{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AWDYUMBFVDWNRTE5KSE7SZ33QI","short_pith_number":"pith:AWDYUMBF","canonical_record":{"source":{"id":"1906.09538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-23T02:34:30Z","cross_cats_sorted":[],"title_canon_sha256":"5fdae9361d47a8f5d30c78f4d5aac4bb27f981cbb748dc31da81164367f9fe11","abstract_canon_sha256":"db9d566d26ee2f5a5581b7fd7255ad2d0e64a145ad85977a2340e006a85817cb"},"schema_version":"1.0"},"canonical_sha256":"05878a3025a8ecd8cc9d5489f9677b823df1af4fb308b8279553bfffd0d6ffa1","source":{"kind":"arxiv","id":"1906.09538","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09538","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09538v1","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09538","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"AWDYUMBFVDWN","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AWDYUMBFVDWNRTE5","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AWDYUMBF","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AWDYUMBFVDWNRTE5KSE7SZ33QI","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-23T02:34:30Z","cross_cats_sorted":[],"title_canon_sha256":"5fdae9361d47a8f5d30c78f4d5aac4bb27f981cbb748dc31da81164367f9fe11","abstract_canon_sha256":"db9d566d26ee2f5a5581b7fd7255ad2d0e64a145ad85977a2340e006a85817cb"},"schema_version":"1.0"},"canonical_sha256":"05878a3025a8ecd8cc9d5489f9677b823df1af4fb308b8279553bfffd0d6ffa1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:37.660120Z","signature_b64":"usTUa2S5YshMcvTKbqb3C46i4rJZPc2/lvHEbXyW7mV4UPEGO2e+mFEywrnKpTetVGObOT+CiNDrgji8uDFUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05878a3025a8ecd8cc9d5489f9677b823df1af4fb308b8279553bfffd0d6ffa1","last_reissued_at":"2026-05-17T23:42:37.659233Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:37.659233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09538","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":"2026-05-17T23:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EO8TLz3AIg1/MnPm2Nzw/4rl6zv+KSdMHx0WJpqL+mA+CtZpRN8PJg6bdtq346/T0nzGARDt3VjM49B+rNbjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:55:30.361581Z"},"content_sha256":"dbdd01d665607c96430af61027aef76dfdceac47f7c213baa09f9fda12aa759b","schema_version":"1.0","event_id":"sha256:dbdd01d665607c96430af61027aef76dfdceac47f7c213baa09f9fda12aa759b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AWDYUMBFVDWNRTE5KSE7SZ33QI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the non-existence of $\\kappa$-mad families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Haim Horowitz, Saharon Shelah","submitted_at":"2019-06-23T02:34:30Z","abstract_excerpt":"Starting from a model with a Laver-indestructible supercompact cardinal $\\kappa$, we construct a model of $ZF+DC_{\\kappa}$ where there are no $\\kappa$-mad families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09538","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":"2026-05-17T23:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCpsHdnDKAglrAMSy8LjyEM47/dDQ1yqkpc+5pfI9PgW6gBzc7P8ZvlBACkgraXSJZ3yrLj1TXlMgSEQwfIWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:55:30.361964Z"},"content_sha256":"bfbad11fe86a7b5181295831e2691908da9610c9bef81c1ad4a906c6de482454","schema_version":"1.0","event_id":"sha256:bfbad11fe86a7b5181295831e2691908da9610c9bef81c1ad4a906c6de482454"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI/bundle.json","state_url":"https://pith.science/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI/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":"2026-06-12T06:55:30Z","links":{"resolver":"https://pith.science/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI","bundle":"https://pith.science/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI/bundle.json","state":"https://pith.science/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWDYUMBFVDWNRTE5KSE7SZ33QI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AWDYUMBFVDWNRTE5KSE7SZ33QI","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":"db9d566d26ee2f5a5581b7fd7255ad2d0e64a145ad85977a2340e006a85817cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-23T02:34:30Z","title_canon_sha256":"5fdae9361d47a8f5d30c78f4d5aac4bb27f981cbb748dc31da81164367f9fe11"},"schema_version":"1.0","source":{"id":"1906.09538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09538","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09538v1","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09538","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"AWDYUMBFVDWN","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AWDYUMBFVDWNRTE5","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AWDYUMBF","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:bfbad11fe86a7b5181295831e2691908da9610c9bef81c1ad4a906c6de482454","target":"graph","created_at":"2026-05-17T23:42:37Z","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":"Starting from a model with a Laver-indestructible supercompact cardinal $\\kappa$, we construct a model of $ZF+DC_{\\kappa}$ where there are no $\\kappa$-mad families.","authors_text":"Haim Horowitz, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-23T02:34:30Z","title":"On the non-existence of $\\kappa$-mad families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09538","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:dbdd01d665607c96430af61027aef76dfdceac47f7c213baa09f9fda12aa759b","target":"record","created_at":"2026-05-17T23:42:37Z","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":"db9d566d26ee2f5a5581b7fd7255ad2d0e64a145ad85977a2340e006a85817cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-23T02:34:30Z","title_canon_sha256":"5fdae9361d47a8f5d30c78f4d5aac4bb27f981cbb748dc31da81164367f9fe11"},"schema_version":"1.0","source":{"id":"1906.09538","kind":"arxiv","version":1}},"canonical_sha256":"05878a3025a8ecd8cc9d5489f9677b823df1af4fb308b8279553bfffd0d6ffa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05878a3025a8ecd8cc9d5489f9677b823df1af4fb308b8279553bfffd0d6ffa1","first_computed_at":"2026-05-17T23:42:37.659233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:37.659233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"usTUa2S5YshMcvTKbqb3C46i4rJZPc2/lvHEbXyW7mV4UPEGO2e+mFEywrnKpTetVGObOT+CiNDrgji8uDFUAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:37.660120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbdd01d665607c96430af61027aef76dfdceac47f7c213baa09f9fda12aa759b","sha256:bfbad11fe86a7b5181295831e2691908da9610c9bef81c1ad4a906c6de482454"],"state_sha256":"ab11ec0fbd1e6df959a2b5906620212436a296e6c468196f62c6d3f7f54b8f8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/b6mTsJo/J2Pdw9Xa/yD58ogoxZYN3T4eazaxn2oKEN2cJdlMYPGuzBvZAw+drPVIqw8IzZGGjp0/UPpsCtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:55:30.364633Z","bundle_sha256":"49d0b8150a3409248edbfe031883500ec4cf06da19b87ed02a35ef646735895c"}}