{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7MTIQ7MTJBPV2IBV3JT5TUENAT","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":"ae5e5e32c25e2b25e2427c7b13628f989608b3567c9e532f71058333808c4341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-07T21:52:29Z","title_canon_sha256":"a93b16d90f1d2a94d99176b5fd4edd01180cb9888369ebef7d36f01b9887a8e3"},"schema_version":"1.0","source":{"id":"1510.02147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02147","created_at":"2026-05-18T01:30:44Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02147v1","created_at":"2026-05-18T01:30:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02147","created_at":"2026-05-18T01:30:44Z"},{"alias_kind":"pith_short_12","alias_value":"7MTIQ7MTJBPV","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7MTIQ7MTJBPV2IBV","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7MTIQ7MT","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:c3c1a4f477c7a823e8787f08d7742910ac7f561316451d98303cf8ef85bcad59","target":"graph","created_at":"2026-05-18T01:30:44Z","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 realizability model in which the realizers are the reals not just Turing computable in a fixed real but rather the reals in a countable ideal of Turing degrees. This is then applied to prove several separation results involving variants of the Fan Theorem.","authors_text":"Michael Rathjen, Robert S. Lubarsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-07T21:52:29Z","title":"Realizability Models Separating Various Fan Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02147","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":"sha256:18f171c44de03a28b36a65ba0927c7ff269fa3970287e4162b5920f6280f9020","target":"record","created_at":"2026-05-18T01:30:44Z","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":"ae5e5e32c25e2b25e2427c7b13628f989608b3567c9e532f71058333808c4341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-07T21:52:29Z","title_canon_sha256":"a93b16d90f1d2a94d99176b5fd4edd01180cb9888369ebef7d36f01b9887a8e3"},"schema_version":"1.0","source":{"id":"1510.02147","kind":"arxiv","version":1}},"canonical_sha256":"fb26887d93485f5d2035da67d9d08d04f023bd57cb92076cdb3e1c30e1df3b74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb26887d93485f5d2035da67d9d08d04f023bd57cb92076cdb3e1c30e1df3b74","first_computed_at":"2026-05-18T01:30:44.640986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:44.640986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7GuasUrIzGjH5M/KGZ0ji/mZlS54tpJDIACL/ImPelIVmXJmE95Jl8QR+5dWRhJX8OxWAbOmPx7yK3BW9TeEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:44.641589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18f171c44de03a28b36a65ba0927c7ff269fa3970287e4162b5920f6280f9020","sha256:c3c1a4f477c7a823e8787f08d7742910ac7f561316451d98303cf8ef85bcad59"],"state_sha256":"73050b78b140c2d09ed27ae0c1f4c1b38c96c0a6c63685766b891182b0a8b059"}