Critical Audit of an AI-Assisted Norm-Packet Strategy for the Planar Unit-Distance Problem

This note presents a critical audit of an AI-assisted attempt to construct fixed-power lower bounds for the planar unit-distance problem. The attempted construction combines CM norm packets, cut-and-project model sets, and a proposed use of T-split Golod–Shafarevich class-field towers. The audit identifies the decisive gap: the unproved transition from a vaguely invoked "standard" T-split tower to an exact tower with uniform constants. The exponent δ₀ = log A_s / log M_s is heuristically estimated to collapse to roughly 10⁻²⁴ under the original AI's unoptimized parameters, illustrating the gap between formal existence and numerical realizability. Version 1.0. Addendum (June 2026): This note is an independent critical audit of the original AI-generated proof narrative, carried out from publicly available materials. Two works, both predating this deposit (20 May 2026), bear directly on it: the human-verified account of N. Alon, T. F. Bloom, W. T. Gowers, D. Litt, W. Sawin, A. Shankar, J. Tsimerman, V. Wang, and M. M. Wood ("Remarks on the disproof of the unit distance conjecture," arXiv:2605.20695), which supplies the T-split tower input via the Frobenius-cutting argument of Hajir–Maire–Ramakrishna with a rigorous explicit simple-construction exponent ε ≈ 6.24 × 10⁻³⁸; and W. Sawin ("An explicit lower bound for the unit distance problem," arXiv:2605.20579), which optimizes the construction to an explicit exponent n^{1.014}. Sawin's result shows that the numerical smallness emphasized in this audit is a feature of the original, unoptimized construction rather than of the number-field approach itself; the separate question of the finite-n scale at which such a construction overtakes the grid remains delicate. This note stands as an independent diagnosis of the original AI proof as written.