Paper · every file published with it

The unfolded zeros of the Riemann zeta function do not form a Riesz basis of exponentials

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Everything published with the paper The unfolded zeros of the Riemann zeta function do not form a Riesz basis of exponentials: the PDF and its source, the two panels of its figure, four reviews with the written answers to their findings (the first review's answers are the last section of its report), and two checkers, programs that recompute the paper's numbers, with the three outputs they recorded. Claude Fable 5.1, a model made by Anthropic, wrote the paper at the owner's direction; its title block is dated September 29, 2026, and its text was revised through October 2. As of October 3, 2026, no human mathematician has read it.

Where its question came from: it is the only paper of the four whose chain of entries begins with a small model's own line. On August 12, 2026, asked which known result a notebook entry resembled, one of the three small models wrote ten words naming Kadec's 1/4 theorem, and the judge kept the line as a question; over five weeks more lines came in, the judge wrote sharper questions from them, and ten programs measured what the questions asked. On September 28 a session the owner started scored six chains of entries and chose this one; the paper says its main theorem answers the question the notebook posed. Every question in the chain was written by the judge, and the theorem and its argument are Claude Fable 5.1's.

The reviews, in the order they were made: Claude Opus 5.5, a different model from the writer's company, on September 29; GPT-6 Astra (OpenAI), the other company's model, the same day, the only review to find a blocking error (Theorem 6.1 had counted ordinates with multiplicity where completeness depends only on the distinct points, and it was restated); GPT-6 Astra again on October 1, which found that Conrey's theorem gives an unconditional lower bound the paper had denied, now in Theorem 6.1(a); and Claude Opus 5.5 on October 2. Every reviewer is an AI model. The reviews keep the private repository's internal names, and their line numbers point to the version each one read, since revised.

What cannot be rerun: both checkers read a table of the first 100,000 zeros that the harness computed and that is not published, so these files do not rerun them. Their recorded outputs are here; the second review reran both programs on that table and matched every printed digit, and the fourth recomputed every printed number on its own. The figure was drawn from values the harness computed, by a program that is not published. The paper reports these numbers separately from its arguments, which do not depend on them.