{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:C6Q54UT6WZ6QPVSB35QNX6DXML","short_pith_number":"pith:C6Q54UT6","schema_version":"1.0","canonical_sha256":"17a1de527eb67d07d641df60dbf87762eb1f17362f6147576914273dfdf7c381","source":{"kind":"arxiv","id":"0911.0068","version":1},"attestation_state":"computed","paper":{"title":"On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"Andrej Bauer","submitted_at":"2009-10-31T10:43:24Z","abstract_excerpt":"In the effective topos there exists a chain-complete distributive lattice with a monotone and progressive endomap which does not have a fixed point. Consequently, the Bourbaki-Witt theorem and Tarski's fixed-point theorem for chain-complete lattices do not have constructive (topos-valid) proofs."},"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":"0911.0068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-10-31T10:43:24Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"11a16e6f8920f48e7ce51f4aef8aa2f371e43b0155f197c5e2c7c61987e77c8d","abstract_canon_sha256":"efe7aa27be799d3db75b43cf8d180e2f88fea5ddd3fe3cdf035dcc57f257169c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:16.615697Z","signature_b64":"9eJpLHMERL37SOU2STHfauzhaYNa0Z0nWsjjlSNC2ohrbB5V9dTTQ392G2+9jumF5dqjc0+S1bGFmyTaLYmSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a1de527eb67d07d641df60dbf87762eb1f17362f6147576914273dfdf7c381","last_reissued_at":"2026-05-18T04:05:16.615082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:16.615082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"Andrej Bauer","submitted_at":"2009-10-31T10:43:24Z","abstract_excerpt":"In the effective topos there exists a chain-complete distributive lattice with a monotone and progressive endomap which does not have a fixed point. Consequently, the Bourbaki-Witt theorem and Tarski's fixed-point theorem for chain-complete lattices do not have constructive (topos-valid) proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0068","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":"0911.0068","created_at":"2026-05-18T04:05:16.615188+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.0068v1","created_at":"2026-05-18T04:05:16.615188+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0068","created_at":"2026-05-18T04:05:16.615188+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6Q54UT6WZ6Q","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6Q54UT6WZ6QPVSB","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6Q54UT6","created_at":"2026-05-18T12:25:58.837520+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/C6Q54UT6WZ6QPVSB35QNX6DXML","json":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML.json","graph_json":"https://pith.science/api/pith-number/C6Q54UT6WZ6QPVSB35QNX6DXML/graph.json","events_json":"https://pith.science/api/pith-number/C6Q54UT6WZ6QPVSB35QNX6DXML/events.json","paper":"https://pith.science/paper/C6Q54UT6"},"agent_actions":{"view_html":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML","download_json":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML.json","view_paper":"https://pith.science/paper/C6Q54UT6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.0068&json=true","fetch_graph":"https://pith.science/api/pith-number/C6Q54UT6WZ6QPVSB35QNX6DXML/graph.json","fetch_events":"https://pith.science/api/pith-number/C6Q54UT6WZ6QPVSB35QNX6DXML/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML/action/storage_attestation","attest_author":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML/action/author_attestation","sign_citation":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML/action/citation_signature","submit_replication":"https://pith.science/pith/C6Q54UT6WZ6QPVSB35QNX6DXML/action/replication_record"}},"created_at":"2026-05-18T04:05:16.615188+00:00","updated_at":"2026-05-18T04:05:16.615188+00:00"}