{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:OWXMBZW3JRSR7SNADBETBVPWO7","short_pith_number":"pith:OWXMBZW3","canonical_record":{"source":{"id":"math/0407487","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2004-07-28T14:23:21Z","cross_cats_sorted":["math.CO","math.GN"],"title_canon_sha256":"c0d123c6d686ad7fb4f38470d0afb8b2e1bc0f2164c66e976f23b1ae916984b9","abstract_canon_sha256":"7b575723d052ca765d675e367f6d31976786b24223744b42c77c8b8a1acca9f2"},"schema_version":"1.0"},"canonical_sha256":"75aec0e6db4c651fc9a0184930d5f677dba99fade8d8608607f81e48d1fb0b80","source":{"kind":"arxiv","id":"math/0407487","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407487","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407487v4","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407487","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"OWXMBZW3JRSR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OWXMBZW3JRSR7SNA","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OWXMBZW3","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:OWXMBZW3JRSR7SNADBETBVPWO7","target":"record","payload":{"canonical_record":{"source":{"id":"math/0407487","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2004-07-28T14:23:21Z","cross_cats_sorted":["math.CO","math.GN"],"title_canon_sha256":"c0d123c6d686ad7fb4f38470d0afb8b2e1bc0f2164c66e976f23b1ae916984b9","abstract_canon_sha256":"7b575723d052ca765d675e367f6d31976786b24223744b42c77c8b8a1acca9f2"},"schema_version":"1.0"},"canonical_sha256":"75aec0e6db4c651fc9a0184930d5f677dba99fade8d8608607f81e48d1fb0b80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:23.171387Z","signature_b64":"L5GYPEOIPjgYh4cRjM36fLfElrScfo6t7bm+uTlPkwa/qH3X6gAnAq9liMdWCSsgJjmZZjw6fDsKUAKC1Z5tBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75aec0e6db4c651fc9a0184930d5f677dba99fade8d8608607f81e48d1fb0b80","last_reissued_at":"2026-05-18T04:37:23.170978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:23.170978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0407487","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:37:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06119PAEvRRbCKPCVFDrOyLPsflRk5eFFX3ZtnbYi6x8OPEMAP7CIsb1AwLomvbICezHctrYyLvykhR3I61qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:28:38.777712Z"},"content_sha256":"b5b846e21fda69abddff0a094a83025ff774cb789a85c633e7c56cab37836252","schema_version":"1.0","event_id":"sha256:b5b846e21fda69abddff0a094a83025ff774cb789a85c633e7c56cab37836252"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:OWXMBZW3JRSR7SNADBETBVPWO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covering the Baire space by families which are not finitely dominating","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GN"],"primary_cat":"math.LO","authors_text":"Boaz Tsaban, Heike Mildenberger, Saharon Shelah","submitted_at":"2004-07-28T14:23:21Z","abstract_excerpt":"It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower w^w/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407487","kind":"arxiv","version":4},"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":"2026-05-18T04:37:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81hlwp9EpVwSePcDzSD80acfFvyYwO1Va182z7CaegGdO6LoZmuSAHlWi0BOxfUvO7SJQVngVcKBi6Dk3LJ6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:28:38.778069Z"},"content_sha256":"d3861c51b7cb256877c6eb65315de925e31bfa230882a20ad00b0f0a4de7aaf7","schema_version":"1.0","event_id":"sha256:d3861c51b7cb256877c6eb65315de925e31bfa230882a20ad00b0f0a4de7aaf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWXMBZW3JRSR7SNADBETBVPWO7/bundle.json","state_url":"https://pith.science/pith/OWXMBZW3JRSR7SNADBETBVPWO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWXMBZW3JRSR7SNADBETBVPWO7/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":"2026-06-02T08:28:38Z","links":{"resolver":"https://pith.science/pith/OWXMBZW3JRSR7SNADBETBVPWO7","bundle":"https://pith.science/pith/OWXMBZW3JRSR7SNADBETBVPWO7/bundle.json","state":"https://pith.science/pith/OWXMBZW3JRSR7SNADBETBVPWO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWXMBZW3JRSR7SNADBETBVPWO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:OWXMBZW3JRSR7SNADBETBVPWO7","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":"7b575723d052ca765d675e367f6d31976786b24223744b42c77c8b8a1acca9f2","cross_cats_sorted":["math.CO","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2004-07-28T14:23:21Z","title_canon_sha256":"c0d123c6d686ad7fb4f38470d0afb8b2e1bc0f2164c66e976f23b1ae916984b9"},"schema_version":"1.0","source":{"id":"math/0407487","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407487","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407487v4","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407487","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"OWXMBZW3JRSR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OWXMBZW3JRSR7SNA","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OWXMBZW3","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d3861c51b7cb256877c6eb65315de925e31bfa230882a20ad00b0f0a4de7aaf7","target":"graph","created_at":"2026-05-18T04:37:23Z","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":"It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower w^w/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.","authors_text":"Boaz Tsaban, Heike Mildenberger, Saharon Shelah","cross_cats":["math.CO","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2004-07-28T14:23:21Z","title":"Covering the Baire space by families which are not finitely dominating"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407487","kind":"arxiv","version":4},"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:b5b846e21fda69abddff0a094a83025ff774cb789a85c633e7c56cab37836252","target":"record","created_at":"2026-05-18T04:37:23Z","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":"7b575723d052ca765d675e367f6d31976786b24223744b42c77c8b8a1acca9f2","cross_cats_sorted":["math.CO","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2004-07-28T14:23:21Z","title_canon_sha256":"c0d123c6d686ad7fb4f38470d0afb8b2e1bc0f2164c66e976f23b1ae916984b9"},"schema_version":"1.0","source":{"id":"math/0407487","kind":"arxiv","version":4}},"canonical_sha256":"75aec0e6db4c651fc9a0184930d5f677dba99fade8d8608607f81e48d1fb0b80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75aec0e6db4c651fc9a0184930d5f677dba99fade8d8608607f81e48d1fb0b80","first_computed_at":"2026-05-18T04:37:23.170978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:23.170978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L5GYPEOIPjgYh4cRjM36fLfElrScfo6t7bm+uTlPkwa/qH3X6gAnAq9liMdWCSsgJjmZZjw6fDsKUAKC1Z5tBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:23.171387Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0407487","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b846e21fda69abddff0a094a83025ff774cb789a85c633e7c56cab37836252","sha256:d3861c51b7cb256877c6eb65315de925e31bfa230882a20ad00b0f0a4de7aaf7"],"state_sha256":"b74c1471a510df298bb248a56d3200f7db609c75b56e2c351201b7809b1f5fdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJPsN3D+yPXA2mmgXD2uYIl2OMFSNVfwjTqMMpd2ZhJ+2mjZiQ8vvvdq476sAstsLs2Rn0PuhuRlSM3wobKkBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:28:38.780104Z","bundle_sha256":"fb99888c44d1a3caf058551d0716924d7185e9b07808d4fb111251c3113a728f"}}