mass-gap-inconsistency

A minimal reductio argument identifying a logical tension in the standard formulation of the Yang–Mills mass gap problem.

This repository documents a logical tension in the standard formulation of the Yang–Mills mass gap problem as posed by the Clay Mathematics Institute.

Under the assumptions of a single vacuum and an intrinsically four-dimensional mass gap, known observations concerning vacuum energy, under standard interpretations, lead to a contradiction.
The repository presents a minimal reductio argument that makes this tension explicit.

Purpose

This work does not propose a solution to the Yang–Mills mass gap problem. Its purpose is to clarify assumptions that are implicit in the current problem formulation and to show where these assumptions conflict with established physical observations.
The aim is to separate the mathematical content of the problem from physical assumptions that may be too restrictive in light of current observations.

Contents

• paper/
  A short (2–3 page) inconsistency note presenting the core reductio argument.
  The PDF is the primary document of this repository.

• logic/
  Explicit statements of the axioms, theorem, and proof structure underlying the inconsistency argument.

• physics-background/
  Supplemental notes providing physical context (vacuum energy, interlayer interpretations).
  These materials provide intuition only and are not used in the theorem, proof, or any logical step.

• diagrams/
  Visual representations of the structural tension identified in the paper.

Scope and Limitations

• This repository does not challenge the validity of experimental observations.
• It does not introduce new physical theories or models.
• It does not claim to resolve the mass gap problem.

The sole claim is that the standard axiomatic framing of the problem, when read literally, is in logical tension with minimal and widely accepted physical facts.

Status

This repository is intended as a transparent and minimal documentation of a foundational issue in problem formulation.
Further theoretical developments, if any, are beyond its scope.
The repository is stable and not intended as an evolving theoretical or interpretive proposal.