{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZGRU7L4GOPZORNQBKHFIKHS72B","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":"462483f2bd680fe1d53860cc219afadfb4aaefb5562107068a6f20d7f01e997e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-02T17:29:52Z","title_canon_sha256":"e31f03083df5cfc69d8c428c79d7c7c8dcfafd7cf5f42791abec48d1dadc571d"},"schema_version":"1.0","source":{"id":"1610.00319","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00319","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00319v3","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00319","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZGRU7L4GOPZO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZGRU7L4GOPZORNQB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZGRU7L4G","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:009e4b2611268a63d94d406d5e33e6d0f883c80605ee42b056c2e3a301b0071e","target":"graph","created_at":"2026-05-17T23:53:12Z","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 a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\\textsf{IGMP}$, $\\textsf{GMP}$ together with $2^\\omega \\le \\omega_2$ is consistent with the existence of an $\\omega_1$-distributive nowhere c.c.c. forcing poset of size $\\omega_1$. We introduce the idea of a weakly guessing model, and prove that many of the strong consequences of the principle $\\textsf{GMP}$ follow from the existence of stationarily many weakly guessing models. Using Namba forcing, we construct a model in which there are stationarily many indestructibly","authors_text":"John Krueger, Sean Cox","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-02T17:29:52Z","title":"Namba forcing, weak approximation, and guessing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00319","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:ebc65e00b21f684aab1384fe5b6516da02f355ebda0278d731061470fbe4e7c5","target":"record","created_at":"2026-05-17T23:53:12Z","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":"462483f2bd680fe1d53860cc219afadfb4aaefb5562107068a6f20d7f01e997e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-02T17:29:52Z","title_canon_sha256":"e31f03083df5cfc69d8c428c79d7c7c8dcfafd7cf5f42791abec48d1dadc571d"},"schema_version":"1.0","source":{"id":"1610.00319","kind":"arxiv","version":3}},"canonical_sha256":"c9a34faf8673f2e8b60151ca851e5fd0492bb3e1cc85100d4b82521c343981e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9a34faf8673f2e8b60151ca851e5fd0492bb3e1cc85100d4b82521c343981e0","first_computed_at":"2026-05-17T23:53:12.991562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:12.991562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nGWhlrmqpDQ/N/6UZpIOWEdWuTCtXdX6glFQX4Gg75kbAuli8VN1ciDo7CFQns6947+AXWDk4eXdY4FNQdqkDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:12.992043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00319","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebc65e00b21f684aab1384fe5b6516da02f355ebda0278d731061470fbe4e7c5","sha256:009e4b2611268a63d94d406d5e33e6d0f883c80605ee42b056c2e3a301b0071e"],"state_sha256":"efc1aefbfc30829ec9984128ba3351cd22901acb58d3c0bdfa961a624de4eb53"}