About this project
Editorial policy updated: 24 October 2026. Source-inspection dates belong to individual records; this policy date is not a scientific review date.
yangmills.qft.org is an independent educational and research-navigation project about Yang–Mills existence and the mass gap. Its aim is to help a graduate student enter the literature and help a researcher identify the precise scope of a result quickly.
The intended starting point is no more than two semesters of quantum field theory, including QED and gauge theory. Mathematical ideas beyond that background are introduced when they become necessary, with bridges to distributions, spectral theory, measures, semigroups, and uniform estimates.
One problem, two ways into it
Section titled “One problem, two ways into it”The course develops a sequence of physical questions: what the gap means, what correlations reveal, why a cutoff helps, and what must survive its removal. The research atlas starts from individual contributions and their assumptions.
Both routes use the same distinctions. A beginner should not have to unlearn an exaggerated claim later. A specialist should be able to find the dimension, gauge group, regulator, model, and remaining step without decoding promotional language.
The formal target comes from the official Jaffe–Witten problem description. The project is not affiliated with the Clay Mathematics Institute and does not adjudicate the Millennium Prize.
What the evidence labels mean
Section titled “What the evidence labels mean”| Label | What it communicates |
|---|---|
| Theorem | The source states a mathematical result under identified hypotheses |
| Numerical | The result rests on computation with statistical or systematic considerations |
| Controlled | An analytic approximation is tied to a specified regime or hierarchy |
| Method | A construction, algorithm, identity, or framework enables further work |
These categories are not a ranking of intellectual value. They explain how an argument supports its conclusion. A journal article can fall into any category; a preprint can state a theorem. Publication information is therefore kept separate.
What “source scope checked” means
Section titled “What “source scope checked” means”The text is prepared with AI assistance. Each source record must say what was actually inspected: metadata, abstract, exact statement, selected proof sections or a more extensive reading. A generic “reviewed” label is insufficient. These editorial checks are not independent expert verification of an entire proof, simulation, or software implementation.
Each dossier identifies its source, exact version, inspected locator, check date, setting, conclusion, and limitations. Where access limits the available detail, the text narrows its claim rather than inventing assumptions. Mathematical derivations included for teaching are distinguished from theorems attributed to a paper.
An author’s claim, the site’s technical assessment, evidence of community acceptance, and formal Clay recognition are separate states. None is inferred from the others. Conditional results retain their premises; numerical estimates retain their uncertainty; controlled approximations retain their regime. Publication is recorded independently of all these distinctions.
Primary papers remain the authority for their results. Readers should consult the linked statements before using a claim in research.
Selection and update principles
Section titled “Selection and update principles”The initial collection is curated. Inclusion reflects usefulness for understanding a direction and its relationship to the target; it is not a declaration that one approach is uniquely closest to a solution. Foundational work and recent work can serve different purposes on the same page.
Dates identify what happened: first submission, revision, publication, or editorial review. A new journal reference should update bibliographic status without silently changing the scientific summary. A revised theorem should trigger a review of every page that relies on its assumptions.
The research notes show the current selection. They do not promise an automatic monitoring service. The status page states the collection’s present assessment and its limits.
Making corrections useful
Section titled “Making corrections useful”A useful correction identifies the page and sentence, the proposed replacement, and a primary reference with a theorem, equation, section, or table location. If the issue concerns scope, specify which quantifier, dimension, limit, boundary condition, or evidence category changes.
Editorial corrections should preserve a dated account of material changes and update linked summaries consistently. Uncertain claims should be narrowed or marked unresolved while the source is checked. A claim of a full solution needs the same explicit accounting of assumptions and limits as any other result.
This version does not operate a public submission form or represent an established advisory board. The standards above describe how future maintenance should remain accountable as the project develops.
Start with the problem, inspect the proof map, or open the primary bibliography to follow a result directly.