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The visible Universe contains hardly any antimatter, but plenty of matter. The known fundamental forces barely distinguish between matter and antimatter so there must be undiscovered forces that account for this asymmetry. Understanding them, and how they led to an excess of matter, is one of the greatest challenges in fundamental physics. The new forces must influence the shapes of the fundamental particles, making them slightly aspherical. Measuring this distortion – known as the electric dipole – will reveal the existence and nature of the new forces. So far, measurements have detected only spherical particles, showing that their electric dipoles are tiny. We aim to determine the shape of the electron by measuring the energy of its electric dipole in an electric field. This energy is enhanced when the electron is bound up in a polar molecule, an effect of relativity. We will use a gas of ytterbium fluoride molecules, whose enhancement factor is a million, cooled to a temperature of 50 microkelvin. This deep cooling is a new advance that will make our measurement hundreds of times more sensitive than previous experiments. We will be sensitive to fundamental forces lying far beyond the detection range of any particle collider, but we will not need one – the experiment will be done in a small laboratory in London. Our measurement will help distinguish between the many hypothetical models that introduce new forces to explain matter-antimatter asymmetry. Our result will either point to the correct model, or will send theorists back to the drawing board. The specific objective of this proposal is to design and build the apparatus needed to make the measurement, optimise each part of the apparatus, then demonstrate its sensitivity to the electron’s shape. This new instrument will be the main output of the project, together with the research manuscripts and conference presentations that describe the instrument and its performance.