mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
111 lines
2.7 KiB
Markdown
111 lines
2.7 KiB
Markdown
# Gauge Storage Models
|
||
|
||
**Purpose:** Document storage models for lattice gauge field simulations
|
||
|
||
**Status:** Draft for Review
|
||
**Date:** 2026-04-29
|
||
|
||
---
|
||
|
||
## 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
|
||
|
||
---
|
||
|
||
## 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
|
||
|
||
---
|
||
|
||
## 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
|