How much noise does it take to make entropy behave? An Evidence Press briefing. Take two independent copies of a random signal, add Gaussian noise to each, and blend the two noisy copies, with a mixing weight that runs from all of one copy to an even blend. Mixing tends to make things more Gaussian, and Gaussians have the most entropy, so a natural guess is that entropy rises smoothly as you blend, with no dips: in mathematical terms, that it is a concave function of the mixing weight. Ball, Nayar and Tkocz conjectured exactly this. This year Luo disproved it, and showed that tiny symmetric bumps on a Gaussian signal can still create a dip at an even blend whenever the signal makes up more than four sevenths of the total variance. Below one half, a positive result was already known. The question was what happens in between. This paper answers it. For any signal fraction below four sevenths, every symmetric signal close enough to a Gaussian gives a concave entropy curve. In noise terms: concavity is guaranteed once the noise variance exceeds three quarters of the signal variance, a signal-to-noise ratio of four thirds. Above that level the paper sharpens the counterexamples, with an exact formula for the dip's curvature. Part of that sign was proposed shortly before, in a public online argument, which the paper cites. It also explains where four sevenths comes from: the fixed point of a sharp Gaussian smoothing inequality. Two cautions. These are local results, and the effects are minute, dips of around ten to the minus thirteen in entropy. And whether exactly four sevenths itself qualifies is still open. The proofs are written out, and checked by standard-library scripts that must catch sixteen deliberately broken copies. This is an anonymous, AI-assisted, unrefereed candidate, published on the third of November twenty twenty-six; its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.