623525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:32.623525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YuOKObNlB97vtueMBIWIlsfMzhd6tp/k+Mcu091R5B6naDwfx8s+uQkUi0lLLgQowm2S7R6iRjjgCzR2rLrxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:32.623995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6028","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c00ef9ba330e615ef770bc939392652d55c3b555cdb8ff1e9e1285fb16a45df0","sha256:2b508b97f330616d057114511078b28f17449ae24fe6416b6e784e797fed80ee"],"state_sha256":"fb2e9ae7b9517c5fa23b0b5452d8b07d11793e9b38a1168b6bcf38d83ab1c90f"}