{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KQOYE7SWXOTBLMI7VQISHS2NNC","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":"2571bac89b78f9c1e4e872c3e161b34e37b3e6c8c15dc590f9a390c573fefea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-09T22:49:41Z","title_canon_sha256":"687c07f7df18bfd27a92181655aa144b1d3425a91f09ac1ab64fef74cc50d614"},"schema_version":"1.0","source":{"id":"1810.04290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04290","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04290v2","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04290","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"KQOYE7SWXOTB","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KQOYE7SWXOTBLMI7","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KQOYE7SW","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:b3297a01b3d7410d86e70292b3cef9caca04cc4681ac4743d50469a4cb650e9f","target":"graph","created_at":"2026-05-18T00:03:31Z","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":"This paper explores various generalizations of the Mitchell order focusing mostly on a generalization called the internal relation. The internal relation lacks the implicit strength requirement in the definition of the Mitchell order, and therefore can fail to be wellfounded. We establish some constraints on the illfoundedness of the internal relation, which leads to a proof of a conjecture of Steel regarding rank-to-rank cardinals.","authors_text":"Gabriel Goldberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-09T22:49:41Z","title":"The internal relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04290","kind":"arxiv","version":2},"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:d09e3f4b16d8089ae0a42a9f3eb320075d55a75a0de51324d5a7ceae31f1c3cc","target":"record","created_at":"2026-05-18T00:03:31Z","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":"2571bac89b78f9c1e4e872c3e161b34e37b3e6c8c15dc590f9a390c573fefea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-09T22:49:41Z","title_canon_sha256":"687c07f7df18bfd27a92181655aa144b1d3425a91f09ac1ab64fef74cc50d614"},"schema_version":"1.0","source":{"id":"1810.04290","kind":"arxiv","version":2}},"canonical_sha256":"541d827e56bba615b11fac1123cb4d68b4c0fc48f6db41cd9c3a17f6a1f420ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"541d827e56bba615b11fac1123cb4d68b4c0fc48f6db41cd9c3a17f6a1f420ae","first_computed_at":"2026-05-18T00:03:31.479017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:31.479017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X58iV5FGowAODlqT0mA5cyow7lbGpZ+/Zqo221b3ZyKv3pVAGtUHjK0YQ8kkZpDWSWRi/YgSHudY5kkfIVMxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:31.479683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d09e3f4b16d8089ae0a42a9f3eb320075d55a75a0de51324d5a7ceae31f1c3cc","sha256:b3297a01b3d7410d86e70292b3cef9caca04cc4681ac4743d50469a4cb650e9f"],"state_sha256":"aec1f716414f76f33cc965eacb9a5ed4527da155c6c5534084ea704b995c52e3"}