{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QPCWQ4Y7LNUTA76UEA3OQ7JGA6","short_pith_number":"pith:QPCWQ4Y7","canonical_record":{"source":{"id":"1308.5575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-26T13:15:52Z","cross_cats_sorted":[],"title_canon_sha256":"516081a45cf3acc530c5da11e18ee4f2fb27a282a0b9a30997daaf16963a7348","abstract_canon_sha256":"9a18a8546fb7163e46d859c10f4b507ba71aebca1c8049e09c61a217fdb850aa"},"schema_version":"1.0"},"canonical_sha256":"83c568731f5b69307fd42036e87d2607b29dfdf7b2a2396aad552857bb194f61","source":{"kind":"arxiv","id":"1308.5575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5575","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5575v2","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5575","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"QPCWQ4Y7LNUT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QPCWQ4Y7LNUTA76U","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QPCWQ4Y7","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QPCWQ4Y7LNUTA76UEA3OQ7JGA6","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-26T13:15:52Z","cross_cats_sorted":[],"title_canon_sha256":"516081a45cf3acc530c5da11e18ee4f2fb27a282a0b9a30997daaf16963a7348","abstract_canon_sha256":"9a18a8546fb7163e46d859c10f4b507ba71aebca1c8049e09c61a217fdb850aa"},"schema_version":"1.0"},"canonical_sha256":"83c568731f5b69307fd42036e87d2607b29dfdf7b2a2396aad552857bb194f61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:48.441700Z","signature_b64":"GyYzS3TpO2lnfY5mXTWT3ok/Dc3pOO8pOYp5Wdzyd23pFEdTw6eS5FOiZ0JHzsFw4s+QOWMNuDxiyqn9XjKMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83c568731f5b69307fd42036e87d2607b29dfdf7b2a2396aad552857bb194f61","last_reissued_at":"2026-05-18T01:36:48.441100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:48.441100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"padeygEyxeUvWRG0IZWHVSv22roxKGkjsZAaJngOSnjNr+dxyqpHsH1lQMvtcfy49DS69w8yrQkvN6xv3aYDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:51:06.157780Z"},"content_sha256":"8b4ca90ead0c420f36bba95482076e1db4bdaa27dde96814580774ee26c88b34","schema_version":"1.0","event_id":"sha256:8b4ca90ead0c420f36bba95482076e1db4bdaa27dde96814580774ee26c88b34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QPCWQ4Y7LNUTA76UEA3OQ7JGA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wider Thin-Very Tall Superatomic Boolean Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carmi Merimovich","submitted_at":"2013-08-26T13:15:52Z","abstract_excerpt":"For each regular cardinal k > w we show the consistent existence of a thin very tall superatomic Boolean algebra of width k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5575","kind":"arxiv","version":2},"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":"2026-05-18T01:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jl3umXu2uO4r6KY6P1rWrNevvHaOMgBpL90QcqZ1BcyfRNP0gPwUmheWRnIb53e4Zp2xhtbVGPBJ7ukaPiyKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:51:06.158243Z"},"content_sha256":"359f226cb8656531dea2f721df457a690e80bf7e7c36ed4b148b5b4f9c490f7b","schema_version":"1.0","event_id":"sha256:359f226cb8656531dea2f721df457a690e80bf7e7c36ed4b148b5b4f9c490f7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6/bundle.json","state_url":"https://pith.science/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6/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":"2026-06-24T19:51:06Z","links":{"resolver":"https://pith.science/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6","bundle":"https://pith.science/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6/bundle.json","state":"https://pith.science/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPCWQ4Y7LNUTA76UEA3OQ7JGA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QPCWQ4Y7LNUTA76UEA3OQ7JGA6","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":"9a18a8546fb7163e46d859c10f4b507ba71aebca1c8049e09c61a217fdb850aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-26T13:15:52Z","title_canon_sha256":"516081a45cf3acc530c5da11e18ee4f2fb27a282a0b9a30997daaf16963a7348"},"schema_version":"1.0","source":{"id":"1308.5575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5575","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5575v2","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5575","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"QPCWQ4Y7LNUT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QPCWQ4Y7LNUTA76U","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QPCWQ4Y7","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:359f226cb8656531dea2f721df457a690e80bf7e7c36ed4b148b5b4f9c490f7b","target":"graph","created_at":"2026-05-18T01:36:48Z","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":"For each regular cardinal k > w we show the consistent existence of a thin very tall superatomic Boolean algebra of width k.","authors_text":"Carmi Merimovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-26T13:15:52Z","title":"Wider Thin-Very Tall Superatomic Boolean Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5575","kind":"arxiv","version":2},"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":"sha256:8b4ca90ead0c420f36bba95482076e1db4bdaa27dde96814580774ee26c88b34","target":"record","created_at":"2026-05-18T01:36:48Z","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":"9a18a8546fb7163e46d859c10f4b507ba71aebca1c8049e09c61a217fdb850aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-26T13:15:52Z","title_canon_sha256":"516081a45cf3acc530c5da11e18ee4f2fb27a282a0b9a30997daaf16963a7348"},"schema_version":"1.0","source":{"id":"1308.5575","kind":"arxiv","version":2}},"canonical_sha256":"83c568731f5b69307fd42036e87d2607b29dfdf7b2a2396aad552857bb194f61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83c568731f5b69307fd42036e87d2607b29dfdf7b2a2396aad552857bb194f61","first_computed_at":"2026-05-18T01:36:48.441100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:48.441100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GyYzS3TpO2lnfY5mXTWT3ok/Dc3pOO8pOYp5Wdzyd23pFEdTw6eS5FOiZ0JHzsFw4s+QOWMNuDxiyqn9XjKMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:48.441700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b4ca90ead0c420f36bba95482076e1db4bdaa27dde96814580774ee26c88b34","sha256:359f226cb8656531dea2f721df457a690e80bf7e7c36ed4b148b5b4f9c490f7b"],"state_sha256":"d5895f586dd35b084aa1df9cf4923b79a8487877fffdc4e7000904289b61f1af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bSRb7dGR048vMcr2PKFNH6HZqDg7LGKcSJ+q82zN8TGPIIpfreMNeqyBEiOq85CdJWMSNXCywdKAWrVPhfCeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:51:06.160993Z","bundle_sha256":"0f5f93072fc973991d52fe47e5ee68d92b671d83817e5c5fa6974360b15ee892"}}