A Polarisation Test to Separate a Primordial Cold Spot from a Void Imprint: Predicted E-Mode Signatures and the Sensitivity a Decisive Measurement Requires

Temperature alone cannot finally separate a primordial Cold Spot from one cast by a late-time void, because both write in the same channel. Polarisation can, in principle: a primordial adiabatic feature carries the temperature-polarisation correlation imprint of the acoustic era, while an integrated Sachs-Wolfe imprint does not. This paper designs that test quantitatively. The primordial hypothesis predicts a radial E-mode signature of amplitude 2.89 microK around the spot; the void hypothesis bounds the corresponding signal below 0.06 microK. For the single spot the sky provides, the stacked-profile uncertainty reaches the three-sigma discrimination level at a polarisation noise of about 6.08 microK per one-degree pixel in the noise-only accounting; holding large-angle systematics at the same level is the harder requirement, and it places the test within the design envelope of proposed satellite missions rather than of the current data. The test is therefore decisive in principle and not yet executable: a plain statement of what to build toward, with the required sensitivity printed. The study is a design computation, simulated and not measured.