Inter-universal Teichmuller Theory III
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・Changed various references to "Remark 3.9.5" throughout the paper to references to "Remark 3.9.5, (i)" (5 instances)

・Updated the Acknowledgements

・Added Remark 1.1.2

・Added Remark 1.2.5

・Slightly modified the third display of Proposition 3.1, as well as the discussion immediately following this display

・Rewrote various portions of Remark 3.1.1, (iii)

・Slightly modified the final portion of Remark 3.1.1, (iv)

・Corrected misprints (7 instances) in Remark 3.9.1, (i), (ii) ("n" ---> "n_{v_Q}")

・Rewrote Remark 3.9.4 and added references (2 instances) to Remark 3.9.4 at the beginning of Remark 3.9.6

・Rewrote Remark 3.9.5 and added references (2 instances) to Remark 3.9.5 at the end of Remark 3.12.2, (v)

・Slightly modified the discussion following the first display of Remark 3.9.7, (i)

・Rewrote Remark 3.9.7, (ii), and added (iii)

・Slightly modified the final portions of the discussion of "IPL" and "SHE" in Remark 3.11.1, (iii)

・Slightly modified the discussion of Remark 3.11.1, (iv)

・In the Step (xi) of the proof of Corollary 3.12:

　・Slightly modified the discussion of log-shells in Step (xi-a)

　・Slightly modified the discussion of hulls in Step (xi-c)

　・Added references to Remark 3.9.5 [together with supplementary explanatory text] in Step (xi-d)

・In Remark 3.12.2, (ii), slightly reworded (c^{itw}), (d^{itw}), (e^{itw}), (f^{itw}), (b^{toy}), (c^{toy}), (e^{toy}), (f^{toy})


Inter-universal Teichmuller Theory IV
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・Updated the Acknowledgements

・Corrected a misprint in the display of the statement of Corollary 2.2, (iii) (and slightly
　modified the surrounding explanation)