{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:543Y5LRUAFFPVG67V6PH2Z5L54","short_pith_number":"pith:543Y5LRU","canonical_record":{"source":{"id":"1311.3074","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2013-11-13T10:36:25Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"37545142b23d3b8f8cd7010c43677f2419aa3c3a05e8819181a4b2b21c9388fa","abstract_canon_sha256":"5a07ab9e331d8d73ae106462575e2b92f225021561cf4298b5799acf8913f855"},"schema_version":"1.0"},"canonical_sha256":"ef378eae34014afa9bdfaf9e7d67abef11a12bf2e036c7aa06c557103e6b1e57","source":{"kind":"arxiv","id":"1311.3074","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3074","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3074v4","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3074","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"543Y5LRUAFFP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"543Y5LRUAFFPVG67","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"543Y5LRU","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:543Y5LRUAFFPVG67V6PH2Z5L54","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3074","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2013-11-13T10:36:25Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"37545142b23d3b8f8cd7010c43677f2419aa3c3a05e8819181a4b2b21c9388fa","abstract_canon_sha256":"5a07ab9e331d8d73ae106462575e2b92f225021561cf4298b5799acf8913f855"},"schema_version":"1.0"},"canonical_sha256":"ef378eae34014afa9bdfaf9e7d67abef11a12bf2e036c7aa06c557103e6b1e57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:45.758594Z","signature_b64":"0TXO6jHm10/u/TqeiR3C7YIpQlngArxRUPCm0OR/ABXrXuEp7/DWua0GaztCpifY8eyENTJu479SrW7dFNTuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef378eae34014afa9bdfaf9e7d67abef11a12bf2e036c7aa06c557103e6b1e57","last_reissued_at":"2026-05-18T01:34:45.757945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:45.757945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3074","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwK9904Q7QVNjgNpCnqdNt19d00gBBjzvdWoPjbOLGChEUpxJBwvZmw+30s9C3wGijWbIbTtZ1NrUit29BX0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:44:31.540428Z"},"content_sha256":"35d38553191a6461586ca9b872b9cae2bab231abdc91081b323035a0b1ec525f","schema_version":"1.0","event_id":"sha256:35d38553191a6461586ca9b872b9cae2bab231abdc91081b323035a0b1ec525f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:543Y5LRUAFFPVG67V6PH2Z5L54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The weak choice principle WISC may fail in the category of sets","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"David Michael Roberts","submitted_at":"2013-11-13T10:36:25Z","abstract_excerpt":"The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of sets and using an extension of the internal logic of a topos due to Shulman, we show that WISC is independent of the rest of the axioms of the set theory given by a well-pointed topos. This also gives an example of a topos that is not a predicative topos as defined by van den Berg."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3074","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nyb56Rc1wjlJEO+aV9MJ1sQbcrivX/QaNDCM7mf9epwmbJsUh3//Id49DFxpMBQy2vXJD03gRzuF5MhcCVHqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:44:31.540773Z"},"content_sha256":"5464057d3439cc6043e75100ccd64a2aaefb21b696fdc2a18661e70dbab0f3af","schema_version":"1.0","event_id":"sha256:5464057d3439cc6043e75100ccd64a2aaefb21b696fdc2a18661e70dbab0f3af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/543Y5LRUAFFPVG67V6PH2Z5L54/bundle.json","state_url":"https://pith.science/pith/543Y5LRUAFFPVG67V6PH2Z5L54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/543Y5LRUAFFPVG67V6PH2Z5L54/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T16:44:31Z","links":{"resolver":"https://pith.science/pith/543Y5LRUAFFPVG67V6PH2Z5L54","bundle":"https://pith.science/pith/543Y5LRUAFFPVG67V6PH2Z5L54/bundle.json","state":"https://pith.science/pith/543Y5LRUAFFPVG67V6PH2Z5L54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/543Y5LRUAFFPVG67V6PH2Z5L54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:543Y5LRUAFFPVG67V6PH2Z5L54","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":"5a07ab9e331d8d73ae106462575e2b92f225021561cf4298b5799acf8913f855","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2013-11-13T10:36:25Z","title_canon_sha256":"37545142b23d3b8f8cd7010c43677f2419aa3c3a05e8819181a4b2b21c9388fa"},"schema_version":"1.0","source":{"id":"1311.3074","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3074","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3074v4","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3074","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"543Y5LRUAFFP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"543Y5LRUAFFPVG67","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"543Y5LRU","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:5464057d3439cc6043e75100ccd64a2aaefb21b696fdc2a18661e70dbab0f3af","target":"graph","created_at":"2026-05-18T01:34:45Z","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":"The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of sets and using an extension of the internal logic of a topos due to Shulman, we show that WISC is independent of the rest of the axioms of the set theory given by a well-pointed topos. This also gives an example of a topos that is not a predicative topos as defined by van den Berg.","authors_text":"David Michael Roberts","cross_cats":["math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2013-11-13T10:36:25Z","title":"The weak choice principle WISC may fail in the category of sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3074","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":"sha256:35d38553191a6461586ca9b872b9cae2bab231abdc91081b323035a0b1ec525f","target":"record","created_at":"2026-05-18T01:34:45Z","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":"5a07ab9e331d8d73ae106462575e2b92f225021561cf4298b5799acf8913f855","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2013-11-13T10:36:25Z","title_canon_sha256":"37545142b23d3b8f8cd7010c43677f2419aa3c3a05e8819181a4b2b21c9388fa"},"schema_version":"1.0","source":{"id":"1311.3074","kind":"arxiv","version":4}},"canonical_sha256":"ef378eae34014afa9bdfaf9e7d67abef11a12bf2e036c7aa06c557103e6b1e57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef378eae34014afa9bdfaf9e7d67abef11a12bf2e036c7aa06c557103e6b1e57","first_computed_at":"2026-05-18T01:34:45.757945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:45.757945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0TXO6jHm10/u/TqeiR3C7YIpQlngArxRUPCm0OR/ABXrXuEp7/DWua0GaztCpifY8eyENTJu479SrW7dFNTuBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:45.758594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3074","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35d38553191a6461586ca9b872b9cae2bab231abdc91081b323035a0b1ec525f","sha256:5464057d3439cc6043e75100ccd64a2aaefb21b696fdc2a18661e70dbab0f3af"],"state_sha256":"afd1f3a350bc342ac369cdbd8fe986802745f532dda552d8de7931ad8960a69b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyQ/xHbRJqGAdr9uEGrz/Pg3qWFSAyf+VgYlGn6emlDCxKcxas+Oe/1PtMreWm7OxWaiyXHjCR0noSxtpvGZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:44:31.542757Z","bundle_sha256":"53b98b4ae7fa0945354112762ad90548a0b5fc10d0f402f35ac67f4e2666f654"}}