The series

Published papers

Nine papers, in the order they were written. Eight are finished work; the ninth is a draft and is marked as one on its own page. Each 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. Below them: the arXiv selection held to a different standard, two companion papers written after the series closed, and three feedback pieces on results from outside the programme.

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.
Read the full text →
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.
Read the full text →
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.
Read the full text →
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.
Read the full text →
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.
Read the full text →
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.
Read the full text →
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.
Read the full text →
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.
Read the full text →
Paper 9 · draft
The Wall Runs at the Euler Product
An Exhaustive Census of Ten Dirichlet L-Functions, the Class That Provably Cannot Keep Its Zeros, and the Near-Collision Picture That Both Refute
A draft, and the only one here. Both sides of the Euler-product boundary measured by one instrument over one range: 71,271 zeros on the critical line, 1,140 missing from the matched counterexample — and a finite test on the coefficient list that tells the two classes apart before a single zero is computed.
Read the full text →

The official release

A 98-page selection went through thirteen blind referee rounds, plus one cross-model control round, and is the version prepared for arXiv. It carries 28 of the programme's 62 claims — the ones that survived that process. The other 34 live on this site and nowhere else.

The arXiv paper →

Two more papers, after the series closed

A measured design curve for the whole window-argument family, and the programme's oldest filter turned from a reading into a decision procedure and run over every banked result.

The nine-point paper →The elementarity screen →

Feedback on results from outside the programme

Three replies, audited to the same standard as everything above: Anthropic's simple-zeros theorem, @kaizero_ainta's refinement of it, and Kazushi Mizutani's geometric reinterpretation of the hypothesis.

Anthropic feedback →kaizero_ainta feedback →Mizutani feedback →

And the pictures that belong to no paper

Seventeen renders came out of the closing sessions and were never promoted to figures of any paper — the walk drawn near a zero, the skeleton, the spikes, the circle. Several of them record a correction rather than a result. They are here because this site carries the workbench.

Open the workbench →