The series
Published papers
Eight papers, in the order they were written. Each one is here in full — main text, figures with commentary, and the supplementary audit layer that records how every number was checked and what was later corrected.
These are workbench documents. This site is a record of a workbench, not a record of finished results. Rigorous standards were applied to the arXiv paper alone.
Paper 1
Packet Centroids
A Smoothing Identity and a Displacement Sum Rule
The framework and the census. Partial sums of ζ travel in packets; each packet's centroid misses ζ by a computable amount. Two theorems, a seven-window census, and the spacing statistics that started everything.
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Paper 2
Packet Centroids II
The Fresnel Mechanism, Coil Geometry, and Zero Conditions of the Partial-Sum Walk
What the error term actually is, measured to a parameter-free prediction, plus the coil law and the first structural obstruction: every line-selective invariant of the walk turns out to be deterministic.
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Paper 3
Packet Centroids III
The Aperture-Crop Law, Carrier Dynamics, and the Euler-Product Stem
Small-value geometry. How close ζ comes to zero on a fixed line, why one close pair of zeros governs it, and the first construction in the programme that separates ζ from its counterexample by using multiplicativity at step one.
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Paper 4
Packet Centroids IV
The Spectral-Dual Support Law, the Prime-Steering Bridge, and the Primitivity Frame
The counterexample put under the instruments as the measured object. A zero set reads its own coefficient arithmetic back, to 12–14 digits, on five different constructions.
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Paper 5
Packet Centroids V
The Per-Event Witness Law, the Three-Register Count, and the Measured Gap
An exact per-event law of the critical line — and the same motion that proves it exact shows it cannot do the job, for a reason that is measured rather than asserted.
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Paper 6
Packet Centroids VI
The Multiplicativity Dial, the Value Region, and the Shape of What Is Missing
A controlled experiment on the Euler-product boundary, run on a family that crosses it continuously. It returns a clean null — and corrects two of the programme's own conclusions.
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Paper 7
Packet Centroids VII
The Positivity Register — What an Inequality Can and Cannot See
Weil and Li positivity, calibrated against certified counterexamples for the first time. It detects the class from the sign of one eigenvalue, then prices itself out of the only use that would have mattered.
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Paper 8
The Symmetry Register
What a Reflection Can and Cannot See
The matched half of Paper 7: the symmetry side of the same sentence, and the closing of the two-arm route.
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