{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"775ec411cea1277ec3877bc84e427357d8681809e9e1453b197607d9994a2710","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"2159c8e423a4ff7fc7d16fd0bdbec8914f29fc85ea76cca907e1c32b0bba7904","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"grav.qft-curved-backreaction.quantum-focusing","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"The classical singularity theorems assume energy is never negative, which quantum fields violate. A quantum replacement based on the entropy of the fields plus the area of a surface would restore the theorems, but its original strong form fails in simple models and a weaker form is still a conjecture.","posed_since":"2022","precise":"Define the generalized entropy $S_{\\mathrm{gen}} = A c^3/(4 G \\hbar) + S_{\\mathrm{out}}$ of a codimension-2 surface (entropy in units of $k_{\\mathrm{B}}$, $S_{\\mathrm{out}}$ the entropy of fields outside it) and the quantum expansion $\\Theta$ as its variation per unit transverse area along a null congruence with affine parameter $\\lambda$. The original quantum focusing conjecture dTheta/dlambda <= 0 (Bousso, Fisher, Leichenauer, Wall 2015) has explicit counterexamples in two-dimensional dilaton gravity coupled to quantum fields (2025); the restricted version requires dTheta/dlambda <= 0 only where $\\Theta = 0$ (Shahbazi-Moghaddam 2022). Prove the restricted conjecture for interacting quantum fields coupled to semiclassical gravity in spacetime dimension $d > 2$, or construct a violation.","problem_ref":null,"references":"","settled_by":"A proof of restricted quantum focusing in $d > 2$ for interacting fields, or an explicit violating configuration.","status_note":"Restricted focusing is proved in braneworld models (2022) and in JT gravity coupled to a field theory, where the original conjecture is also shown to fail (Franken, Kaya, Rondeau, Shahbazi-Moghaddam, Tran, arXiv:2510.13961, 2025); the general case in $d>2$ is open as of 2026.","title":"Prove the restricted quantum focusing conjecture for semiclassical 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