The Riemann Program

An independent, computer-assisted research program on the Riemann Hypothesis (RH), offered as a serious, fully-traceable contribution to one of mathematics' hardest open problems.

This is not a claimed proof. It is a long, honest investigation that reduces RH to a single named, classical open input, and maps every wall, dead end, and self-correction along the way — with reproducible code and a complete record.

Governing principle: a false victory would be worse than a failure. Where the program reached a rigorous result, it says so. Where it hit a wall, it names the wall. Where it fooled itself and corrected, it records the correction.

Start here

Read	What it gives you
Human explanation	RH and what we learned, in plain language — layer by layer, no proof assumed
Program map	The whole road traveled, from the survey to the wall, in one picture
Master plan	Audit of the corpus, its structure, and the open route ahead
Complete program summary	Every paper, phase, no-go, and wall, end to end
No-go list	The permanent registry of everything that failed or hit a wall
Papers index	The 36 publishable papers, in order, with what each one establishes

How the work is organized

The program has two layers:

• Research Programs 1–9 — 01-context/: nine large computational research programs (627 tasks). The empirical base.
• Program 10 — 03-research/: the theoretical program built on that base, run as a sequence of numbered phases, currently through phase 76.

Supporting material: the validated computational core (02-foundations/), the publishable papers (04-papers/, 36 of them, catalogued in 04-papers/README.md), external reference material (00-references/), and the planning and audit notes (05-meta-and-planning/).

Where the program ended

The program reduced RH, by a chain of proved equivalences (the arithmetic Pick/Nevanlinna architecture, ARP-P — see paper 36), to a single classical open input: the Li–Keiper criterion, $\lambda_n \ge 0$ for all $n$. Fourteen of the chain's fifteen steps are fully closed; the remaining one terminates exactly at that criterion. Being equivalent to RH, it carries the full difficulty of the Hypothesis — the reduction closes nothing by itself, but it is the precise place every major route explored in this corpus independently arrives at (see 00-MAP.md and NO-GO-LIST.md for the six structural walls, MW-1 through MW-6, that block every other approach).

Along the way the program produced genuinely new RH-independent mathematics (the ω-class / multiplicative-chaos dictionary, the information barrier, Pontryagin rigidity, an unconditional finite bottom, a Stepanov almost-periodicity theorem, among others) and a complete, precise map of the obstructions.

Status

Area	Status
Arc A / ω-class (Research Programs 1–9)	Documented; descriptive, did not beat convexity
Localized Weil detector	Rigorous in parts; the finite-defect route closed
Program 10 (phases 0–76)	Dense theory, the full no-go catalogue, and the reduction to Li–Keiper
RH itself	Open. The wall now has one name.

Philosophy

Read everything here as an autonomous mathematical program: not a promise of victory, but a serious collaboration with the community to push a very hard problem forward — with traceability, honesty, and a memory of the useful failures.