{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KXNFZDOPGA7VCXCDQF2TGEG66C","short_pith_number":"pith:KXNFZDOP","canonical_record":{"source":{"id":"1801.09369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-29T05:54:28Z","cross_cats_sorted":[],"title_canon_sha256":"da7165e1d5c5111c3a2763ff351caeef404b97141136eb7fe70e98b1eb5e9870","abstract_canon_sha256":"d8d05c676b59c4106598a16fe829031770d80821dc9f543d807793447ecc7dd5"},"schema_version":"1.0"},"canonical_sha256":"55da5c8dcf303f515c4381753310def099297548a3bf48750d72fc309339402a","source":{"kind":"arxiv","id":"1801.09369","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09369","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09369v1","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09369","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"KXNFZDOPGA7V","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KXNFZDOPGA7VCXCD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KXNFZDOP","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KXNFZDOPGA7VCXCDQF2TGEG66C","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-29T05:54:28Z","cross_cats_sorted":[],"title_canon_sha256":"da7165e1d5c5111c3a2763ff351caeef404b97141136eb7fe70e98b1eb5e9870","abstract_canon_sha256":"d8d05c676b59c4106598a16fe829031770d80821dc9f543d807793447ecc7dd5"},"schema_version":"1.0"},"canonical_sha256":"55da5c8dcf303f515c4381753310def099297548a3bf48750d72fc309339402a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:57.613155Z","signature_b64":"nmUboWwBev5GiHa/IpSCov21LW/Pns6raL0pSncwxVGsmJskNKCg3gL9/1mLkizfwTKyJf208EmyPPFU77JVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55da5c8dcf303f515c4381753310def099297548a3bf48750d72fc309339402a","last_reissued_at":"2026-05-18T00:24:57.612537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:57.612537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09369","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B1Uzh85fkcYGs9jqLy81qOPl6gG3aYU4H6b/cmZR5sT509yaWIFljrax5QokWkDvcQjoDbc1WZn9mq3vHDqhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:27:59.660906Z"},"content_sha256":"13438c5749ea06d55626a8e016b4eff1da8442f88b707476c6288e7d34c432c0","schema_version":"1.0","event_id":"sha256:13438c5749ea06d55626a8e016b4eff1da8442f88b707476c6288e7d34c432c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KXNFZDOPGA7VCXCDQF2TGEG66C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two results on cardinal invariants at uncountable cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dilip Raghavan, Saharon Shelah","submitted_at":"2018-01-29T05:54:28Z","abstract_excerpt":"We prove two ZFC theorems about cardinal invariants above the continuum which are in sharp contrast to well-known facts about these same invariants at the continuum. It is shown that for an uncountable regular cardinal $\\kappa$, $\\mathfrak{b}(\\kappa) = {\\kappa}^{+}$ implies $\\mathfrak{a}(\\kappa) = {\\kappa}^{+}$. This improves an earlier result of Blass, Hyttinen, and Zhang. It is also shown that if $\\kappa \\geq {\\beth}_{\\omega}$ is an uncountable regular cardinal, then $\\mathfrak{d}(\\kappa) \\leq \\mathfrak{r}(\\kappa)$. This result partially dualizes an earlier theorem of the authors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09369","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+QB2Rwqad+qmx6qfXXZz1tHGvJfetwKtA5Legj7LKooUKCh6IVEI3KQZliHJnqggwt4aoT6BDNyNrp/Ep88cCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:27:59.661247Z"},"content_sha256":"51e22eb81a1d8456dc3dce63ff08d9a2b72c820b7c81032201dd858b6f9bb1aa","schema_version":"1.0","event_id":"sha256:51e22eb81a1d8456dc3dce63ff08d9a2b72c820b7c81032201dd858b6f9bb1aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXNFZDOPGA7VCXCDQF2TGEG66C/bundle.json","state_url":"https://pith.science/pith/KXNFZDOPGA7VCXCDQF2TGEG66C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXNFZDOPGA7VCXCDQF2TGEG66C/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":"2026-06-21T20:27:59Z","links":{"resolver":"https://pith.science/pith/KXNFZDOPGA7VCXCDQF2TGEG66C","bundle":"https://pith.science/pith/KXNFZDOPGA7VCXCDQF2TGEG66C/bundle.json","state":"https://pith.science/pith/KXNFZDOPGA7VCXCDQF2TGEG66C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXNFZDOPGA7VCXCDQF2TGEG66C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KXNFZDOPGA7VCXCDQF2TGEG66C","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":"d8d05c676b59c4106598a16fe829031770d80821dc9f543d807793447ecc7dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-29T05:54:28Z","title_canon_sha256":"da7165e1d5c5111c3a2763ff351caeef404b97141136eb7fe70e98b1eb5e9870"},"schema_version":"1.0","source":{"id":"1801.09369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09369","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09369v1","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09369","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"KXNFZDOPGA7V","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KXNFZDOPGA7VCXCD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KXNFZDOP","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:51e22eb81a1d8456dc3dce63ff08d9a2b72c820b7c81032201dd858b6f9bb1aa","target":"graph","created_at":"2026-05-18T00:24:57Z","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":"We prove two ZFC theorems about cardinal invariants above the continuum which are in sharp contrast to well-known facts about these same invariants at the continuum. It is shown that for an uncountable regular cardinal $\\kappa$, $\\mathfrak{b}(\\kappa) = {\\kappa}^{+}$ implies $\\mathfrak{a}(\\kappa) = {\\kappa}^{+}$. This improves an earlier result of Blass, Hyttinen, and Zhang. It is also shown that if $\\kappa \\geq {\\beth}_{\\omega}$ is an uncountable regular cardinal, then $\\mathfrak{d}(\\kappa) \\leq \\mathfrak{r}(\\kappa)$. This result partially dualizes an earlier theorem of the authors.","authors_text":"Dilip Raghavan, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-29T05:54:28Z","title":"Two results on cardinal invariants at uncountable cardinals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09369","kind":"arxiv","version":1},"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":"sha256:13438c5749ea06d55626a8e016b4eff1da8442f88b707476c6288e7d34c432c0","target":"record","created_at":"2026-05-18T00:24:57Z","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":"d8d05c676b59c4106598a16fe829031770d80821dc9f543d807793447ecc7dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-29T05:54:28Z","title_canon_sha256":"da7165e1d5c5111c3a2763ff351caeef404b97141136eb7fe70e98b1eb5e9870"},"schema_version":"1.0","source":{"id":"1801.09369","kind":"arxiv","version":1}},"canonical_sha256":"55da5c8dcf303f515c4381753310def099297548a3bf48750d72fc309339402a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55da5c8dcf303f515c4381753310def099297548a3bf48750d72fc309339402a","first_computed_at":"2026-05-18T00:24:57.612537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:57.612537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nmUboWwBev5GiHa/IpSCov21LW/Pns6raL0pSncwxVGsmJskNKCg3gL9/1mLkizfwTKyJf208EmyPPFU77JVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:57.613155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13438c5749ea06d55626a8e016b4eff1da8442f88b707476c6288e7d34c432c0","sha256:51e22eb81a1d8456dc3dce63ff08d9a2b72c820b7c81032201dd858b6f9bb1aa"],"state_sha256":"ecf8fd6299898a03ae7cf46277d45b93d784b0dfccd543f20c95bfd92ee7abe1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ulAqCV1ln4noAYv7fLgqEFRy5MztqnlglEoTKMDwIQtjKYgUm7Q5GC5m4NdklPg1s/13Be+RCwUo+q3iWjl+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:27:59.663172Z","bundle_sha256":"c0c03d5bf21def79083aabdb742e3efc20186c15bafacd1b2d85db768a99189a"}}