{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MLKFA7FFEORDSI4ZTNSUCVBG5A","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":"12679eff83ca34ddc7decdc23ca93ff5996544567b571fe64644a1e4de44b386","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-08T15:16:13Z","title_canon_sha256":"2a4cc7d9c1f18d2619f7e0a2bc262d5f15df1cd4c7e6329eb3740cd11a19947a"},"schema_version":"1.0","source":{"id":"1601.01899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01899","created_at":"2026-05-18T01:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01899v1","created_at":"2026-05-18T01:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01899","created_at":"2026-05-18T01:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"MLKFA7FFEORD","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MLKFA7FFEORDSI4Z","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MLKFA7FF","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:8fc8da64c1ce696dac90646cd0f29e96fd497301f916bff41319ef6295a67400","target":"graph","created_at":"2026-05-18T01:23:11Z","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 introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch reducibility. We give sample applications by showing that certain (algebraic) constructions are not effective in the OTM-sense and considerung the effective equivalence of various versions of the axiom of choice.","authors_text":"Merlin Carl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-08T15:16:13Z","title":"Generalized Effective Reducibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01899","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":"sha256:78ae0fdf69bcbb1096d5fdd4334235af75f1fb0da472ba68ceacc4084e1482fc","target":"record","created_at":"2026-05-18T01:23:11Z","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":"12679eff83ca34ddc7decdc23ca93ff5996544567b571fe64644a1e4de44b386","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-08T15:16:13Z","title_canon_sha256":"2a4cc7d9c1f18d2619f7e0a2bc262d5f15df1cd4c7e6329eb3740cd11a19947a"},"schema_version":"1.0","source":{"id":"1601.01899","kind":"arxiv","version":1}},"canonical_sha256":"62d4507ca523a23923999b65415426e805ab123d05f7b2ce89d6f4f55228156c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62d4507ca523a23923999b65415426e805ab123d05f7b2ce89d6f4f55228156c","first_computed_at":"2026-05-18T01:23:11.121088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:11.121088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OU9zK3DRLjjrKQYvNiio3ztqDmynpwzTwhU/vi47HeCkogc0K3r8Mh1TgZruwzKHOopUQtmqNxstjfz8zzXUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:11.121515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78ae0fdf69bcbb1096d5fdd4334235af75f1fb0da472ba68ceacc4084e1482fc","sha256:8fc8da64c1ce696dac90646cd0f29e96fd497301f916bff41319ef6295a67400"],"state_sha256":"ed2b00f9b96e7f9660421c1214febef18d2eaedd558b56ab392e80db7c994d53"}