{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:575QVOKU43RFTMB6X2KRETNWDC","short_pith_number":"pith:575QVOKU","canonical_record":{"source":{"id":"1110.6690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-31T04:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"a4533e18b8e4ff342a21de1b9f28c5c01fbfe1a3c4ecb6abdab96305e658c895","abstract_canon_sha256":"df9f04e69124bdd309f0a5d0b4028c67852673616ea7d3b1c1e4750dafdd09c2"},"schema_version":"1.0"},"canonical_sha256":"effb0ab954e6e259b03ebe95124db618b410b550094a9e7138e95bc52628bddf","source":{"kind":"arxiv","id":"1110.6690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6690","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6690v1","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6690","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"575QVOKU43RF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"575QVOKU43RFTMB6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"575QVOKU","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:575QVOKU43RFTMB6X2KRETNWDC","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-31T04:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"a4533e18b8e4ff342a21de1b9f28c5c01fbfe1a3c4ecb6abdab96305e658c895","abstract_canon_sha256":"df9f04e69124bdd309f0a5d0b4028c67852673616ea7d3b1c1e4750dafdd09c2"},"schema_version":"1.0"},"canonical_sha256":"effb0ab954e6e259b03ebe95124db618b410b550094a9e7138e95bc52628bddf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:54.808047Z","signature_b64":"wde6Sy0dPj7JfrRbf2Av93X7SkEDgECKnqJqKzejSactVyhj1VnM7Rsb79SJzh92OfaijHIy0nSo5vknN5zDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"effb0ab954e6e259b03ebe95124db618b410b550094a9e7138e95bc52628bddf","last_reissued_at":"2026-05-18T04:09:54.807354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:54.807354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6690","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":"2026-05-18T04:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xGb6XBP/O6oBQfoPm0fDZ5wCzh33maPOc/QmtxBkR8qerjYvwMk0svMZ8wdYwWSggrwcfxC71AsrdSqxZY9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:19:51.404774Z"},"content_sha256":"5dd3dcfadd1671e796b08312b5155bd95c0c658dc82d1e49daa91fc5f4bdb27e","schema_version":"1.0","event_id":"sha256:5dd3dcfadd1671e796b08312b5155bd95c0c658dc82d1e49daa91fc5f4bdb27e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:575QVOKU43RFTMB6X2KRETNWDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparing the closed almost disjointness and dominating numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dilip Raghavan, Saharon Shelah","submitted_at":"2011-10-31T04:33:29Z","abstract_excerpt":"We prove that if there is a dominating family of size ${\\aleph}_{1}$, then there is are ${\\aleph}_{1}$ many compact subsets of ${\\omega}^{\\omega}$ whose union is a maximal almost disjoint family of functions that is also maximal with respect to infinite partial functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6690","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":"2026-05-18T04:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJaDafrp6tvq2EZzoeT3qhcsNeIq2OVzneo9TJNZ6xxY0sgsR3Sic9hgtUtIHBnCJ+8ymzzoW2K0aI8+kKCcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:19:51.405115Z"},"content_sha256":"6d0648ffd6d3405a445cc4cfb8140231de3a1d271b11f692041c7a68b1b91c04","schema_version":"1.0","event_id":"sha256:6d0648ffd6d3405a445cc4cfb8140231de3a1d271b11f692041c7a68b1b91c04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/575QVOKU43RFTMB6X2KRETNWDC/bundle.json","state_url":"https://pith.science/pith/575QVOKU43RFTMB6X2KRETNWDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/575QVOKU43RFTMB6X2KRETNWDC/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":"2026-06-21T19:19:51Z","links":{"resolver":"https://pith.science/pith/575QVOKU43RFTMB6X2KRETNWDC","bundle":"https://pith.science/pith/575QVOKU43RFTMB6X2KRETNWDC/bundle.json","state":"https://pith.science/pith/575QVOKU43RFTMB6X2KRETNWDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/575QVOKU43RFTMB6X2KRETNWDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:575QVOKU43RFTMB6X2KRETNWDC","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":"df9f04e69124bdd309f0a5d0b4028c67852673616ea7d3b1c1e4750dafdd09c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-31T04:33:29Z","title_canon_sha256":"a4533e18b8e4ff342a21de1b9f28c5c01fbfe1a3c4ecb6abdab96305e658c895"},"schema_version":"1.0","source":{"id":"1110.6690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6690","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6690v1","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6690","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"575QVOKU43RF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"575QVOKU43RFTMB6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"575QVOKU","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:6d0648ffd6d3405a445cc4cfb8140231de3a1d271b11f692041c7a68b1b91c04","target":"graph","created_at":"2026-05-18T04:09:54Z","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":"We prove that if there is a dominating family of size ${\\aleph}_{1}$, then there is are ${\\aleph}_{1}$ many compact subsets of ${\\omega}^{\\omega}$ whose union is a maximal almost disjoint family of functions that is also maximal with respect to infinite partial functions.","authors_text":"Dilip Raghavan, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-31T04:33:29Z","title":"Comparing the closed almost disjointness and dominating numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6690","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":"sha256:5dd3dcfadd1671e796b08312b5155bd95c0c658dc82d1e49daa91fc5f4bdb27e","target":"record","created_at":"2026-05-18T04:09:54Z","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":"df9f04e69124bdd309f0a5d0b4028c67852673616ea7d3b1c1e4750dafdd09c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-31T04:33:29Z","title_canon_sha256":"a4533e18b8e4ff342a21de1b9f28c5c01fbfe1a3c4ecb6abdab96305e658c895"},"schema_version":"1.0","source":{"id":"1110.6690","kind":"arxiv","version":1}},"canonical_sha256":"effb0ab954e6e259b03ebe95124db618b410b550094a9e7138e95bc52628bddf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"effb0ab954e6e259b03ebe95124db618b410b550094a9e7138e95bc52628bddf","first_computed_at":"2026-05-18T04:09:54.807354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:54.807354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wde6Sy0dPj7JfrRbf2Av93X7SkEDgECKnqJqKzejSactVyhj1VnM7Rsb79SJzh92OfaijHIy0nSo5vknN5zDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:54.808047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dd3dcfadd1671e796b08312b5155bd95c0c658dc82d1e49daa91fc5f4bdb27e","sha256:6d0648ffd6d3405a445cc4cfb8140231de3a1d271b11f692041c7a68b1b91c04"],"state_sha256":"d864afe3fc8dab395f40892b2300b2e8ccd33fde18ca51cd4bfdb1cc3fb51819"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0f2pLAZkZu8qAMTH9IUZlobZKBhscRuoY9jco7sSixEiXU2M2URr7Ke8BtW/MSEuU4HR6gDshuWUhARU1mACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:19:51.407049Z","bundle_sha256":"a7094bab2fd6f93bd36eb01ca2cf13c276f4fac99ae0ebcbe3baedc8c925155e"}}