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The Long Shot: Firing at Riemann Zeros from the Prime Beat Alone

Year: 2026
Type: preprint
Abstract: One shot per zero, from the zero's number alone. The prime beat, every prime and prime power to 100,000 played as a bank of tones, says where Riemann zero number N sits, in a twentieth of a second at any height. Every shot was sealed with SHA-256 before the true zero was worked out. The proof structure, rung by rung: 1. The count (identity). Riemann's counting formula places every zero once the full prime bank is known. 2. The shot (derived). Cut the bank and solve for zero N: one shot per zero, nothing near the target looked at first. 3. The lock (derived). The shot lands on zero N itself whenever the primes left out add up to less than half a gap. 4. The seals (measured). 155 of 155 sealed and record shots on the right zero, from zero one million to zero number 10^36 (Bober and Hiary). Odds of luck about 1 in 5 x 10^22. 5. Every zero in a row (measured). The first 100,000 zeros: temperature on the right zero 100,000 times out of 100,000. Odlyzko's 30,000 published zeros: 99.4% or better, and 100% with the bank to 10 million. 6. The line (measured). Every zero hit, from zero 1 to zero number 10^36, sits on the half line. 7. The tracker (measured). Holding the miss steady, the bank grows as the height to the power 0.48. 8. The fold (identity). The Riemann-Siegel formula folds the sum at the square root of the height, power 0.5. The tracker's pace lands on the fold's. 9. The curl in the defects (derived and measured). The miss turns at the pitch of the first prime past the cut; at the fold that pitch is exactly one half. 10. For every height (the step above, for the referee). The lock holding at every height, with the bank growing at the fold's pace, is the step a referee rules on; the university test paper included here is built to check it independently.
DOI: 10.5281/zenodo.24005419
Language: English
Open Access status: green
OpenAlex ID: W7225405955
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