{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:M5KT4ZUSEEFK7F4QOHMMOXL45M","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":"db5374fb975f18c0a5ddef074ed52b219f81ba7fad786b8cd88e74cfe11246c5","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-03-20T00:00:00Z","title_canon_sha256":"8026c55607ed846f6d1659e80c5b66c277d6b5364b2ca94a72b8a3ae55e29d3b"},"schema_version":"1.0","source":{"id":"math/9503208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9503208","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9503208v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9503208","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"M5KT4ZUSEEFK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"M5KT4ZUSEEFK7F4Q","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"M5KT4ZUS","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:04a7e70b489398ba80ea7d1a2f806b991a65ada8f045c16ef5473aa0ede9fb9c","target":"graph","created_at":"2026-05-18T01:05:50Z","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 show that all finite powers of a Hausdorff space X do not contain uncountable weakly separated subspaces iff there is a c.c.c poset P such that 1_P forces that ``X is a countable union of 0-dimensional subspaces of countable weight.''\n  We also show that this theorem is sharp in two different senses:\n (i) we can't get rid of using generic extensions,\n (ii) we have to consider all finite powers of $X$.","authors_text":"I. Juh\\'asz, Lajos Soukup, Z. Szentmikl\\'ossy","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-03-20T00:00:00Z","title":"Forcing countable networks for spaces satisfying R(X^omega)=omega."},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9503208","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":"sha256:24c81551389c886bec6852a10111b8a15ded2b06c97484d13196f8debe5cb1b2","target":"record","created_at":"2026-05-18T01:05:50Z","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":"db5374fb975f18c0a5ddef074ed52b219f81ba7fad786b8cd88e74cfe11246c5","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-03-20T00:00:00Z","title_canon_sha256":"8026c55607ed846f6d1659e80c5b66c277d6b5364b2ca94a72b8a3ae55e29d3b"},"schema_version":"1.0","source":{"id":"math/9503208","kind":"arxiv","version":1}},"canonical_sha256":"67553e6692210aaf979071d8c75d7ceb22ac15bb8f1ac84b85c7a1f7d1fd8f86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67553e6692210aaf979071d8c75d7ceb22ac15bb8f1ac84b85c7a1f7d1fd8f86","first_computed_at":"2026-05-18T01:05:50.410146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.410146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6kZ3Hj6XIBUv8C+qOxqwENCT1niQeYVxynEeuflhCajw+sIfQmtR3LBBp8p0SWiPPh5fD24LJmvwOdPJp/k5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.410599Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9503208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24c81551389c886bec6852a10111b8a15ded2b06c97484d13196f8debe5cb1b2","sha256:04a7e70b489398ba80ea7d1a2f806b991a65ada8f045c16ef5473aa0ede9fb9c"],"state_sha256":"64285c1cf28dbbef1926279748cd8a61b786eb2e5caa56695b8b16c8d5cb2d48"}