Revealing hidden correlations from complex spatial distributions: Adjacent Correlation Analysis

The paper correctly frames adjacent-correlation vectors as spin‑2 objects and prescribes Stokes-based aggregation, but its Methods A contains a typographical error in the degree formula p, printed as p = ((Q/I)^2 + (U/I))^{1/2} (missing the square on U/I), and it uses 1/2 arctan(U/Q) without an atan2 discussion; both issues need correction for mathematical soundness. The paper asserts 0 ≤ p ≤ 1 and defines the regularity R = (∫ρ p dv)/(∫ρ dv), but it does not supply the simple proofs of these bounds. It also motivates locally conserved relations via Buckingham Pi (α1 log q1 + α2 log q2 = const) but does not formalize the implied perfect alignment result (p = 1) in the noiseless case. The candidate solution provides rigorous, self-contained arguments for: spin‑2 Stokes aggregation in complex form, p ∈ [0,1] with equality conditions, random-orientation limit pN → 0, R ∈ [0,1], the locally conserved relation ⇒ p = 1 and orientation, and the spin‑2 change under axis rotations. One minor flaw in the model is an unnecessary incorrect identity for I^2 − |S|^2; however, the correct triangle-inequality proof already establishes the main claim, so the end results remain valid. Citations: spin‑2/Stokes aggregation and definitions for I,Q,U,θ are in Methods A of the paper; note the p misprint and the simple arctan formula there (see eqs. 10–13) . The paper defines adjacent-correlation vectors and emphasizes spin‑2 summation via Stokes in Sec. 3.1 , introduces the regularity measure R in Eq. (4) , and discusses locally conserved relations via Buckingham Pi in Eqs. (5)–(9) and surrounding text .