{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Z7V2VCETBYR4RB5FGYJW6ZWFFO","short_pith_number":"pith:Z7V2VCET","canonical_record":{"source":{"id":"1811.10568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-26T18:17:57Z","cross_cats_sorted":[],"title_canon_sha256":"c0fb420228956eebd062739c2016b360dfb4c41ad458483ae2ea4d650020dd73","abstract_canon_sha256":"73cb0f95b7748d3e9b99ed6d0ec657315db5fa059d2a4d03f270985c33fdf388"},"schema_version":"1.0"},"canonical_sha256":"cfebaa88930e23c887a536136f66c52b97be7043ddf48a60e86c399e118641f3","source":{"kind":"arxiv","id":"1811.10568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10568","created_at":"2026-05-17T23:59:54Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10568v1","created_at":"2026-05-17T23:59:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10568","created_at":"2026-05-17T23:59:54Z"},{"alias_kind":"pith_short_12","alias_value":"Z7V2VCETBYR4","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z7V2VCETBYR4RB5F","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z7V2VCET","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Z7V2VCETBYR4RB5FGYJW6ZWFFO","target":"record","payload":{"canonical_record":{"source":{"id":"1811.10568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-26T18:17:57Z","cross_cats_sorted":[],"title_canon_sha256":"c0fb420228956eebd062739c2016b360dfb4c41ad458483ae2ea4d650020dd73","abstract_canon_sha256":"73cb0f95b7748d3e9b99ed6d0ec657315db5fa059d2a4d03f270985c33fdf388"},"schema_version":"1.0"},"canonical_sha256":"cfebaa88930e23c887a536136f66c52b97be7043ddf48a60e86c399e118641f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:54.315011Z","signature_b64":"mgQLUwKvaYvEjdG2iBYaWC849Gq7GyfGAjHYGp2j9OQBanORsy7H5BaDpLn3lVMSSuuGRsw8al8hoVYIsg/0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfebaa88930e23c887a536136f66c52b97be7043ddf48a60e86c399e118641f3","last_reissued_at":"2026-05-17T23:59:54.314467Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:54.314467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.10568","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":"2026-05-17T23:59:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etrSz+QJWhzAOhm02YtQ4MnbakHEBv/NGFKVJ5XciXNRCcjuHY644UqRR52BvoYTpqp/K9EX8svwIGwJq0OvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T21:59:12.188059Z"},"content_sha256":"0657bc580ef439f47ca7784842bb04393e86c7699afebed57c78b59ade06a79c","schema_version":"1.0","event_id":"sha256:0657bc580ef439f47ca7784842bb04393e86c7699afebed57c78b59ade06a79c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Z7V2VCETBYR4RB5FGYJW6ZWFFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On intermediate extensions of generic extensions by a random real","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vassily Lyubetsky, Vladimir Kanovei","submitted_at":"2018-11-26T18:17:57Z","abstract_excerpt":"The paper is the second of our series of notes aimed to bring back in circulation some bright ideas of early modern set theory, mainly due to Harrington and Sami, which have never been adequately presented in set theoretic publications. We prove that if a real $a$ is random over a model $M$ and $x\\in M[a]$ is another real then either (1) $x\\in M$, or (2) $M[x]=M[a]$, or (3) $M[x]$ is a random extension of $M$ and $M[a]$ is a random extension of $M[x]$. This is a less-known result of old set theoretic folklore, and, as far as we know, has never been published. As a corollary, we prove that $\\Si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10568","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":"2026-05-17T23:59:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dURFNZffOFJDTu3pxR2AK84rm62HjqvFcMJuYnD2/7hWnOCDcVSQZ1AvIZdK/mT5uYvs0LWJZjgULgg+400zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T21:59:12.188430Z"},"content_sha256":"b579a6b357b7c93f8951199516264a8991396777204bc273bc8b5d975dc8e2f4","schema_version":"1.0","event_id":"sha256:b579a6b357b7c93f8951199516264a8991396777204bc273bc8b5d975dc8e2f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO/bundle.json","state_url":"https://pith.science/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO/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":"2026-05-19T21:59:12Z","links":{"resolver":"https://pith.science/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO","bundle":"https://pith.science/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO/bundle.json","state":"https://pith.science/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7V2VCETBYR4RB5FGYJW6ZWFFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z7V2VCETBYR4RB5FGYJW6ZWFFO","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":"73cb0f95b7748d3e9b99ed6d0ec657315db5fa059d2a4d03f270985c33fdf388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-26T18:17:57Z","title_canon_sha256":"c0fb420228956eebd062739c2016b360dfb4c41ad458483ae2ea4d650020dd73"},"schema_version":"1.0","source":{"id":"1811.10568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10568","created_at":"2026-05-17T23:59:54Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10568v1","created_at":"2026-05-17T23:59:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10568","created_at":"2026-05-17T23:59:54Z"},{"alias_kind":"pith_short_12","alias_value":"Z7V2VCETBYR4","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z7V2VCETBYR4RB5F","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z7V2VCET","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:b579a6b357b7c93f8951199516264a8991396777204bc273bc8b5d975dc8e2f4","target":"graph","created_at":"2026-05-17T23:59:54Z","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":"The paper is the second of our series of notes aimed to bring back in circulation some bright ideas of early modern set theory, mainly due to Harrington and Sami, which have never been adequately presented in set theoretic publications. We prove that if a real $a$ is random over a model $M$ and $x\\in M[a]$ is another real then either (1) $x\\in M$, or (2) $M[x]=M[a]$, or (3) $M[x]$ is a random extension of $M$ and $M[a]$ is a random extension of $M[x]$. This is a less-known result of old set theoretic folklore, and, as far as we know, has never been published. As a corollary, we prove that $\\Si","authors_text":"Vassily Lyubetsky, Vladimir Kanovei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-26T18:17:57Z","title":"On intermediate extensions of generic extensions by a random real"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10568","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":"sha256:0657bc580ef439f47ca7784842bb04393e86c7699afebed57c78b59ade06a79c","target":"record","created_at":"2026-05-17T23:59:54Z","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":"73cb0f95b7748d3e9b99ed6d0ec657315db5fa059d2a4d03f270985c33fdf388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-26T18:17:57Z","title_canon_sha256":"c0fb420228956eebd062739c2016b360dfb4c41ad458483ae2ea4d650020dd73"},"schema_version":"1.0","source":{"id":"1811.10568","kind":"arxiv","version":1}},"canonical_sha256":"cfebaa88930e23c887a536136f66c52b97be7043ddf48a60e86c399e118641f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfebaa88930e23c887a536136f66c52b97be7043ddf48a60e86c399e118641f3","first_computed_at":"2026-05-17T23:59:54.314467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:54.314467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mgQLUwKvaYvEjdG2iBYaWC849Gq7GyfGAjHYGp2j9OQBanORsy7H5BaDpLn3lVMSSuuGRsw8al8hoVYIsg/0BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:54.315011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0657bc580ef439f47ca7784842bb04393e86c7699afebed57c78b59ade06a79c","sha256:b579a6b357b7c93f8951199516264a8991396777204bc273bc8b5d975dc8e2f4"],"state_sha256":"9ceff64f616ef2cd2a4cacdd1fd094fb121b842796636f06e674a3938ebb70ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6LiMTA+k7bEoavasRB1B+KGYz5YQaJCU0/ywzIkUSlE+g/e5TJjXeETPyTVkH2noVIx81UbuvaiGzYrdBrmBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T21:59:12.190369Z","bundle_sha256":"fc0ac4355c386ad16c00c7a4ad7b9e1455af1b0abe507a66421c2296560bdef2"}}