{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ZHTTIAXHOUQXZS4GA5KFRSHATI","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":"3578ec32b09893d74dea5d3324246ba26b683f9498c2cfe97d1b2b045647528a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-05T22:03:25Z","title_canon_sha256":"38ff1f60de0b9cf591a1eb6971e2d4935961df6a4aaeaa60fa2c26bba188ce38"},"schema_version":"1.0","source":{"id":"2008.02380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.02380","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2008.02380v1","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02380","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZHTTIAXHOUQX","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZHTTIAXHOUQXZS4G","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZHTTIAXH","created_at":"2026-07-05T01:25:04Z"}],"graph_snapshots":[{"event_id":"sha256:fd2622ab4d83d82d0bcaa3f207bda34a9f65200fe410353c65f060f95629ea5e","target":"graph","created_at":"2026-07-05T01:25:04Z","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/2008.02380/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the $\\{1234, 3412\\}$ pattern-replacement equivalence relation on the set $S_n$ of permutations of length $n$, which is conceptually similar to the Knuth relation. In particular, we enumerate and characterize the nontrivial equivalence classes, or equivalence classes with size greater than 1, in $S_n$ for $n \\geq 7$ under the $\\{1234, 3412\\}$-equivalence. This proves a conjecture by Ma, who found three equivalence relations of interest in studying the number of nontrivial equivalence classes of $S_n$ under pattern-replacement equivalence relations with patterns of length $4$, enumerate","authors_text":"Alexander Lu Zhang, Bella Xu, Quinn Perian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-05T22:03:25Z","title":"Counting the Nontrivial Equivalence Classes of $S_n$ under $\\{1234,3412\\}$-Pattern-Replacement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02380","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:ec6df1a7e3b9ea76a45a410406e11f78c6ad3711d1d12a46faf92f2b77cb6fa4","target":"record","created_at":"2026-07-05T01:25:04Z","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":"3578ec32b09893d74dea5d3324246ba26b683f9498c2cfe97d1b2b045647528a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-05T22:03:25Z","title_canon_sha256":"38ff1f60de0b9cf591a1eb6971e2d4935961df6a4aaeaa60fa2c26bba188ce38"},"schema_version":"1.0","source":{"id":"2008.02380","kind":"arxiv","version":1}},"canonical_sha256":"c9e73402e775217ccb86075458c8e09a36011c96736262c802c4661961c83343","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9e73402e775217ccb86075458c8e09a36011c96736262c802c4661961c83343","first_computed_at":"2026-07-05T01:25:04.533213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:04.533213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9EbkZeKh64IQr4Ll4JUlxfYVNwRzcO+wEns8XyfWrWk5erybIdNRXDoT99u4NBDBAojmZdbTSbTmIBO4T0EPCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:04.533660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.02380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec6df1a7e3b9ea76a45a410406e11f78c6ad3711d1d12a46faf92f2b77cb6fa4","sha256:fd2622ab4d83d82d0bcaa3f207bda34a9f65200fe410353c65f060f95629ea5e"],"state_sha256":"12019791fb547e414c55a6f11882b1a399f93d8388eaf5db4a9b402ad833c923"}