The Mirror: verified classical structure of the Riemann zeta function - checks, figures, and verification reports
收藏资源简介:
Expository and computational verification collection around the Riemann functional equation. No new theorems are claimed and the Riemann Hypothesis is not claimed in either direction. Contents: the Mirror note (the functional equation Lambda(s)=Lambda(1-s) as the proven stage; verified zero locations as the finite load-bearing layer; RH honestly open, with an explicit-formula demonstration of why zero locations rather than symmetry control finite-scale applications); machine checks at 30 decimal places (functional equation, mirror pairing of the first 50 nontrivial zeros, special values, the right-edge halving law); a fresh sieve reproduction of Chebyshev's bias to 10^8 including Leech's first lead change at x=26,861; a partial-Euler-product illustration of the Deep Riemann Hypothesis framing of Aoki-Koyama (J. Number Theory 2023) for L(s,chi_4) at s=1/2; an independent verification that the first 1000 nontrivial zeros lie on the critical line (Hardy Z sign changes matched against a Backlund/Turing strip count); six figures; and independent re-run reports of the author's related verification studies, including a Weil-positivity numerical study whose headline is that positivity searches cannot detect an RH violation by roughly 35 orders of magnitude. All scripts are standard-library-plus-mpmath/numpy Python and regenerate every result and figure.



