Correction: the problem says "until each subset contains exactly one atom" — implies only when possible. But 64000 is not a power of 2 — so it never reaches 1. But since halving stops when size is 1, we assume: after n splits, size = 64000 / 2ⁿ. Set equal to 1: 2ⁿ = 64000 → n = log₂(64000).

["Correction: Clarifying the Splitting Condition — Why Perfect Partitioning by Powers of Two Isn’t Always Possible", "When explaining a splitting process — especially one described as "dividing until each subset contains exactly one atom" — a critical technical truth must be acknowledged: this idealized condition only holds under strict mathematical constraints. The initial problem statement mentions splitting until "each subset contains exactly one atom," but identifies a fundamental obstacle: 64000 is not a power of 2, meaning we can never reduce it to a single element through successive halving.", "Let’s clarify the core logic. Starting with 64,000 elements, each split halves a subset by dividing it into two equal parts. We continue until subsets are of size 1 — but only if 64,000 is divisible by 2 enough times to reach exactly that state. However, 64000 = 2ⁿ × k, where k ≠ 1. Since 64000 is not a power of two (its binary logarithm is ~15.99), a perfect one-at-a-time split isn’t fully achievable.", "Still, the process stops once all subsets are reduced to size 1 — meaning n = ⌊log₂(64000)⌋ = 15 splits — leaving 64000 / 2¹⁵ = 2.5 elements — an impossible fractional size. This inconsistency reveals the need for correction: splitting halts only when all subsets are size 1 where possible, and rounds up or adjusts when exact powers of two fail.", "Instead of insisting on splitting until every single item is isolated through exact halving, the proper interpretation is: we split repeatedly by dividing large subsets, halting only when no more divisions are feasible — i.e., when all subsets shrink to the smallest possible size, which for 64000 is 2. Thus, the splitting process completes after ⌈log₂(64000)⌉ = 16 steps, reducing the largest subset to size 1 while accepting that not every individual "atom" gets isolated unless forced by strict halving rules.", "In summary, the problem’s original framing overlooks real-world computational limits: dividing 64000 atoms isn’t cleanly reducible to 1 using only binary splitting. The accurate model recognizes hierarchical halving that stops when subsets reach minimal size — aligning more closely with log₂(64000) ≈ 15.99 → n = 16 splits — emphasizing practical efficiency over idealized uniformity.", "Keywords: splitting process, binary halving, log₂(64000), subset partitioning, computational divisors, halving until size 1, perfect split limits, algorithmic efficiency", "---", "SEO Meta Description:\nWhy splitting 64,000 atoms by halving doesn’t always yield one per subset: discover how powers of two limit perfect division and why 16 splits are sufficient to reduce 64000 to near-one elements. Learn the real limits of recursive splitting in computational systems.", "Topics Covered: binary splitting, log₂ calculations, 64000 size reduction, why 64000 isn’t a power of two, practical limits of division, algorithmic halving strategies"]