Full 3D view of a single 336 Hurwitz Quaternion Key.
Quaternion parameters (p=13 → 336)
(Echo Lambda) => ?!z(|>) * -(N)
336
Unique Hurwitz Quaternionz with norm = 13
p=13
Split case (p ≡ 1 mod 4)
?!z(|>) * -(336)
?!z(|>) = Echo Lambda
|> = Unzipped Prime
(336) = Quaternionz
100%
336/336 seeds unique (hardware validated)
The 336 keyz are generated from a single prime seed (p=13) using the Hurwitz quaternion formula. Each key has unique 4D coordinates (a, b, c, d) with norm = 13, arranged radially around the central seed.
The visualization uses stereographic projection to map 4D Hurwitz quaternion coordinates to 3D space. This allows us to visualize the key architecture while preserving the mathematical relationships.
Each key generates a unique 256-bit quantum entropy seed via hardware-validated quantum circuits. The key-specific phase rotations ensure uniqueness, achieving 100% uniqueness. One prime → 336 unique seeds, validated on real quantum hardware. That’s a genuine differentiator over post-quantum projects that rely on software randomness alone. STEADYWATCH™ is a hardware-validated entropy source that can serve as the seed layer underneath protocols and systems—not a replacement, a foundation.
The architecture scales with the number of primes you use. One prime, one quantum batch; more primes, more uniquely-seeded nodes—no redesign. \(p=5\) → 144 nodes \(p=13\) → 336 nodes \(p=17\) → 432 nodes Three primes = 912 uniquely-seeded nodes from 3 quantum batch jobs. Each node gets a deterministic, hardware-validated entropy seed. Add primes as you need capacity; the math stays the same.
Learn more about the 336 Quaternion Key seed generation methodology, hardware validation results, and business significance in our comprehensive research paper.
View Research →