Steiner trees with infinitely many terminals on the sides of an angle

The paper’s Theorem 1 proves that, under 0 < α < π/6, 0 < λ ≤ 1/2 and √λ < cos(π/3+α)/cos(π/3−α), every Steiner solution for A1 is a union of full 5-terminal trees and has length H1(St1) = |cosα + √3 sinα + (2λ/(1−λ^2)) e^{π i/6} sinα + (2λ^2/(1−λ^2)) e^{−π i/6} sinα|, exactly matching the candidate’s formula and structural claim . The paper obtains this via a Maxwell-type length formula, Melzak reduction, and a wind-rose/parallelogram analysis that forces an alternating choice of directions, ultimately selecting the odd/even split of indices to minimize length (Lemmas 8–10) . The candidate instead argues using a local 4-point flip, the classical 3-point Steiner length in the isosceles configuration, and a calibration in a hexagonal norm to certify optimality; this is consistent with the paper’s framework (they also appeal to Maxwell/calibration-style identities), but is a different proof strategy. Minor omissions in the candidate (e.g., not discussing the 2^N family of mirrored solutions noted in the paper) do not affect correctness of the main claims .