{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"70c9885cf0354b2d577cf4ee5e012ade1c646897aac16208780ae6b5f5d8712d","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["75b7b83537c0f3d60e2005415e11f4bb54b1f3dceca46a614d549cae347dca99","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"ee598e2ddd15821ed843f0df49c472e737dd4c38eab8491cbd8efdfecd85f9a2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.yang-mills.mass-gap","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Prove that the quantum theory of gluons exists as a well-defined mathematical object and that its lightest particle has a strictly positive mass. This is the Clay Millennium problem on Yang-Mills theory.","posed_since":"2000","precise":"For every compact simple gauge group $G$ ($SU(2)$ is the minimal case), construct a quantum Yang-Mills theory on $R^4$ satisfying the Osterwalder-Schrader or Wightman axioms, and prove a mass gap: the Hamiltonian $H$ has spectrum contained in $\\{0\\}\\cup[\\Delta, \\infty)$ for some $\\Delta > 0$. Answer: a proof of both statements (Jaffe-Witten formulation for the Clay Mathematics Institute).","problem_ref":"75b7b83537c0f3d60e2005415e11f4bb54b1f3dceca46a614d549cae347dca99","references":"","settled_by":"An accepted proof of existence and $\\Delta > 0$ for every compact simple $G$, as the Clay statement requires; a proof for $\\mathrm{SU}(2)$ alone would be a major partial result.","status_note":"No accepted proof as of 2026; several claimed proofs posted on arXiv have not been accepted.","title":"Existence and mass gap of four-dimensional quantum Yang-Mills theory","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8a53ee950be4ed2496bcf8e9cd4373425548743371aa6ad9133ab6dff9f0066c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"1818d562f35b0ff8e48a4c42b0074ad7300ba49e12ef011a0df00bafb872f663","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"mxG-Uu4j7n6uzOY2QphbevZ-rTfKbdPE8fszt83La1T7bp5pFryYjcsjGo78W6k5tkK0CWvnodsj11Gdx-R7BQ"},"schema":"pubphys.envelope/1"},"record_hash":"8a53ee950be4ed2496bcf8e9cd4373425548743371aa6ad9133ab6dff9f0066c","leaf_index":3458}