{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AQFXWDYO32DKDR3NEZI2YRTMVH","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":"31b6c230f0532a285db30cc76e8a232959eb7d024fa027683b105f2f8a54a225","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-24T22:46:00Z","title_canon_sha256":"6db68c0ca48092aab0338111ad39435d1b163b147091f09dd93c23edcce11b9b"},"schema_version":"1.0","source":{"id":"1907.10766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10766","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10766v1","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10766","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"pith_short_12","alias_value":"AQFXWDYO32DK","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AQFXWDYO32DKDR3N","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AQFXWDYO","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:ac3fb8fd8e5c29139a05c0819424c4c4697ba8fe8d513260083cc3e4e90e6ef6","target":"graph","created_at":"2026-05-17T23:39:34Z","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 show that part I of uniform Martin's conjecture follows from a local phenomenon, namely that if a non-constant Turing invariant function goes from the Turing degree $\\boldsymbol x$ to the Turing degree $\\boldsymbol y$, then $\\boldsymbol x \\le_T \\boldsymbol y$. Besides improving our knowledge about part I of uniform Martin's conjecture (which turns out to be equivalent to Turing determinacy), the discovery of such local phenomenon also leads to new results that did not look strictly related to Martin's conjecture before. In particular, we get that computable reducibility $\\le_c$ on equivalen","authors_text":"Vittorio Bard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-24T22:46:00Z","title":"Uniform Martin's conjecture, locally"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10766","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:c0e03663be41fa081e954cd8d6a1673b78cb4e68d5fc93a7171197ae2084d14e","target":"record","created_at":"2026-05-17T23:39:34Z","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":"31b6c230f0532a285db30cc76e8a232959eb7d024fa027683b105f2f8a54a225","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-24T22:46:00Z","title_canon_sha256":"6db68c0ca48092aab0338111ad39435d1b163b147091f09dd93c23edcce11b9b"},"schema_version":"1.0","source":{"id":"1907.10766","kind":"arxiv","version":1}},"canonical_sha256":"040b7b0f0ede86a1c76d2651ac466ca9c0a4aaeec92375d0c84c1b69c40d6f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"040b7b0f0ede86a1c76d2651ac466ca9c0a4aaeec92375d0c84c1b69c40d6f72","first_computed_at":"2026-05-17T23:39:34.545733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:34.545733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87KNPb8BYeyPWCxOe3+yqdYkKG9b5yzAHBYZx1uyjJ40QKtDsoPVH8SaiJLUkOZ1oqZ25eVXCfqpd/ix3g9ABQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:34.546291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.10766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0e03663be41fa081e954cd8d6a1673b78cb4e68d5fc93a7171197ae2084d14e","sha256:ac3fb8fd8e5c29139a05c0819424c4c4697ba8fe8d513260083cc3e4e90e6ef6"],"state_sha256":"4d04e06193344ff060e3a72b0ca0b5e8dd391a0b46c1124d81672731bf066dca"}