{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:64IKY37YMX7JPHWEJVP4L5DYEZ","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":"06ab656f8b41c6a672153f685bac09662f3489c1c6139ef836e20f66ef5bdeab","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-10-12T14:15:08Z","title_canon_sha256":"57c152cfd1d9db73054dd868c3d06c283d6500b35593e87bc5a6dd8fe8ebd846"},"schema_version":"1.0","source":{"id":"1010.2396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2396","created_at":"2026-05-18T04:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2396v1","created_at":"2026-05-18T04:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2396","created_at":"2026-05-18T04:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"64IKY37YMX7J","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"64IKY37YMX7JPHWE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"64IKY37Y","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ca2094570167b51660515484e0545d4c8352636455b16598d80c95610e31658f","target":"graph","created_at":"2026-05-18T04:39:28Z","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"},"paper":{"abstract_excerpt":"We prove that the Kleene-Kreisel space $N^N^N$ does not satisfy Normann's condition. A topological space $X$ is said to fulfil Normann's condition, if every functionally closed subset of $X$ is an intersection of clopen sets. The investigation of this property is motivated by its strong relationship to a problem in Computable Analysis. D. Normann has proved that in order to establish non-coincidence of the extensional hierarchy and the intensional hierarchy of functionals over the reals it is enough to show that $N^N^N$ fails the above condition.","authors_text":"Matthias Schroeder","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-10-12T14:15:08Z","title":"N^N^N does not satisfy Normann's condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2396","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":"sha256:7a3fba1a4b2549378dce42256771dc02a6869ca2bc487029a1f73ee31463bea6","target":"record","created_at":"2026-05-18T04:39:28Z","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":"06ab656f8b41c6a672153f685bac09662f3489c1c6139ef836e20f66ef5bdeab","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-10-12T14:15:08Z","title_canon_sha256":"57c152cfd1d9db73054dd868c3d06c283d6500b35593e87bc5a6dd8fe8ebd846"},"schema_version":"1.0","source":{"id":"1010.2396","kind":"arxiv","version":1}},"canonical_sha256":"f710ac6ff865fe979ec44d5fc5f4782671d60d655570f9b313de19e7a0136ca6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f710ac6ff865fe979ec44d5fc5f4782671d60d655570f9b313de19e7a0136ca6","first_computed_at":"2026-05-18T04:39:28.080794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:28.080794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y7f3s74BszyYmxtjCWdaqjb44/Rhiy8sks1gaJb7SWbqT9dy7RQnUSO7Htug04HIjIWqDGBQCpqjYLfw4AqJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:28.081287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a3fba1a4b2549378dce42256771dc02a6869ca2bc487029a1f73ee31463bea6","sha256:ca2094570167b51660515484e0545d4c8352636455b16598d80c95610e31658f"],"state_sha256":"4436d867a24fa7a53dfe2363c214aa77ba77b476996bb7d9764317bf68b5e176"}