Add moving sofa constant

constants/41a.md

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+# Moving Sofa Constant
+
+## Description of constant
+
+The moving sofa constant $A$ is the maximum area of a connected, rigid planar shape that can maneuver through an L-shaped corridor of unit width. 
+The corridor is formed by two semi-infinite strips of width 1 meeting at a right angle. 
+The problem asks for the shape of the largest area (the "sofa") that can be moved from one end of the corridor to the other by a continuous rigid motion (translation and rotation).
+
+## Known upper bounds
+
+| Bound | Reference | Comments |
+| ----- | --------- | -------- |
+| $2 \sqrt{2}$ | [Hammersley1968] | Initial upper bound |
+| 2.37 | [kallus2018] | The current best upper bound, proved using a computer-assisted proof scheme. |
+
+## Known lower bounds
+
+| Bound | Reference | Comments |
+| ----- | --------- | -------- |
+| $\pi/2 + 2/\pi$ | [Hammersley1968] | Initial lower bound |
+| 2.2195 | [Gerver1992] | The current best lower bound |
+
+## Additional comments
+
+It was claimed in a recent preprint [baek2024] that Gerver's sofa [Gerver1992] is the optimal solution, which if true would solve the moving sofa problem.
+
+## References
+
+- [Hammersley1968] Dr. J. M. Hammersley (1968). 
+On the enfeeblement of mathematical skills by modern mathematics and by similar soft intellectual trash in schools and universities. Bulletin of the Institute of Mathematics and Its Applications. 
+4: 66–85. See Appendix IV, Problems, Problem 8, p. 84.
+
+- [kallus2018] Kallus, Y., & Romik, D. (2018). 
+Improved upper bounds in the moving sofa problem. 
+Advances in Mathematics, 340, 960-982.
+
+- [Gerver1992] Gerver, Joseph L. (1992). 
+On Moving a Sofa Around a Corner. 
+Geometriae Dedicata. 
+42 (3): 267–283.
+
+- [baek2024] Baek, J. (2024). 
+Optimality of Gerver's Sofa. 
+arXiv preprint arXiv:2411.19826.
+
+## Contribution notes
+
+Prepared with assistance from Gemini 3 Pro.