DialSort · by Alexander Narvaez — anarvae1@eafit.edu.co

DialSort — Sovereign Dial Model
Order is not computed. It is revealed.

This simulator demonstrates the Sovereign Dial Model of DialSort — the conceptual foundation of Tier 2 and Tier 3 of the paper, targeting massively parallel hardware implementations: FPGAs, GPUs, neuromorphic architectures, and photonic computing. Each number in the unsorted input vector falls simultaneously into its own sovereign tube, stopping at the exact height corresponding to its value — not next to the previous one, but at its own vertical coordinate. The upward light beam represents a light wave propagating through an array of optical resonators: each tube is a resonator that, when active, couples energy and emits as the wave passes — exactly as in real photonic implementations where no comparator circuit or control signal evaluates anything. The wave simply propagates and active resonators respond through resonance, at the speed of light. In FPGAs the sweep is discrete and clock-driven; in photonics it is continuous and simultaneous — the Sovereign Model captures both. The Big-O complexity metrics shown during the animation reflect the real cost of each operation: O(1) per drop, O(1) per level resonance, O(U+n) total — zero key comparisons, zero prefix-sum.

Drop of each key k
O(1)
Value k determines the stopping height. The tube is already assigned. One direct access — no search, no magnitude comparison.
Value k → height k. The same number acts as data and as vertical coordinate simultaneously.
Total ingestion (n keys)
O(n)
n simultaneous and independent drops. Each tube is unaware of its neighbors. No forced sequentiality.
Counting sort: 3 mandatory sequential passes. Sovereign model: 1 parallel drop + 1 sweep.
Read at level k
O(1)
The beam passes through level k. If a marker is there, it illuminates. No evaluation — it is a physical property of the medium.
No internal tube traversal. No neighbor comparison. Present or absent state.
Full geometric sweep
O(U + n)
U levels traversed + n elements emitted. The beam does not evaluate order — it reads it from the already-fixed heights.
Order emerges from the ascending geometric scan, not from key comparisons.
Prefix-sum pass
ELIMINATED
Counting sort requires O(U) to convert frequencies into output positions. Here position is already encoded in height.
Average 1.65× speedup over classic counting sort (46/48 benchmark configurations).
Collisions
IMPOSSIBLE
Each tube is sovereign and exclusive. Two keys sharing the same value are structurally impossible in the pure model.
The CRN handles duplicates in parallel variants through additive accumulation — no magnitude comparison.
Load the example or add numbers (0–15)
Waiting  → 
Phase 1: Simultaneous drop — O(1) per key  → 
Phase 2: Level-by-level sweep — O(U+n)
Active tubes
0
out of U=16
Total ingestion
O(n)
0 × O(1) in parallel
Prefix-sum
O(0)
does not exist here
Comparisons
0
never evaluated
Beam level
—
current sweep
Emitted
0
by the sweep
Load the example and press ↓ Simultaneous drop. All numbers will fall at once — each to its own height — with no staircase pattern.
Order revealed by sweep: [ press ↑ Light beam sweep ] ← read from heights, not computed
Manual photonic beam control Drag the slider to explore the sweep level by level — after running Phase 1
level 0 level 15
0
Run ↓ Simultaneous drop first, then drag the slider to see which resonators the photonic wave activates at each level.
active marker (at its height)
revealed by beam
light beam (current level)
empty tube
falling