{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3EQPD2VJ4R3D6TFEVUKDT5I5U4","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":"5db1c7f49a4da6ad948ef73c231bf7e0ec781bf5c57aed47ff87e69faf65577c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-21T10:59:58Z","title_canon_sha256":"468ae2d8a90ec98cc01cfc39f2e70c326aed2ee1b6350ceb1f57e906682d341a"},"schema_version":"1.0","source":{"id":"2605.22314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22314","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22314v1","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22314","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"3EQPD2VJ4R3D","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"pith_short_16","alias_value":"3EQPD2VJ4R3D6TFE","created_at":"2026-05-22T01:04:37Z"},{"alias_kind":"pith_short_8","alias_value":"3EQPD2VJ","created_at":"2026-05-22T01:04:37Z"}],"graph_snapshots":[{"event_id":"sha256:3f1b1f43f848bbc06243cf26bab0d7e90fba43b591f877543cbcfc9883bc21c1","target":"graph","created_at":"2026-05-22T01:04:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.22314/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Answering a question of Goode, we show that $k$-triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a relational language of bounded arity is trivial.\n  We use our collapse result, along with other facts about $k$-triviality and $k$-total triviality, to generate examples of (strongly) $k$-distal theories. The collapse result immediately implies that no stable theory can be strictly $k$-distal for some $k\\geq 3$, partially answering a question of Walker. Moreover, all known examples of non-distal (strongly) $k$-distal t","authors_text":"Mervyn Tong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-21T10:59:58Z","title":"Higher-arity distality and forking triviality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22314","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":"sha256:10040e352ab48f30dd97e268f431cd6dae561bf1039b954374de00958c705abe","target":"record","created_at":"2026-05-22T01:04:37Z","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":"5db1c7f49a4da6ad948ef73c231bf7e0ec781bf5c57aed47ff87e69faf65577c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-21T10:59:58Z","title_canon_sha256":"468ae2d8a90ec98cc01cfc39f2e70c326aed2ee1b6350ceb1f57e906682d341a"},"schema_version":"1.0","source":{"id":"2605.22314","kind":"arxiv","version":1}},"canonical_sha256":"d920f1eaa9e4763f4ca4ad1439f51da731ea6b8ced653dd69c78323a338967b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d920f1eaa9e4763f4ca4ad1439f51da731ea6b8ced653dd69c78323a338967b5","first_computed_at":"2026-05-22T01:04:37.334311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:37.334311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Jo8cC9+er780HQx6UCxSFc9f522/CeDa0x1HdGds+/Xe6uLFveBZju/xFgC17m6zgCJ0xdKgTtd2E97ndycAw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:37.334931Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10040e352ab48f30dd97e268f431cd6dae561bf1039b954374de00958c705abe","sha256:3f1b1f43f848bbc06243cf26bab0d7e90fba43b591f877543cbcfc9883bc21c1"],"state_sha256":"985be4ba2fa4b1162f79a5688dc245e109d3760ad9b4ac1226b4042585afb55b"}