{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:7Z4UM2WJIOICNS2K3ZHDPVP3FY","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":"893d4b072c777300eeda6685451991ffb0cb6b169d77008e45450d1954255898","cross_cats_sorted":["math.CO","math.GN"],"license":"","primary_cat":"math.LO","submitted_at":"2003-07-16T15:27:45Z","title_canon_sha256":"961e6cf61dababb706f75b773ed3f58c71e989f54b4c5eef388359d73e0b7ad7"},"schema_version":"1.0","source":{"id":"math/0307226","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307226","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307226v4","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307226","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"7Z4UM2WJIOIC","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"7Z4UM2WJIOICNS2K","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"7Z4UM2WJ","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:5898edbb978052f5e117f500f3db7a1b67c35439a8dd88c2252697f630af27db","target":"graph","created_at":"2026-05-18T04:42:44Z","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 describe a simple machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are:\n  1. The product of a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measure zero/is strongly meager, respectively.\n  2. Using Scheepers' notation for selection principles: Sfin(Omega,Omega^gp)\\cap S1(O,O)=S1(Omega,Omega^gp), and Borel's Conjecture for S1(Omega,Omega) (or just S1(Omega,Omega^gp)) implies Borel's Conjecture.\n  These results extend results of Scheepers an","authors_text":"Boaz Tsaban, Tomasz Weiss","cross_cats":["math.CO","math.GN"],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"2003-07-16T15:27:45Z","title":"Products of special sets of real numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307226","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:a1a2526f34721b94ccfec4ae26fcc28471806651885a0490571437faaae6b6ca","target":"record","created_at":"2026-05-18T04:42:44Z","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":"893d4b072c777300eeda6685451991ffb0cb6b169d77008e45450d1954255898","cross_cats_sorted":["math.CO","math.GN"],"license":"","primary_cat":"math.LO","submitted_at":"2003-07-16T15:27:45Z","title_canon_sha256":"961e6cf61dababb706f75b773ed3f58c71e989f54b4c5eef388359d73e0b7ad7"},"schema_version":"1.0","source":{"id":"math/0307226","kind":"arxiv","version":4}},"canonical_sha256":"fe79466ac9439026cb4ade4e37d5fb2e229ecf0aec4d8f664c56b0439eeecb5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe79466ac9439026cb4ade4e37d5fb2e229ecf0aec4d8f664c56b0439eeecb5b","first_computed_at":"2026-05-18T04:42:44.960269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:44.960269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ovM+bUS1TrA4Kr7Yx4/P0TdX/chjJ4GU0PgnRG5ZbFnmA/OjJ1k8ZfeCBU63VmhQx19a1+YdXORb6IXJM3q0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:44.960830Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0307226","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1a2526f34721b94ccfec4ae26fcc28471806651885a0490571437faaae6b6ca","sha256:5898edbb978052f5e117f500f3db7a1b67c35439a8dd88c2252697f630af27db"],"state_sha256":"8944c8e5a086d3c8b7388225336288450dfb0c81a54afa5d46dc4eeccb91662d"}