Domain 06 · Yang–Mills Existence and Mass Gap

Campaign ID: YM-001
Mathematical status: open problem
Programme state: WP00 promoted; WP01 promoted as eliminative infrastructure; WP02 promoted as theorem/dependency interface ledger
Research routing: native MATHSOLVE restricted-target selection open only against YM-D001 through YM-D005
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 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. Their July 2026 package was integrated through PR #115 and passed Programme policy CI. The later MATHFORGE provider audits independently resolved the imported-source locator/scope obligation and the four moving external-source debts YM-D006 through YM-D009.

The post-merge disposition promotes WP01/WP02 only as bounded research infrastructure. YM-D001 through YM-D005 remain open mathematical debts. The current routing gate opens restricted-target selection in grandchallenge/MATHSOLVE only so that one of those debts can be attacked under an exact target contract. Unrestricted mechanism generation, free-standing numerical experimentation, novelty claims, and terminal solution claims remain closed.

A protected 2026-09-18 D003 supplement now admits the Balaban four-dimensional large-field/ultraviolet-stability spine as bounded theorem input and records the Magnen–Rivasseau–Sénéor fixed-infrared-cutoff UV-removal construction with its explicit proof-completeness, IR, topology, and OS limitations. D003 therefore no longer treats 4d large-field control as wholly absent; its live residual frontier is infrared/infinite-volume removal, uniqueness/full continuum identification, complete OS reconstruction, and physical scale identification.

Canonical artifacts

Claim boundary

The programme has not constructed four-dimensional quantum Yang–Mills theory, proved a physical mass gap, confinement, an area law, regulator-independent continuum control, or a complete Osterwalder–Schrader limiting hierarchy. Promotion of WP01/WP02 changes research routing only; it does not establish that any open dependency debt has been solved.