{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"babc38a8b6b4c6c4d9fea4394e36c3b1b80ecb03eb2935d3e5e61123dca0f45c","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ec94f27ed8efde92a057c2f8215ebc7e29df200d3fe1aaa138b0e8c6a1075c95","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"qi.monitored-circuits.charge-sharpening-universality","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"When circuits conserve a quantity like total charge, a second transition appears: below it, an observer cannot quickly learn the total charge from the measurements. Which universal class this learning transition belongs to is not settled.","posed_since":"2022","precise":"In $1+1\\mathrm{D}$ monitored circuits conserving $U(1)$ charge, a charge-sharpening transition at $p_{\\#} < p_{c}$ separates phases where the total charge can or cannot be inferred from the measurement record in time $\\operatorname{O}(L)$. Determine its universality class; a Kosterlitz-Thouless-type field theory was proposed (Barratt et al. 2022).","problem_ref":null,"references":"","settled_by":"Large-scale numerics of finite-q circuits matched to field-theory predictions for the scaling of charge variance and learning time.","status_note":"","title":"Universality of the charge-sharpening transition in U(1) monitored 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