{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DQZTYDYESQWMHHKULLC7TCVV5X","short_pith_number":"pith:DQZTYDYE","canonical_record":{"source":{"id":"1704.00511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-03T10:16:18Z","cross_cats_sorted":[],"title_canon_sha256":"8518a77d34a02d2e2351a5e4bb2989b268bd2fd74b98ad8c03e2ee1f20239cca","abstract_canon_sha256":"5099e8c7eac98397e28caa2899102f72b6078c488e7ef51c412342b5c822c449"},"schema_version":"1.0"},"canonical_sha256":"1c333c0f04942cc39d545ac5f98ab5edf2b0ded4f9435afd3e3833c6719d6305","source":{"kind":"arxiv","id":"1704.00511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00511","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00511v1","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00511","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"DQZTYDYESQWM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQZTYDYESQWMHHKU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQZTYDYE","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DQZTYDYESQWMHHKULLC7TCVV5X","target":"record","payload":{"canonical_record":{"source":{"id":"1704.00511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-03T10:16:18Z","cross_cats_sorted":[],"title_canon_sha256":"8518a77d34a02d2e2351a5e4bb2989b268bd2fd74b98ad8c03e2ee1f20239cca","abstract_canon_sha256":"5099e8c7eac98397e28caa2899102f72b6078c488e7ef51c412342b5c822c449"},"schema_version":"1.0"},"canonical_sha256":"1c333c0f04942cc39d545ac5f98ab5edf2b0ded4f9435afd3e3833c6719d6305","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:22.138056Z","signature_b64":"i5jZzvpwmx00/bEe4P/b0QFZGsDhlxx1+4aG4F9Yq1Zpr/nXrAs2B75KRLUzEEeE41yE349C1KuvWCo1xB1dBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c333c0f04942cc39d545ac5f98ab5edf2b0ded4f9435afd3e3833c6719d6305","last_reissued_at":"2026-05-18T00:47:22.137472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:22.137472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.00511","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":"2026-05-18T00:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mnhQAnqAKhXj/15eYD6OVXM6NCzzP37MEerDmXrRPTAqfhUqb1YcEdID1TBqbFmrr0ZEVw84QgA+08Ron2jMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:20:31.378262Z"},"content_sha256":"cd502823c4f2165b6b37f525e9cc037738e817c752ae9802a2b236acd7867e37","schema_version":"1.0","event_id":"sha256:cd502823c4f2165b6b37f525e9cc037738e817c752ae9802a2b236acd7867e37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DQZTYDYESQWMHHKULLC7TCVV5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measurable cardinals and good $\\Sigma_1(\\kappa)$-wellorderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Philipp L\\\"ucke, Philipp Schlicht","submitted_at":"2017-04-03T10:16:18Z","abstract_excerpt":"We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals $\\kappa$ with the property that the collection of all initial segments of the wellordering is definable by a $\\Sigma_1$-formula with parameter $\\kappa$. A short argument shows that the existence of a measurable cardinal $\\delta$ implies that such wellorderings do not exist at $\\delta$-inaccessible cardinals of cofinality not equal to $\\delta$ and their successors. In contrast, our main result shows that these wellorderings exist at all other uncountable cardinals in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00511","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":"2026-05-18T00:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xMAtuXVlEpukCtYxbSiyf3E662w5HuwLtGebzhQOjdlw9m6qUl3GGiS4I4QxxWDbn4S/cZCBieZv6AoH4OxzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:20:31.378946Z"},"content_sha256":"ab35a850a039401148a7c98dc32a13d5f161894df648b5e270fc46f3833f4b43","schema_version":"1.0","event_id":"sha256:ab35a850a039401148a7c98dc32a13d5f161894df648b5e270fc46f3833f4b43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQZTYDYESQWMHHKULLC7TCVV5X/bundle.json","state_url":"https://pith.science/pith/DQZTYDYESQWMHHKULLC7TCVV5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQZTYDYESQWMHHKULLC7TCVV5X/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":"2026-06-06T16:20:31Z","links":{"resolver":"https://pith.science/pith/DQZTYDYESQWMHHKULLC7TCVV5X","bundle":"https://pith.science/pith/DQZTYDYESQWMHHKULLC7TCVV5X/bundle.json","state":"https://pith.science/pith/DQZTYDYESQWMHHKULLC7TCVV5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQZTYDYESQWMHHKULLC7TCVV5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DQZTYDYESQWMHHKULLC7TCVV5X","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":"5099e8c7eac98397e28caa2899102f72b6078c488e7ef51c412342b5c822c449","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-03T10:16:18Z","title_canon_sha256":"8518a77d34a02d2e2351a5e4bb2989b268bd2fd74b98ad8c03e2ee1f20239cca"},"schema_version":"1.0","source":{"id":"1704.00511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00511","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00511v1","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00511","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"DQZTYDYESQWM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQZTYDYESQWMHHKU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQZTYDYE","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:ab35a850a039401148a7c98dc32a13d5f161894df648b5e270fc46f3833f4b43","target":"graph","created_at":"2026-05-18T00:47:22Z","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 study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals $\\kappa$ with the property that the collection of all initial segments of the wellordering is definable by a $\\Sigma_1$-formula with parameter $\\kappa$. A short argument shows that the existence of a measurable cardinal $\\delta$ implies that such wellorderings do not exist at $\\delta$-inaccessible cardinals of cofinality not equal to $\\delta$ and their successors. In contrast, our main result shows that these wellorderings exist at all other uncountable cardinals in ","authors_text":"Philipp L\\\"ucke, Philipp Schlicht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-03T10:16:18Z","title":"Measurable cardinals and good $\\Sigma_1(\\kappa)$-wellorderings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00511","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:cd502823c4f2165b6b37f525e9cc037738e817c752ae9802a2b236acd7867e37","target":"record","created_at":"2026-05-18T00:47:22Z","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":"5099e8c7eac98397e28caa2899102f72b6078c488e7ef51c412342b5c822c449","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-03T10:16:18Z","title_canon_sha256":"8518a77d34a02d2e2351a5e4bb2989b268bd2fd74b98ad8c03e2ee1f20239cca"},"schema_version":"1.0","source":{"id":"1704.00511","kind":"arxiv","version":1}},"canonical_sha256":"1c333c0f04942cc39d545ac5f98ab5edf2b0ded4f9435afd3e3833c6719d6305","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c333c0f04942cc39d545ac5f98ab5edf2b0ded4f9435afd3e3833c6719d6305","first_computed_at":"2026-05-18T00:47:22.137472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:22.137472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i5jZzvpwmx00/bEe4P/b0QFZGsDhlxx1+4aG4F9Yq1Zpr/nXrAs2B75KRLUzEEeE41yE349C1KuvWCo1xB1dBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:22.138056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd502823c4f2165b6b37f525e9cc037738e817c752ae9802a2b236acd7867e37","sha256:ab35a850a039401148a7c98dc32a13d5f161894df648b5e270fc46f3833f4b43"],"state_sha256":"6f4ac35cdd45726a481004cd16fc9f84d5cfb9642b8f2612d474da5f695939fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qToJQBkVU5MA6JeZ10oc3pxxhyk0lrHA3OyHWotaloBkmRM0aksfXFdRpBhmo626t4bJMWJsztHNKd1zd4RODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:20:31.382975Z","bundle_sha256":"1695b97240d398f929bada6cb722e889cad8566990580db455ebbfe96bc266f7"}}