{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KMYI3RTVUG63BYWXKLYSCIR2WB","short_pith_number":"pith:KMYI3RTV","canonical_record":{"source":{"id":"1907.08581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-19T17:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"9239bd66dd68711e11e9c3b8307ea3f1080855361601731e1e622f01f996901a","abstract_canon_sha256":"276c0b8b7b70885d0ca19550c7445a56f2c2fbf4f10fb4a6ea9e13ee9811b039"},"schema_version":"1.0"},"canonical_sha256":"53308dc675a1bdb0e2d752f121223ab066ab555b9bc3f9d502806537730125d9","source":{"kind":"arxiv","id":"1907.08581","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08581","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08581v1","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08581","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"KMYI3RTVUG63","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KMYI3RTVUG63BYWX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KMYI3RTV","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KMYI3RTVUG63BYWXKLYSCIR2WB","target":"record","payload":{"canonical_record":{"source":{"id":"1907.08581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-19T17:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"9239bd66dd68711e11e9c3b8307ea3f1080855361601731e1e622f01f996901a","abstract_canon_sha256":"276c0b8b7b70885d0ca19550c7445a56f2c2fbf4f10fb4a6ea9e13ee9811b039"},"schema_version":"1.0"},"canonical_sha256":"53308dc675a1bdb0e2d752f121223ab066ab555b9bc3f9d502806537730125d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:09.375849Z","signature_b64":"aioh0CTB8OH2qiHJM1rfMieF4DBwtds6KPxooK2zr9NiVhQUIy6/q9IN+IfP7klFUGnFmJN5ufL5GMWbWO0QBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53308dc675a1bdb0e2d752f121223ab066ab555b9bc3f9d502806537730125d9","last_reissued_at":"2026-05-17T23:40:09.375138Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:09.375138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.08581","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oZkz/7QhzUt9dCQsfzs5huYQz0VHsUUDSeEF1maFh3/FtmldzypRqnYT2o2Yeu3sRgXGxXWcVLdG4CI2VPtSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:19:54.898670Z"},"content_sha256":"9df30ab161823ba428452930a152de4d51516d9811368edad587be100f8c36ab","schema_version":"1.0","event_id":"sha256:9df30ab161823ba428452930a152de4d51516d9811368edad587be100f8c36ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KMYI3RTVUG63BYWXKLYSCIR2WB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partitioning a reflecting stationary set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Assaf Rinot, Maxwell Levine","submitted_at":"2019-07-19T17:22:01Z","abstract_excerpt":"We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer that it is never the case that there exists a singular cardinal all of whose scales are very good."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08581","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDvkQHERo+U8xsj0NVICE7wtYCXllbvadf9kiCFEBLQeEEAfbb3q6oiNWsKBdE6GDoqFo1/PrnWAcsxldCwaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:19:54.899486Z"},"content_sha256":"0491f9bd73d2d43a9bc97b20d5672ef1146cf8b3a7386d6b3edcb8d230ee3c21","schema_version":"1.0","event_id":"sha256:0491f9bd73d2d43a9bc97b20d5672ef1146cf8b3a7386d6b3edcb8d230ee3c21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMYI3RTVUG63BYWXKLYSCIR2WB/bundle.json","state_url":"https://pith.science/pith/KMYI3RTVUG63BYWXKLYSCIR2WB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMYI3RTVUG63BYWXKLYSCIR2WB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T18:19:54Z","links":{"resolver":"https://pith.science/pith/KMYI3RTVUG63BYWXKLYSCIR2WB","bundle":"https://pith.science/pith/KMYI3RTVUG63BYWXKLYSCIR2WB/bundle.json","state":"https://pith.science/pith/KMYI3RTVUG63BYWXKLYSCIR2WB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMYI3RTVUG63BYWXKLYSCIR2WB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KMYI3RTVUG63BYWXKLYSCIR2WB","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":"276c0b8b7b70885d0ca19550c7445a56f2c2fbf4f10fb4a6ea9e13ee9811b039","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-19T17:22:01Z","title_canon_sha256":"9239bd66dd68711e11e9c3b8307ea3f1080855361601731e1e622f01f996901a"},"schema_version":"1.0","source":{"id":"1907.08581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08581","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08581v1","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08581","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"KMYI3RTVUG63","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KMYI3RTVUG63BYWX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KMYI3RTV","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:0491f9bd73d2d43a9bc97b20d5672ef1146cf8b3a7386d6b3edcb8d230ee3c21","target":"graph","created_at":"2026-05-17T23:40:09Z","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 address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer that it is never the case that there exists a singular cardinal all of whose scales are very good.","authors_text":"Assaf Rinot, Maxwell Levine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-19T17:22:01Z","title":"Partitioning a reflecting stationary set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08581","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":"sha256:9df30ab161823ba428452930a152de4d51516d9811368edad587be100f8c36ab","target":"record","created_at":"2026-05-17T23:40:09Z","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":"276c0b8b7b70885d0ca19550c7445a56f2c2fbf4f10fb4a6ea9e13ee9811b039","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-19T17:22:01Z","title_canon_sha256":"9239bd66dd68711e11e9c3b8307ea3f1080855361601731e1e622f01f996901a"},"schema_version":"1.0","source":{"id":"1907.08581","kind":"arxiv","version":1}},"canonical_sha256":"53308dc675a1bdb0e2d752f121223ab066ab555b9bc3f9d502806537730125d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53308dc675a1bdb0e2d752f121223ab066ab555b9bc3f9d502806537730125d9","first_computed_at":"2026-05-17T23:40:09.375138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:09.375138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aioh0CTB8OH2qiHJM1rfMieF4DBwtds6KPxooK2zr9NiVhQUIy6/q9IN+IfP7klFUGnFmJN5ufL5GMWbWO0QBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:09.375849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df30ab161823ba428452930a152de4d51516d9811368edad587be100f8c36ab","sha256:0491f9bd73d2d43a9bc97b20d5672ef1146cf8b3a7386d6b3edcb8d230ee3c21"],"state_sha256":"02f6828ca14edd81430201667f3d6929f4e859a40bf9cc13cb44d933c3542960"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"55T4WvZV2Xl4bIE9tayBdMwYP9o9UkMPodPpk1MNvp+Dn/AXzj2KzxdCRTsDWStSdziAHVU1BTpAkJ4UatycDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:19:54.903628Z","bundle_sha256":"7911abb541e3a820bb1e6f9cf1ed0ec5b920d7704dd89eff9298d441700255c0"}}