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| year = 2017| doi-access = free
}}; see also [https://terrytao.wordpress.com/2016/11/22/an-integration-approach-to-the-toeplitz-square-peg-problem/ Tao's blog post on the same set of results]</ref>
In 2024, Joshua Greene and Andrew Lobb published a preprint improving this result to curves with Lipschitz constant less than <math>1 + \sqrt{2}</math>. <ref>{{cite arXiv
| last1 = Greene
| first1 = Joshua
| last2 = Lobb
| first2 = Andrew
| date = 2024
| title = Square pegs between two graphs
| eprint = 2407.07798
}}
</ref>
=== Jordan curves close to a <math>C^2</math> Jordan curve ===
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