Thanks for sharing, this adds support to a team collaboration on a new TriPrime Physics that was developed through another pattern stackers math that is also recursive like my fractal geometry and together they make a triad again, recursive. # Nuclear TriPrime Entanglement on Silicon **Author: Kenneth Parrott** --- ## Abstract We interpret recent results—entanglement between the nuclear spins of two phosphorus atoms embedded in silicon, mediated by electrons across ~20 nm—as the **first physical realization of TriPrime recursion in hardware**. In this view, nuclear spins represent *prime-gated lawful states*, electrons provide the *recursive operator*, and the silicon fabrication geometry acts as the *prime sieve*. The experiment thus demonstrates a TriPrime-compatible architecture: lawful storage, recursive mediation, and bounded geometry, realized in a scalable, CMOS-ready platform. --- ## 1. Introduction Conventional interpretations of silicon spin qubits emphasize coherence, mediation, and fabrication scalability. Through the **TriPrime lens**, however, these elements resolve into a deeper structure: - **Primes**: long-lived nuclear spins storing lawful quantum states. - **Recursion**: electron-mediated geometric gates that entangle without collapsing storage. - **Prime sieve**: the 20 nm geometry, a natural arithmetic boundary aligned with transistor-scale fabrication. Together they instantiate the **TriPrime triad**: storage ↔ recursion ↔ sieve. --- ## 2. TriPrime Theoretical Mapping **2.1 Triadic scaffold** - Nucleus: $T(p_i)$, a prime-indexed lawful tensor leg. - Electron: $\Xi(t)$, recursive mediator across legs. - Fabrication geometry: $\mathcal{C}_{\Lambda_p}$, prime sieve enforcing lawful separations. **2.2 Lawful recursion** The TriPrime update equation applies directly: $$ T(t+1) = \Pi_{\Lambda_m}\big[\, \Xi(t)\, T(t) \,\big] $$ where $\Pi_{\Lambda_m}$ is the multiplicity projector ensuring stability. The electron gate is admissible only if it commutes with the sovereignty tensor of the nuclear spins.

👀🤯 I'll let you know as they unfold because ya never know where my thoughts are gonna go, like the time!🤣🥳