Mass gap > 0

For any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on ℝ⁴ and has a mass gap Δ > 0. Construct the theory in a mathematically complete way (Wightman or equivalent) and prove the gap.

GATE STATUS (honest): Clay Yang–Mills existence and mass gap remain OPEN. Classical asymptotic freedom (Gross–Wilczek / —gate→ Mass gap > 0

GATE STATUS (honest): Wilson 1974 lattice YM / Wilson-loop area law is classical scaffolding for confinement and motivat —gate→ Mass gap > 0

GATE STATUS (honest): Osterwalder–Schrader 1973/75 reconstruction is classical Euclidean→Wightman scaffolding for constr —gate→ Mass gap > 0

GATE STATUS (honest): Glimm–Jaffe constructive QFT proves rigorous existence of nontrivial interacting continuum scalar —lemma→ Mass gap > 0

GATE STATUS (honest): Classical 2D pure Yang–Mills is exactly solvable and has a positive mass gap (Migdal / Witten 1991 —lemma→ Mass gap > 0

GATE STATUS (honest): Balaban UV stability / block-spin RG for lattice YM controls ultraviolet continuum limits in finit —gate→ Mass gap > 0

GATE STATUS (honest): Polyakov 1975 establishes confinement + mass gap for compact U(1) in 3D via monopole plasma. It do —gate→ Mass gap > 0

GATE STATUS (honest): Creutz 1980 gives lattice Monte Carlo evidence of confinement (area law / string tension) in SU(2) —gate→ Mass gap > 0

GATE STATUS (honest): Schwinger 1962 gives an exact abelian 1+1-dimensional example of dynamical photon mass / charge sc —gate→ Mass gap > 0

GATE STATUS (honest): Seiberg–Witten 1994 gives an exact low-energy solution of N=2 supersymmetric SU(2) Yang–Mills (mon —gate→ Mass gap > 0

GATE STATUS (honest): Fradkin–Shenker 1979 establishes analytic connection of confinement and Higgs regimes in lattice g —gate→ Mass gap > 0

GATE STATUS (honest): ’t Hooft 1974 planar large-N organizes non-abelian gauge perturbation theory and motivates confine —gate→ Mass gap > 0

OPEN gate update (Cycle 106): BPST 1975 instantons are classical topological scaffolding for non-abelian YM; they do NOT —gate→ Mass gap > 0

OPEN gate update (Cycle 112): ADHM 1978 constructs the full classical instanton moduli for SU(2) YM; it does NOT prove c —gate→ Mass gap > 0

OPEN gate update (Cycle 118): Uhlenbeck 1982 gives classical removable singularities / ε-regularity for YM connections; —gate→ Mass gap > 0

GATE STATUS (honest, Cycle 124): Donaldson 1983 ASD Yang–Mills → 4-manifold topology is classical geometric scaffolding; —gate→ Mass gap > 0

GATE STATUS (honest, Cycle 130): Atiyah–Bott 1983 Yang–Mills over Riemann surfaces is classical 2D gauge / moduli scaffo —gate→ Mass gap > 0

GATE STATUS (honest, Cycle 135): Taubes 1982 ASD/SD Yang–Mills existence on suitable 4-manifolds is classical differenti —gate→ Mass gap > 0

OPEN gate update (Cycle 140): Atiyah–Hitchin–Singer 1978 gives classical ASD moduli index scaffolding for Yang–Mills; it —gate→ Mass gap > 0

OPEN gate update (Cycle 145): Narasimhan–Seshadri 1965 gives classical stable-bundle / unitary-representation scaffoldin —gate→ Mass gap > 0

OPEN gate update (Cycle 150): Hitchin 1987 gives classical self-duality/Higgs moduli scaffolding on Riemann surfaces; it —gate→ Mass gap > 0

OPEN gate update (Cycle 155): Uhlenbeck–Yau 1986 gives classical Hermitian–Einstein / DUY scaffolding for YM/gauge theor —gate→ Mass gap > 0

OPEN gate update (Cycle 160): Corlette 1988 gives classical harmonic-metric / flat reductive G-bundle scaffolding; it do —gate→ Mass gap > 0

OPEN gate update (Cycle 165): Simpson 1992 gives classical Higgs-bundle / flat local-system (nonabelian Hodge) scaffoldi —gate→ Mass gap > 0