{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:64IKY37YMX7JPHWEJVP4L5DYEZ","short_pith_number":"pith:64IKY37Y","schema_version":"1.0","canonical_sha256":"f710ac6ff865fe979ec44d5fc5f4782671d60d655570f9b313de19e7a0136ca6","source":{"kind":"arxiv","id":"1010.2396","version":1},"attestation_state":"computed","paper":{"title":"N^N^N does not satisfy Normann's condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Matthias Schroeder","submitted_at":"2010-10-12T14:15:08Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1010.2396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-10-12T14:15:08Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"57c152cfd1d9db73054dd868c3d06c283d6500b35593e87bc5a6dd8fe8ebd846","abstract_canon_sha256":"06ab656f8b41c6a672153f685bac09662f3489c1c6139ef836e20f66ef5bdeab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:28.081287Z","signature_b64":"y7f3s74BszyYmxtjCWdaqjb44/Rhiy8sks1gaJb7SWbqT9dy7RQnUSO7Htug04HIjIWqDGBQCpqjYLfw4AqJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f710ac6ff865fe979ec44d5fc5f4782671d60d655570f9b313de19e7a0136ca6","last_reissued_at":"2026-05-18T04:39:28.080794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:28.080794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"N^N^N does not satisfy Normann's condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Matthias Schroeder","submitted_at":"2010-10-12T14:15:08Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2396","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1010.2396","created_at":"2026-05-18T04:39:28.080885+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.2396v1","created_at":"2026-05-18T04:39:28.080885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2396","created_at":"2026-05-18T04:39:28.080885+00:00"},{"alias_kind":"pith_short_12","alias_value":"64IKY37YMX7J","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"64IKY37YMX7JPHWE","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"64IKY37Y","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ","json":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ.json","graph_json":"https://pith.science/api/pith-number/64IKY37YMX7JPHWEJVP4L5DYEZ/graph.json","events_json":"https://pith.science/api/pith-number/64IKY37YMX7JPHWEJVP4L5DYEZ/events.json","paper":"https://pith.science/paper/64IKY37Y"},"agent_actions":{"view_html":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ","download_json":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ.json","view_paper":"https://pith.science/paper/64IKY37Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.2396&json=true","fetch_graph":"https://pith.science/api/pith-number/64IKY37YMX7JPHWEJVP4L5DYEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/64IKY37YMX7JPHWEJVP4L5DYEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ/action/storage_attestation","attest_author":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ/action/author_attestation","sign_citation":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ/action/citation_signature","submit_replication":"https://pith.science/pith/64IKY37YMX7JPHWEJVP4L5DYEZ/action/replication_record"}},"created_at":"2026-05-18T04:39:28.080885+00:00","updated_at":"2026-05-18T04:39:28.080885+00:00"}