OpenAI · 282-01 · 2026-09-26 · Mathematical physics
Scale and conformal symmetry in four-dimensional operational quantum field theory
preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026
Family 282. Scale-to-conformal enhancement in four-dimensional QFT.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Low-energy completion. Field-theory or renormalization language is not an ultraviolet completion of this series. Oai282-A does not verify Family 282 and does not construct an ultraviolet completion. Oai282-B does not verify Family 282 and does not construct an ultraviolet completion. Oai069-A does not verify Family 069 and does not construct an ultraviolet completion. O.1 stays NOT_CLOSED. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. Oai069-A · Oai282-B · Oai282-A · VI · III · XVI-P
Under the stated bounded-local-net and field-reconstruction hypotheses, proves that scale symmetry implies local conformal symmetry for four-dimensional unitary positive-energy theories with a discrete bounded-below scaling spectrum of finite multiplicity, finite scaling support and a physical local scale current. The stress tensor has a traceless improvement with unchanged spacetime charges. The conclusion concerns local Ward identities, not a global conformal action on the whole net.
We prove that scale symmetry implies local conformal symmetry for a class of four-dimensional unitary, positive-energy quantum field theories with a Poincaré- and scale-invariant vacuum. The class has a discrete, bounded-below spectrum of scaling dimensions with finite multiplicities, and each original field has finite scaling support. The original fields and their adjoints have compatible affiliated realizations in a causally commuting bounded local net, and a physical local dilatation current generates scale transformations through its local Ward identities. The operational framework admits sharply localized reconstructed fields after their joint products and compatible affiliated realizations in the same net have been established. Under these hypotheses, the stress tensor admits a symmetric, conserved, traceless improvement with unchanged translation and Lorentz charges. The corresponding conformal currents satisfy unbroken local Ward identities on the physical field algebra. The conclusion is local; integration to a global conformal action on the whole bounded net remains a separate question.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. Family 282's scale-to-conformal claim is a source record. Oai282-A does not verify it. Oai282-B constructs one free local action and does not verify the claim, integrate the generators, or construct a metric. No compilation is asserted.
Low-energy completion
Scale-to-conformal enhancement is not an ultraviolet completion
Family 282 records a conditional scale-to-conformal theorem in four-dimensional quantum field theory. The stated conclusion is local Ward identities, not a global conformal action. That theorem is not an ultraviolet completion of the Enter series, not Einstein dynamics, and not spacetime emergence. Oai282-A records the claim and does not verify the preprint. Oai282-B constructs the free local action and does not verify the preprint. Coverage in one homogeneous class is not a general scale-to-conformal theorem. The catalogue reports no Lean scope note. The authors are OpenAI. The companion does not verify those proofs. O.1 stays NOT_CLOSED.
Low-energy completionOai282-B free Ward actionOai282-A local Ward certificateVII-H free-field susceptibilityEm02-E relational lapseEn05-C tensor-free comparisonIII jet descentVI low-energy sheet