{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C2J2ESU4KWG5UEWLOW24QL4WSO","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":"d795bc9d868f2debdde0fcb856c3ed799011d7125f32570e13d72f1317cc1f1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:17:52Z","title_canon_sha256":"88d57f711d31a4cf741f379d5736f93070a9d46367ee8206c402f21b0896ba21"},"schema_version":"1.0","source":{"id":"1611.08140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08140","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08140v1","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08140","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"C2J2ESU4KWG5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C2J2ESU4KWG5UEWL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C2J2ESU4","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:4b475669059864c654c92e1b3e54c16926f9b2cf43fd4bb7c6586cc86d614fc6","target":"graph","created_at":"2026-05-18T00:56:44Z","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 develop a version of Cichon's diagram for cardinal invariants on the generalized Cantor space 2^kappa or the generalized Baire space kappa^kappa where kappa is an uncountable regular cardinal. For strongly inaccessible kappa, many of the ZFC-results about the order relationship of the cardinal invariants which hold for omega generalize; for example we obtain a natural generalization of the Bartoszynski-Raisonnier-Stern Theorem. We also prove a number of independence results, both with <kappa-support iterations and kappa-support iterations and products, showing that we consistently have stri","authors_text":"Andrew Brooke-Taylor, Diana Montoya, Joerg Brendle, Sy-David Friedman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:17:52Z","title":"Cichon's Diagram for uncountable cardinals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08140","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:ab47cac5370e881da46edfd8a6c3f5fa25fb7dc7a4be895375832284ff4d1c17","target":"record","created_at":"2026-05-18T00:56:44Z","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":"d795bc9d868f2debdde0fcb856c3ed799011d7125f32570e13d72f1317cc1f1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:17:52Z","title_canon_sha256":"88d57f711d31a4cf741f379d5736f93070a9d46367ee8206c402f21b0896ba21"},"schema_version":"1.0","source":{"id":"1611.08140","kind":"arxiv","version":1}},"canonical_sha256":"1693a24a9c558dda12cb75b5c82f9693aebad5aed2cb0254f898900f9afe4d9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1693a24a9c558dda12cb75b5c82f9693aebad5aed2cb0254f898900f9afe4d9c","first_computed_at":"2026-05-18T00:56:44.263982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:44.263982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n5Gd/Mt7GL0NbmXz2dLWpzjpIcJDKOFtqECK7WALPO471MPKEH6+zi6Cmzp29336EIk1/DH3e+Frlj+W1a+oDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:44.264474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab47cac5370e881da46edfd8a6c3f5fa25fb7dc7a4be895375832284ff4d1c17","sha256:4b475669059864c654c92e1b3e54c16926f9b2cf43fd4bb7c6586cc86d614fc6"],"state_sha256":"bd1a0491f90499417b17eaff1df9281c1557f48321f205c2bd071c78b2b04e1d"}