{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2QEDZFOFNFCN7DRDGDL6VZFUHK","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":"1e1c13c417ecb5dbfc78a02fdb86c27ad592bd5857721b3fa85c85cae0cf4354","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-18T19:45:51Z","title_canon_sha256":"067d626ecc3396e286819b0cbc9aee8e7b53fa8bee9715cd4bee896cb28e3c6e"},"schema_version":"1.0","source":{"id":"1510.05297","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05297","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05297v3","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05297","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"pith_short_12","alias_value":"2QEDZFOFNFCN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QEDZFOFNFCN7DRD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QEDZFOF","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:147bdfdd3ffb6e618385e3a893bc5062e19245a0927b3132b6b62dcf8b1dfe22","target":"graph","created_at":"2026-05-17T23:41:22Z","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 introduce a stronger version of an $\\omega_1$-guessing model, which we call an indestructibly $\\omega_1$-guessing model. The principle IGMP states that there are stationarily many indestructibly $\\omega_1$-guessing models. This principle, which follows from PFA, captures many of the consequences of PFA, including the Suslin hypothesis and the singular cardinal hypothesis. We prove that IGMP is consistent with the continuum being arbitrarily large.","authors_text":"John Krueger, Sean Cox","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-18T19:45:51Z","title":"Indestructible Guessing Models and the Continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05297","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":"sha256:6d333f4ed71a644e17483d11598f4278039398d6f395406de5704f64de102cf1","target":"record","created_at":"2026-05-17T23:41:22Z","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":"1e1c13c417ecb5dbfc78a02fdb86c27ad592bd5857721b3fa85c85cae0cf4354","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-18T19:45:51Z","title_canon_sha256":"067d626ecc3396e286819b0cbc9aee8e7b53fa8bee9715cd4bee896cb28e3c6e"},"schema_version":"1.0","source":{"id":"1510.05297","kind":"arxiv","version":3}},"canonical_sha256":"d4083c95c56944df8e2330d7eae4b43a92995801c724a32e913a7e8d25251147","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4083c95c56944df8e2330d7eae4b43a92995801c724a32e913a7e8d25251147","first_computed_at":"2026-05-17T23:41:22.399246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:22.399246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DtSN7AYqsSTTfFBDW33XPIsJsWP1/eGiw+hQ3w4H9X2H0TlH8KNCRU5ND2braxf5EebFxu+/aKgo0b5Eqr6GDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:22.399934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05297","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d333f4ed71a644e17483d11598f4278039398d6f395406de5704f64de102cf1","sha256:147bdfdd3ffb6e618385e3a893bc5062e19245a0927b3132b6b62dcf8b1dfe22"],"state_sha256":"1cc03667bea3f4126c43398ef5ab4f866801995469581eebb38b99152fe5c512"}