The Riemann hypothesis is false

We demonstrate that the supremum of the real parts of the zeros of the Riemann zeta function is equal to 1, which disproves the Riemann Hypothesis.ADDENDUM 1 (5 June 2024): The latest version estimates I_1 in a more rigorous and clearer way.<br>ADDENDUM 2(a) (8 JUNE 2024): The current version corrects a few minor but potentially confusing typos that were in the previous version. E.g., in Remark 2, eq. (17) was mistakenly referred to as (16). The mathematical arguments all remain as they were.ADDENDUM 2(b) (12 June 2024): The current version corrects a few minor but potentially confusing typos that escaped the previous amendment. E.g., on p. 2, the bound for the sum of I_2 + I_4 in the paragraph after (6) was mistakenly written as &lt;&lt; T^{3/4}log^{2} T instead of &lt;&lt; T^{1/2}log^{2} T. All other parts of the paper remain as they were.ADDENDUM 2(c) (13 June 2024): Recently added is Remark 4, at the bottom of page 4. All other parts of the paper remain as they were.ADDENDUM 2(d) (18 June 2024): In the previous version, the author mistakenly bounded the respective sums in (12) and (13) by &lt;&lt; 1. The correct bound is &lt;&lt; log T, though this doesn't affect the subsequent calculations. The current version addresses this typo. All other parts of the paper remain as they were.ADDENDUM 2(e) (22/06/2024): The current version makes the inequality before (14) a bit more precise.ADDENDUM 2(f) (28 June 2024): In the paragraph between (13) and (14), the author didn't specify the range for r. Though it is obvious from (13), the author thought he should edit the paper and include the range, for the sake of completeness. All other parts of the paper remain as they were.<br>ADDENDUM 2(g) (13 JULY 2024): The current version is exactly the same as the previous three versions, except that the elementary details of the routine partial summation in the estimation of I_1, have now been added. These were kindly requested by some readers. Also, a few typos have been corrected. For example, the previous version mistakenly referred to equation (20) as equation (18).<br>ADDENDUM 2(h) (15 July 2024): The revised version is exactly the same as the previous version. The author only added a few new sentences in Remark4, explaining why Theorem 4.11 of [6] cannot be modified to cater for the sigma = sigma_t arbitrarily close to 0. This was asked for, by some readers.ADDENDUM 2(i) (22 July 2024): The revised version is exactly the same as the previous version. The author only added the details for the derivation of the bound for |chi(sigma+it)|. This was asked for by some readers.ADDENDUM 2(j) (9 September 2024): Some readers pointed out that derivation of the bounds for the sum of (16) and (15) over T/(log^{2} T) &lt; n &lt; T is somewhat obscure. The latest version rigorously addresses this issue. <b>All other parts of the paper remain unchanged.</b><br>ADDENDUM 2(h) (20 October 2024): The paper rigorously estimates the sum of I_1over T/log^{2} T &lt; n &lt; T. This is achieved by appealing to Van der Corput type estimates for exponential sums. A few typos were also corrected.<br>ADDENDUM 2(k) (6 January 2025): The current version corrects a few typos in the previous version, for the sake of clarity. Everything else remains as it was.