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In particular we describe how maps evolve near the creation of a discontinuity.\n  We show that the natural way to create discontinuities in the maps associated with both threshold systems and Cherry flows results in a square root singularity in the map as the discontinuity is approached fr"},"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":"1903.06968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T18:24:47Z","cross_cats_sorted":[],"title_canon_sha256":"1b9fe95b165271fb7da08acc7cfd089403e8967e391c20f14cf1a781016f98db","abstract_canon_sha256":"13816f08f03403759c4a7ad9e6f5d65aab3c70918fea540bbe9708556770dc87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:06.612092Z","signature_b64":"NTzCRh7MyIpj4R21pxnrNPSkstQA9R+ag3STHxWY3D/vMYtqlfxKqYE2ERTtztAGXn0d9mxNPwMyxLJRomVHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a6cda8a333f830843f2dabbec2ffdd6fdb0e0fe145f57fedcef0128f092ba60","last_reissued_at":"2026-05-17T23:51:06.611469Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:06.611469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Creation of discontinuities in circle maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anne C. 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