Sorting has long been defined under the comparison model and its Ω(n log n) lower bound. This work challenges that paradigm for bounded-universe integer keys. DialSort introduces a non-comparative sorting microarchitecture based on the self-indexing principle, where each key k directly corresponds to its position in the ordered address space 0, U−1. Instead of comparing keys or computing prefix sums, DialSort performs direct address activation and resolves concurrent write conflicts using a Conflict Resolution Network (CRN), a pipelined additive reduction structure based solely on equality checks. The sorted order is not explicitly constructed; it is revealed through a geometric scan of memory. No order comparisons (, ≤) are evaluated at any stage. A software prototype on an 8-thread Intel x86-64 CPU achieves peak throughput of 115.9 M keys/s and up to 39.77× speedup over std::sort (N=10⁷, U=1024, uniform). For the full int32 range, a radix-based extension achieves up to 14.61× speedup. Direct comparison against classical Counting Sort across 48 configurations shows that DialSort-Counting outperforms it in 46 cases, achieving an average speedup of 1.65× and up to 4.3× in the best scenario. All 208 benchmark configurations passed correctness verification. Full benchmark source (v3.1) is available at:https://github.com/elmaestrotic/dsort DialSort demonstrates that, for bounded-universe integer keys, sorting can be interpreted as a geometric reading process rather than a comparison problem.
Alexander Narváez Berrío (Sun,) studied this question.