{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NC6YBVOPQCBQFTIGV37LLGYXB3","short_pith_number":"pith:NC6YBVOP","schema_version":"1.0","canonical_sha256":"68bd80d5cf808302cd06aefeb59b170ec992632663835ac214ac58f64fb2e28f","source":{"kind":"arxiv","id":"1310.3250","version":1},"attestation_state":"computed","paper":{"title":"$\\Sigma^1_2$ and $\\Pi^1_1$ mad families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asger T\\\"ornquist","submitted_at":"2013-10-11T19:17:41Z","abstract_excerpt":"We answer in the affirmative the following question of J\\\"org Brendle: If there is a $\\Sigma^1_2$ mad family, is there then a $\\Pi^1_1$ mad family?"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.3250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T19:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"ea40617ea423f584f4fb1564d336dbfb5db0bdc54aa5bde3c2a9204f39ad5e1c","abstract_canon_sha256":"25041bb8cb1f096d9847bc069a4e6c2723be7127f56e95a4c2a772c64177fb00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:44.511389Z","signature_b64":"AS0AveeUcqiRbHqfndn8JMK/NN6EhslVSJMhlb/EaLtnHCxViflkZvp7eUFBd9nSep+QWcbD6AxY0mXOldYdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68bd80d5cf808302cd06aefeb59b170ec992632663835ac214ac58f64fb2e28f","last_reissued_at":"2026-05-18T03:10:44.510853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:44.510853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\Sigma^1_2$ and $\\Pi^1_1$ mad families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asger T\\\"ornquist","submitted_at":"2013-10-11T19:17:41Z","abstract_excerpt":"We answer in the affirmative the following question of J\\\"org Brendle: If there is a $\\Sigma^1_2$ mad family, is there then a $\\Pi^1_1$ mad family?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3250","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.3250","created_at":"2026-05-18T03:10:44.510937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.3250v1","created_at":"2026-05-18T03:10:44.510937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3250","created_at":"2026-05-18T03:10:44.510937+00:00"},{"alias_kind":"pith_short_12","alias_value":"NC6YBVOPQCBQ","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NC6YBVOPQCBQFTIG","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NC6YBVOP","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3","json":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3.json","graph_json":"https://pith.science/api/pith-number/NC6YBVOPQCBQFTIGV37LLGYXB3/graph.json","events_json":"https://pith.science/api/pith-number/NC6YBVOPQCBQFTIGV37LLGYXB3/events.json","paper":"https://pith.science/paper/NC6YBVOP"},"agent_actions":{"view_html":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3","download_json":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3.json","view_paper":"https://pith.science/paper/NC6YBVOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.3250&json=true","fetch_graph":"https://pith.science/api/pith-number/NC6YBVOPQCBQFTIGV37LLGYXB3/graph.json","fetch_events":"https://pith.science/api/pith-number/NC6YBVOPQCBQFTIGV37LLGYXB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3/action/storage_attestation","attest_author":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3/action/author_attestation","sign_citation":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3/action/citation_signature","submit_replication":"https://pith.science/pith/NC6YBVOPQCBQFTIGV37LLGYXB3/action/replication_record"}},"created_at":"2026-05-18T03:10:44.510937+00:00","updated_at":"2026-05-18T03:10:44.510937+00:00"}