The positive 3-braid knots σ₁³σ₂³σ₁⁶σ₂⁶ and σ₁³σ₂⁵σ₁³σ₂⁷ are not concordant

The closures K1 of σ₁³σ₂³σ₁⁶σ₂⁶ and K2 of σ₁³σ₂⁵σ₁³σ₂⁷ are two non-isotopic positive 3-braid knots with 18 crossings that P. Truöl lists as a pair she could not distinguish in concordance (Oberwolfach Report 43/2024, DOI 10.4171/OWR/2024/43, Question 4: "Are concordant braid positive knots isotopic?"). RESULT: K1 and K2 are not topologically concordant, hence not smoothly concordant. METHOD: the Kirk–Livingston / Herald–Kirk–Livingston twisted Alexander polynomial test (a Casson–Gordon-type invariant), in the form of Theorem "main KL" of Dunfield–Gong, arXiv:2512.21825v1, applied to K1 # −K2 with the 2-fold branched cover and characters to Z/3. H₁(Σ₂(K1 # −K2); F₃) = F₃⁴ gives 40 characters up to scaling; all 40 twisted polynomials fail to be norms, each at a non-cyclotomic factor, so no metabolizer can exist. Two independent implementations: SnapPy 3.3.2 slice_obstruction_HKL((2,3), method='advanced') returns (2,3) on several diagrams and triangulations, and a separately written Fox-calculus code finds 0 norms among the 40. Calibrations: K1 # −K1 and K2 # −K2 (slice) are not obstructed; K12n813 gives (3,7) as documented. WHAT AGREES: Alexander polynomial, determinant 243, the full Levine–Tristram signature function, the Σ₂ linking form (metabolic), the rational Seifert forms, HFK, τ, ν, ε and the UV = 0 local equivalence class, Rasmussen s over Q, F₂, F₃, F₅, F₇, sl₃ invariants and integral Khovanov homology. Only the metabelian layer separates the pair. This answers Truöl's question for this one pair, in the expected direction; it does not answer Question 4 in general, and no new method is claimed. Every number comes from the scripts included and open tools (SnapPy, spherogram, knot_floer_homology, SageMath, GAP, KnotJob); no invariant is computed by an AI. This work was done by Werner Alois Stanggassinger in collaboration with Claude Code (Anthropic): the question and the hardware are Stanggassinger's; the code and the verification were written and run jointly. Code GPL-3.0-or-later, data and text CC BY 4.0. See README.md and SHA256SUMS in the archive.