{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"41c5c726dc94391fb42f70fac183da8ca6dd6bc85859b1101a627fe0fb270403","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a6bd9eb310eed689fec63d56ffe8b70ef02c816a012a6add1fdcbeb3823e0d44","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.lattice-chiral.smg-4d","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Particles normally get mass by breaking a symmetry. The question is whether strong interactions can give mass to sixteen massless fermions in four dimensions while every symmetry is kept, through a smooth (continuous) change from the massless phase.","posed_since":"","precise":"For 16 Weyl fermions in 4D (one Standard Model generation with a right-handed neutrino) with interactions preserving Spin(10) or a subgroup with vanishing 't Hooft anomalies, a lattice model may have a gapped phase with no symmetry breaking, no topological order and vanishing bilinear condensates. Determine whether such a phase is reached from the massless phase by a direct continuous transition, which is what a continuum symmetric-mass-generation theory requires.","problem_ref":null,"references":"","settled_by":"Lattice Monte Carlo of a 4D staggered or domain-wall model showing a direct continuous transition from the massless phase to a gapped phase with unbroken symmetry and no Goldstone modes, or a proof that an intermediate phase is unavoidable.","status_note":"Staggered-fermion lattice studies (Butt, Catterall, Hasenfratz and collaborators, 2021-2026) find a massive symmetric phase in 4D; a 2024 gauge-theory study reports a continuous transition, while a 2026 four-fermion study finds the massless and massive symmetric phases separated by an intermediate antiferromagnetic phase.","title":"Continuous symmetric mass generation for sixteen Weyl fermions in 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