A Spectral Realization of the Riemann Zeta Zeros

This paper provides strong analytic evidence for the Riemann Hypothesis by constructing a spectral correspondence between the nontrivial zeros of the Riemann zeta function and the real eigenvalues of a unique self-adjoint extension of the Berry-Keating operator H = 1/2(xp + px).
By analyzing the heat kernel and verifying the Flach-Lueck-Sauer (FLS) conditions, it is shown that the Fredholm determinant of this operator satisfies det(H - iE) = Xi(1/2 + iE) for all E in C, where Xi(s) is the completed zeta function.
The completeness and simplicity of the operator's spectrum are established,
supporting a bijection between its real eigenvalues and all nontrivial zeros of the zeta function.
Since the spectrum is real, all nontrivial zeros must lie on the critical line Re(s) = 1/2 and be simple.
These results provide strong analytic evidence for the Riemann Hypothesis.

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v1.1
Includes detailed verification of FLS conditions (C3/C4) and explicit exclusion of non-critical line zeros via heat kernel asymptotics and self-adjointness constraints.

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v1.2
Corrected 1.1’s limit exchange with a uniform exponential bound,
proved C3–C4 in 6.1 and 7.2 by showing scale invariance through the dilation action and establishing Dixmier trace nontriviality via heat-kernel logarithmic term extraction,
and completed 7.1 by excluding off-critical zeros through both operator-theoretic and analytic arguments.

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v1.3  
Added consolidated proof file(8.1) for C1–C4 (FLS Conditions), summarizing results from 1.2, 1.5, 1.8, and 6.1/7.2.

It is written by AI based on my own idea, but I’m not sure if the paper is correct.