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We describe and implement an algorithm which, given a non-order-preserving braid $\\beta$, confirms this property and returns a proof that $\\beta$ is indeed not order-preserving. Guided by the algorithm, we prove that the infinite family of simple 3-braids $\\sigma_1\\sigma_2^{2m+1}$ are not order-preserving for any integer $m$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.10595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-10-14T15:07:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1083c90a4da4f7ff32af6397cbd1c5d2553bdd8f018d91744d1a37f103bb4e08","abstract_canon_sha256":"95e0b7ecc1381c43f17b59766af391353d96c50d79f86f317f720a9dbc3ab77d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:06.008259Z","signature_b64":"249Bvj+qNKIulFLfruplw6Baop30Iha9UkcaV2S8wzUL8K2IkY6vg2Grwzh79kioond6yjgck+LMiHCjMXZsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e4e49888bd68e36b48ed54b7fb60d4a106f30b354ea10a8acb972d3b34d37ac","last_reissued_at":"2026-06-12T01:09:06.007243Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:06.007243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Searching for non-order-preserving braids algorithmically","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Hannah Turner, Jonathan Johnson, Nancy Scherich","submitted_at":"2024-10-14T15:07:12Z","abstract_excerpt":"An $n$-strand braid is order-preserving if its action on the free group $F_n$ preserves some bi-order of $F_n$. 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