{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:62IN2ZDGOMU565Y2AXZYV5DHQ6","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":"b4f772bbdb444a0747c3da90af5982e34f5f58c1ca19beecb2d512054789419e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T06:51:52Z","title_canon_sha256":"31682f030b53e247081bc98f2cd3c0660a9cc95c995a5624b96d3ca2e7f5b60e"},"schema_version":"1.0","source":{"id":"1603.06684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06684","created_at":"2026-05-18T00:51:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06684v1","created_at":"2026-05-18T00:51:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06684","created_at":"2026-05-18T00:51:25Z"},{"alias_kind":"pith_short_12","alias_value":"62IN2ZDGOMU5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"62IN2ZDGOMU565Y2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"62IN2ZDG","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:e64e34875de74cf21c12e8f1a67d88a1d74707c65bacf0f1bf385b741651aa2d","target":"graph","created_at":"2026-05-18T00:51:25Z","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 that the Devlin-Shelah weak diamond implies Galvin's property. On the other hand, Galvin's property is consistent with the negation of the weak diamond, and even with Martin's axiom. We show that the proper forcing axiom implies a relative to the negation of Galvin's property for $\\aleph_1$.","authors_text":"Shimon Garti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T06:51:52Z","title":"Weak diamond and Galvin's property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06684","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:a204d29ffedb25efa40d90ad9de361f0f1c02677cb344bfb6db3d9be66917521","target":"record","created_at":"2026-05-18T00:51:25Z","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":"b4f772bbdb444a0747c3da90af5982e34f5f58c1ca19beecb2d512054789419e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T06:51:52Z","title_canon_sha256":"31682f030b53e247081bc98f2cd3c0660a9cc95c995a5624b96d3ca2e7f5b60e"},"schema_version":"1.0","source":{"id":"1603.06684","kind":"arxiv","version":1}},"canonical_sha256":"f690dd64667329df771a05f38af46787a6b804cf4648db3217ee2dc32b409469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f690dd64667329df771a05f38af46787a6b804cf4648db3217ee2dc32b409469","first_computed_at":"2026-05-18T00:51:25.757515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:25.757515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K54+AECDzHaGMKAYJBpNMKSkNTTPo8CE6g4TsCi28wiGhvEeEGikJko02MhbtBFNQv6bDVesTqX3Gn7Qv5TrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:25.758149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a204d29ffedb25efa40d90ad9de361f0f1c02677cb344bfb6db3d9be66917521","sha256:e64e34875de74cf21c12e8f1a67d88a1d74707c65bacf0f1bf385b741651aa2d"],"state_sha256":"1af976d695f11fa9814c008c8706bf1646cb9fd028c9dd297afb80e317b03ca2"}