{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y673ATOUWIVAF44EBYLNODYEVS","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":"400591c8382cb65a9b7aa5f0edd67c671dfe847a19351cb68550004ef4f12423","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-21T19:58:22Z","title_canon_sha256":"5e712d4e2e35f581b223ad38527371639e1836cf340c143ba15524ddcced19a1"},"schema_version":"1.0","source":{"id":"1210.5759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5759","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5759v1","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5759","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"Y673ATOUWIVA","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y673ATOUWIVAF44E","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y673ATOU","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:34c838449d14c2c9677b6387870610325c59ee1ac6be81d8f1ea7bbf958b7cce","target":"graph","created_at":"2026-05-18T03:42:43Z","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 obtain an improvement of some coloring theorems from \\cite{nsbpr}, \\cite{819}, and \\cite{APAL} for the case where the singular cardinal in question has countable cofinality. As a corollary, we obtain an \"idealized\" version of the combinatorial principle $\\pr_1(\\mu^+,\\mu^+,\\mu^+,\\cf(\\mu))$ that maximizes the indecomposability of the associated ideal.","authors_text":"Todd Eisworth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-21T19:58:22Z","title":"On idealized versions of $\\pr_1(\\mu^+,\\mu^+,\\mu^+,\\cf(\\mu))$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5759","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":"sha256:795baf15ba23ac41085a6bc92ba84e79e541dd3a9a5999de9f7b6701dbf4134c","target":"record","created_at":"2026-05-18T03:42:43Z","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":"400591c8382cb65a9b7aa5f0edd67c671dfe847a19351cb68550004ef4f12423","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-21T19:58:22Z","title_canon_sha256":"5e712d4e2e35f581b223ad38527371639e1836cf340c143ba15524ddcced19a1"},"schema_version":"1.0","source":{"id":"1210.5759","kind":"arxiv","version":1}},"canonical_sha256":"c7bfb04dd4b22a02f3840e16d70f04aca71295510bb891ed8b8dfc23304bf6ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7bfb04dd4b22a02f3840e16d70f04aca71295510bb891ed8b8dfc23304bf6ad","first_computed_at":"2026-05-18T03:42:43.159970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:43.159970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AhV58QYI28vtuMHERrQEx/grZbjgMRUF4AsgClzrNnsPoyOOBf4MmFkqYg8fZ2EBIDKXRbO9Jt6/ut1jS8K+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:43.160531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:795baf15ba23ac41085a6bc92ba84e79e541dd3a9a5999de9f7b6701dbf4134c","sha256:34c838449d14c2c9677b6387870610325c59ee1ac6be81d8f1ea7bbf958b7cce"],"state_sha256":"1b5ca69da8ae25366983f4c58595885dd71bfeca7b2f309a971e66475d7763c8"}