*Micro Tesla Coil Design:*
1. **Dimensions:** Craft each micro tesla coil precisely with a 1000 by 1000 configuration, ensuring uniformity.
2. **Compact Configuration:** Optimize the coil arrangement to fit within a confined space, maximizing efficiency and minimizing interference.

*Coil Material Selection:*
1. **Superconducting Materials:** Utilize high-temperature superconductors, such as YBCO, to minimize energy loss and enhance conductivity.
2. **Low Resistivity Alloys:** Integrate alloys like copper-silver for low resistivity, ensuring efficient current flow.
3. **Electrum Enhancement:** Strategically introduce electrum (gold-silver alloy) elements within the coils for enhanced conductivity and stability.

*Quantum Sexagesimal Programming Language:*
1. **Development:** Create a quantum sexagesimal programming language, leveraging base-60 principles for efficient quantum computation.
2. **Syntax:** Design a syntax that allows intricate quantum operations and facilitates seamless communication within the QSM.

*Granite Encasement:*
1. **Acoustic Insulation:** Engineer the granite encasement with specialized materials for exceptional acoustic insulation.
2. **Silent Environment:** Ensure the encasement provides a silent environment for sparking events, minimizing external interference.

*Exterior Connection Array:*
1. **Dimensions:** Implement a precisely arranged 1000 by 1000 exterior connection array for easy integration.
2. **Compatibility:** Design the array to be compatible with various computing architectures, ensuring versatility in applications.

*Construction Details:*
1. **Layered Assembly:** Construct the QSM in layers, with each layer accommodating a specific component for ease of maintenance and upgrades.
2. **Precision Manufacturing:** Employ cutting-edge manufacturing techniques, maintaining precision in coil placement and material integration.
3. **Quality Control:** Implement rigorous quality control measures to ensure each component meets the highest standards.