Research-Stack/6-Documentation/docs/GaugeStorageModels.md

Gauge Storage Models

Purpose: Document storage models for lattice gauge field simulations

Status: Draft for Review
Date: 2026-04-29

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Storage Models

1. 8-Real/Site Model (Toy Model)

Description:

• Stores 8 real numbers per lattice site
• Simplified representation of SU(3) gauge field
• Suitable for small lattice experiments and toy simulations

Storage Calculation:

S = N × 8 × bytesPerReal
where N = L⁴ (lattice sites)

Example:

• L = 8 (8⁴ lattice)
• bytesPerReal = 4 (Q16_16 fixed-point)
• Storage: 8⁴ × 8 × 4 = 16,384 bytes = 16 KB

Advantages:

• Simple storage model
• Easy to implement
• Suitable for toy experiments

Limitations:

• Does not capture full SU(3) structure
• Not suitable for production Yang-Mills simulations
• Loss of gauge invariance information

2. SU(3) Link Model (Full Model)

Description:

• Stores 4 complex numbers per lattice site (link variables)
• Full SU(3) gauge field representation
• Captures gauge invariance structure

Storage Calculation:

S = N × 4 × 2 × bytesPerReal
where N = L⁴ (lattice sites)
4 complex numbers × 2 (real/imag) = 8 reals per site

Example:

• L = 8 (8⁴ lattice)
• bytesPerReal = 8 (Float64)
• Storage: 8⁴ × 4 × 2 × 8 = 32,768 bytes = 32 KB

Advantages:

• Full SU(3) structure
• Preserves gauge invariance
• Suitable for accurate simulations

Limitations:

• Higher storage requirements
• More complex implementation
• Still not suitable for 64⁴ production on small VPS

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Feasibility Analysis

Small Lattice Experiments (L = 4-16)

8-Real/Site Model:

• L = 4: 4⁴ × 8 × 4 = 2,048 bytes = 2 KB (Q16_16)
• L = 8: 8⁴ × 8 × 4 = 16,384 bytes = 16 KB (Q16_16)
• L = 16: 16⁴ × 8 × 4 = 262,144 bytes = 256 KB (Q16_16)

SU(3) Link Model:

• L = 4: 4⁴ × 4 × 2 × 8 = 4,096 bytes = 4 KB (Float64)
• L = 8: 8⁴ × 4 × 2 × 8 = 32,768 bytes = 32 KB (Float64)
• L = 16: 16⁴ × 4 × 2 × 8 = 524,288 bytes = 512 KB (Float64)

Production Lattice (L = 64)

8-Real/Site Model:

• L = 64: 64⁴ × 8 × 4 = 67,108,864 bytes = 64 MB (Q16_16)

SU(3) Link Model:

• L = 64: 64⁴ × 4 × 2 × 8 = 134,217,728 bytes = 128 MB (Float64)
• With Float64: 64⁴ × 4 × 2 × 8 = 1,073,741,824 bytes = 1,024 MB

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Conclusion

Feasible on Small VPS:

• L = 4-16 lattice experiments
• 8-real/site toy model
• SU(3) link model for small lattices

NOT Feasible on Small VPS:

• L = 64 production lattice
• Full Yang-Mills simulations
• Millennium Prize proof work

Recommendation:

• Use small lattice experiments (L = 4-16) for sandbox
• Document storage model clearly in all experiments
• Do not claim 64⁴ feasibility without proper hardware