{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:QOZVIRA7KTGWAIM3ZSSEJMJZQP","short_pith_number":"pith:QOZVIRA7","canonical_record":{"source":{"id":"2104.00506","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-03-31T16:55:17Z","cross_cats_sorted":[],"title_canon_sha256":"ae325a4f158846039c2e3293c001e7f794d0688847435b91579b489edaec83e8","abstract_canon_sha256":"132558628b4769b4f21da9deae4fafc21e5365ec7a68d7c00f9041f0da046d62"},"schema_version":"1.0"},"canonical_sha256":"83b354441f54cd60219bcca444b13983e7292ebb5331c0298e2a30c9457c5b88","source":{"kind":"arxiv","id":"2104.00506","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.00506","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"2104.00506v7","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.00506","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"QOZVIRA7KTGW","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOZVIRA7KTGWAIM3","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOZVIRA7","created_at":"2026-06-08T01:03:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:QOZVIRA7KTGWAIM3ZSSEJMJZQP","target":"record","payload":{"canonical_record":{"source":{"id":"2104.00506","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-03-31T16:55:17Z","cross_cats_sorted":[],"title_canon_sha256":"ae325a4f158846039c2e3293c001e7f794d0688847435b91579b489edaec83e8","abstract_canon_sha256":"132558628b4769b4f21da9deae4fafc21e5365ec7a68d7c00f9041f0da046d62"},"schema_version":"1.0"},"canonical_sha256":"83b354441f54cd60219bcca444b13983e7292ebb5331c0298e2a30c9457c5b88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:03:39.505030Z","signature_b64":"hMSLvRuSgOlmQOZNbw9vol8P2wRl/WNbIvZLovo44qmEqCK7I+hqdhu0fIAyeVWY5elvGlWUD0KbP/znxyydCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83b354441f54cd60219bcca444b13983e7292ebb5331c0298e2a30c9457c5b88","last_reissued_at":"2026-06-08T01:03:39.503920Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:03:39.503920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.00506","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-08T01:03:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZrjqOmDGqjNaUTzaWeVLaYDl18+NZjJmNsVuQm6C0AkhXIENdZJgYSWG06VDKBM76zEW1wOhiSQIQzxfS6tCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:42:56.825854Z"},"content_sha256":"f5915bc297e97a8a0d557269f125bcde6f7665be8e7ed83735a51d2d27fafcb6","schema_version":"1.0","event_id":"sha256:f5915bc297e97a8a0d557269f125bcde6f7665be8e7ed83735a51d2d27fafcb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:QOZVIRA7KTGWAIM3ZSSEJMJZQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite sets, mappings, cardinals, and arithmetic in intuitionistic New Foundations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Michael Beeson","submitted_at":"2021-03-31T16:55:17Z","abstract_excerpt":"NF set theory using intuitionistic logic is called iNF. We develop the theories of finite sets and their power sets and mappings, finite cardinals and their ordering, cardinal exponentiation, addition, and multiplication. We follow Rosser and Specker with appropriate constructive modifications, especially replacing ``arbitrary subset'' by ``separable subset'' in the definitions of exponentiation and order. It is not known whether iNF proves that the set of finite cardinals is infinite, so the whole development must allow for the possibility that there is a maximum integer; arithmetical computa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00506","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.00506/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-08T01:03:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDVQBEALKpMiHuanCjk6vNEoFpJeE9VTg5d6r76w0ppw2WQ4t8Hu97sKXU/C+LExr3Dus9l1icBfHtkkRLkBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:42:56.826248Z"},"content_sha256":"2c446809f12a3c19057177af435d55638758dc99f277f20bc64cc9c23b931320","schema_version":"1.0","event_id":"sha256:2c446809f12a3c19057177af435d55638758dc99f277f20bc64cc9c23b931320"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP/bundle.json","state_url":"https://pith.science/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP/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":"2026-06-26T11:42:56Z","links":{"resolver":"https://pith.science/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP","bundle":"https://pith.science/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP/bundle.json","state":"https://pith.science/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOZVIRA7KTGWAIM3ZSSEJMJZQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:QOZVIRA7KTGWAIM3ZSSEJMJZQP","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":"132558628b4769b4f21da9deae4fafc21e5365ec7a68d7c00f9041f0da046d62","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-03-31T16:55:17Z","title_canon_sha256":"ae325a4f158846039c2e3293c001e7f794d0688847435b91579b489edaec83e8"},"schema_version":"1.0","source":{"id":"2104.00506","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.00506","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"2104.00506v7","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.00506","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"QOZVIRA7KTGW","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOZVIRA7KTGWAIM3","created_at":"2026-06-08T01:03:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOZVIRA7","created_at":"2026-06-08T01:03:39Z"}],"graph_snapshots":[{"event_id":"sha256:2c446809f12a3c19057177af435d55638758dc99f277f20bc64cc9c23b931320","target":"graph","created_at":"2026-06-08T01:03:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.00506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"NF set theory using intuitionistic logic is called iNF. We develop the theories of finite sets and their power sets and mappings, finite cardinals and their ordering, cardinal exponentiation, addition, and multiplication. We follow Rosser and Specker with appropriate constructive modifications, especially replacing ``arbitrary subset'' by ``separable subset'' in the definitions of exponentiation and order. It is not known whether iNF proves that the set of finite cardinals is infinite, so the whole development must allow for the possibility that there is a maximum integer; arithmetical computa","authors_text":"Michael Beeson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-03-31T16:55:17Z","title":"Finite sets, mappings, cardinals, and arithmetic in intuitionistic New Foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00506","kind":"arxiv","version":7},"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:f5915bc297e97a8a0d557269f125bcde6f7665be8e7ed83735a51d2d27fafcb6","target":"record","created_at":"2026-06-08T01:03:39Z","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":"132558628b4769b4f21da9deae4fafc21e5365ec7a68d7c00f9041f0da046d62","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-03-31T16:55:17Z","title_canon_sha256":"ae325a4f158846039c2e3293c001e7f794d0688847435b91579b489edaec83e8"},"schema_version":"1.0","source":{"id":"2104.00506","kind":"arxiv","version":7}},"canonical_sha256":"83b354441f54cd60219bcca444b13983e7292ebb5331c0298e2a30c9457c5b88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83b354441f54cd60219bcca444b13983e7292ebb5331c0298e2a30c9457c5b88","first_computed_at":"2026-06-08T01:03:39.503920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:03:39.503920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hMSLvRuSgOlmQOZNbw9vol8P2wRl/WNbIvZLovo44qmEqCK7I+hqdhu0fIAyeVWY5elvGlWUD0KbP/znxyydCg==","signature_status":"signed_v1","signed_at":"2026-06-08T01:03:39.505030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.00506","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5915bc297e97a8a0d557269f125bcde6f7665be8e7ed83735a51d2d27fafcb6","sha256:2c446809f12a3c19057177af435d55638758dc99f277f20bc64cc9c23b931320"],"state_sha256":"e7c602030de0b9e167097979dd9771bdbd9fb48d4dcca4fdf4a205fc60abd7cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLrYDpaSU/ytRiDqeBd/UPXNQryk7pgDEcSock5WWXOpeYOr2P4rIr0JvLihH40bBYbiupOKjYjGRGEpTLELBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:42:56.828293Z","bundle_sha256":"40d48b2ed5bb8d2dfc0361a380f003136f252596942660686f8c096e80d48ab9"}}