Domain 06 · Yang–Mills Existence and Mass Gap¶

Campaign ID: YM-001
Mathematical status: open problem
Programme state: WP00 promoted; WP01 and WP02 implemented as candidate packages under repository review
Governance: ADR-0009

Canonical challenge¶

For every compact simple gauge group, construct a nontrivial four-dimensional quantum Yang–Mills theory satisfying an accepted axiomatic floor and prove a strictly positive finite physical mass gap.

Existence and mass gap are separate but jointly required theorem trunks. A fixed lattice model, finite-volume gap, perturbative expansion, numerical spectrum, confinement heuristic, or area-law result does not by itself solve the Clay problem.

Programme posture¶

YM-WP00 fixes the official statement, Wightman and Osterwalder–Schrader floor, quantifiers, regulator and reconstruction interfaces, gap normalization, exclusion ledger, and formal proposition schemas. It is a promoted source-normalized non-solution artifact.

YM-WP01 now supplies a twenty-fixture executable false-proof atlas. YM-WP02 supplies a source-normalized theorem and route ledger with explicit composition states and dependency debt. Both packages have completed internal role review but remain unpromoted pending repository CI, independent source-locator review, and Referee review.

Mechanism generation, numerical experimentation, restricted-target selection, and novelty claims remain closed.

Canonical artifacts¶

Claim boundary¶

The programme has not constructed four-dimensional quantum Yang–Mills theory, proved a mass gap, confinement, or an area law, or established that an existing lattice, perturbative, stochastic, numerical, gauge-fixed, or recently claimed construction satisfies the complete theorem target.