{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J7POSTCLQQWU5VPL53B73DFNFL","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":"95d5f7eef26080724d733087f8a545462d24d152375262112b1a688fa0b8697f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-18T10:29:19Z","title_canon_sha256":"6105f49a77f9bf4ad6bf7a0b632413db39ed7e7730a198a75578dd359892490a"},"schema_version":"1.0","source":{"id":"1105.3584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3584","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3584v1","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3584","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"J7POSTCLQQWU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J7POSTCLQQWU5VPL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J7POSTCL","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:7cc2df54e573191205205479b61cb9aaca66741fb253509b45debad0889e8fdc","target":"graph","created_at":"2026-05-18T04:21:52Z","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":"An $\\infty$-step nilsystem is an inverse limit of minimal nilsystems. In this article is shown that a minimal distal system is an $\\infty$-step nilsystem if and only if it has no nontrivial pairs with arbitrarily long finite IP-independence sets. Moreover, it is proved that any minimal system without nontrivial pairs with arbitrarily long finite IP-independence sets is an almost one to one extension of its maximal $\\infty$-step nilfactor, and each invariant ergodic measure is isomorphic (in the measurable sense) to the Haar measure on some $\\infty$-step nilsystem. The question if such a system","authors_text":"A. Maass, P.D. Dong, S. Donoso, S. Shao, X.D. Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-18T10:29:19Z","title":"Infinite-step nilsystems, independence and complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3584","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":"sha256:486e9cbdd8f2743af509221396ebefd31da3ad886969b87c0fecf1d50e7c9d23","target":"record","created_at":"2026-05-18T04:21:52Z","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":"95d5f7eef26080724d733087f8a545462d24d152375262112b1a688fa0b8697f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-18T10:29:19Z","title_canon_sha256":"6105f49a77f9bf4ad6bf7a0b632413db39ed7e7730a198a75578dd359892490a"},"schema_version":"1.0","source":{"id":"1105.3584","kind":"arxiv","version":1}},"canonical_sha256":"4fdee94c4b842d4ed5ebeec3fd8cad2ac15754b393fea5c2186fd21934ba24b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fdee94c4b842d4ed5ebeec3fd8cad2ac15754b393fea5c2186fd21934ba24b2","first_computed_at":"2026-05-18T04:21:52.317704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:52.317704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FHgOX3iyZHgpkCRUkgdVok7OIIowNBxU1n54DF8bD8N2CfFOf3iFz2lWU5WeDrFbbnwXGZUMQkXNnRKBupSFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:52.318232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:486e9cbdd8f2743af509221396ebefd31da3ad886969b87c0fecf1d50e7c9d23","sha256:7cc2df54e573191205205479b61cb9aaca66741fb253509b45debad0889e8fdc"],"state_sha256":"a929609fef780200fc0caaad94a53e8402a4051d6d601c46953c477890165d32"}