{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:A5SMS2D4C5IG22QPXJJYQBG3FC","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":"ad198c643ba36e5149e7881e59f949046535ed8d301621c2bf0b5c921e3b87e4","cross_cats_sorted":["math.LO"],"license":"","primary_cat":"math.GN","submitted_at":"1998-05-04T08:39:17Z","title_canon_sha256":"97fb7a010aee18393a4a575ba29cf9ba7fdaaff593b899df7ad45e55b9f1e6f3"},"schema_version":"1.0","source":{"id":"math/9805008","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9805008","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/9805008v3","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9805008","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"A5SMS2D4C5IG","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"A5SMS2D4C5IG22QP","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"A5SMS2D4","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:948088bc7d77c3a0a6ff081e20d3fba32c52f2d3d01ff977d11413b933b505e7","target":"graph","created_at":"2026-05-18T03:02:18Z","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 every continuum of weight aleph_1 is a continuous image of the Cech-Stone-remainder R^* of the real line. It follows that under CH the remainder of the half line [0,infty) is universal among the continua of weight c --- universal in the `mapping onto' sense.\n  We complement this result by showing that\n 1) under MA every continuum of weight less than c is a continuous image of R^*\n 2) in the Cohen model the long segment of length omega_2+1 is not a continuous image of R^*, and\n 3) PFA implies that I_u is not a continuous image of R^*, whenever u is a c-saturated ultrafilter. We al","authors_text":"Alan Dow, Klaas Pieter Hart","cross_cats":["math.LO"],"headline":"","license":"","primary_cat":"math.GN","submitted_at":"1998-05-04T08:39:17Z","title":"A Universal Continuum of Weight aleph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805008","kind":"arxiv","version":3},"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":"sha256:21e454f15375101a37005054de8c53c9ba5c1421c30707a6dcd4f45039a78f0f","target":"record","created_at":"2026-05-18T03:02:18Z","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":"ad198c643ba36e5149e7881e59f949046535ed8d301621c2bf0b5c921e3b87e4","cross_cats_sorted":["math.LO"],"license":"","primary_cat":"math.GN","submitted_at":"1998-05-04T08:39:17Z","title_canon_sha256":"97fb7a010aee18393a4a575ba29cf9ba7fdaaff593b899df7ad45e55b9f1e6f3"},"schema_version":"1.0","source":{"id":"math/9805008","kind":"arxiv","version":3}},"canonical_sha256":"0764c9687c17506d6a0fba538804db28befa5bcfb67892ebfc417a2401194eed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0764c9687c17506d6a0fba538804db28befa5bcfb67892ebfc417a2401194eed","first_computed_at":"2026-05-18T03:02:18.647914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:18.647914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bmmy8/gHxUi9Lyl7MfhbPK6buzcqTt3o2cxeUerVBW2kNGrcHUFUu6ZBQGrPmSXhk5xjcOLlezCLXsbHWtDRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:18.648899Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9805008","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21e454f15375101a37005054de8c53c9ba5c1421c30707a6dcd4f45039a78f0f","sha256:948088bc7d77c3a0a6ff081e20d3fba32c52f2d3d01ff977d11413b933b505e7"],"state_sha256":"9b3f07397f69bcf66a4d6087f4b8378f34b1ea45549e6924b9732f1452bb7ed4"}