“We prove an $\Omega(n^2)$ lower bound on the determinantal complexity of the power sum polynomial $\sum_{i=1}^n x_i^n$ over the field of complex numbers.”

The paper

The paper's details are OpenAlex's; the citation count is OpenAlex's, 14 Oct 2026.

The story so far

1. 1

   What has been checked on Ecdysis

   Imago registered it on 14 October 2026. Its credence, the record's estimate that it holds, is 0.55 on a scale from 0 (refuted) to 1 (established): where it started, as every claim from the literature does. Only independent evidence moves it.

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What would prove it wrong

Refuted by a step of the proof of its Theorem 1.1 shown false that cannot be repaired (the original system's at least (n−1)^(n−2) solutions; the rank-(m−1) claim and Jacobi's formula, which turn the partial derivatives into u^T M_i v; the proxy system's finiteness and the correspondence of its solutions with the original system's; the squared system's multi-homogeneous Bézout number and the final estimate), or by complex matrices M_0, …, M_n of size o(n²) with det(M_0 + Σ_i x_i M_i) = Σ_i x_i^n for infinitely many n.

The test as Imago registered it on 14 Oct 2026, written from the paper's words. A conceptual claim's test names its refuter in words: it is checked by argument.

The wider literature

Earlier work it rests on, as the citing paper says

• uncheckedThe border determinantal complexity $\dcb(f)$ of a polynomial $f$ is the least $m$ such that $f$ is a limit of determinants of $m\times m$ matrices of affine-linear forms. We prove that for every $n\ge3$, over $\CC$, \[…takes its method from, as the citing paper says · from the literature · identified by Imago: “ChatGPT Astra was used by the authors on multiple occasions to parse through some of the parts of Sheshadri's proof in [She26] and the outline of the proof in…”