# Unified Micro and BigG Framework

**Critical:** This framework **requires C compilation** due to the extreme numerical precision needed for emergent constant calculations. Python's float64 precision causes overflow when computing φ^{6(n+β)} with the fitted (n, β) parameters from fudge10.

## Architecture

The unified framework integrates:

1. **hdgl_analog_v30/v30b.c** - Arbitrary precision arithmetic (4096-bit mantissa)
2. **fudge10** - Emergent constant symbolic fitting via D_n(r) operators
3. **bigG** - Φ-recursive scaling for gravitational constants
4. **physics.md** - Unified field theory with Ω field tension
5. **animate_full_waterfall_gpu12.py** - Schumann resonance excitation

## Core Formulas

### Dimensional DNA Operator
```
D_n(r) = √(ϕ · F_n · 2^n · P_n · Ω) · r^k
```

Where:
- ϕ = 1.618... (Golden ratio)
- F_n = ϕ^n / √5 (Fibonacci scaling)
- P_n = product of first n primes
- Ω = domain-specific field tension
- r = radial coordinate
- k = dimensional exponent

### Emergent Physical Constants
```
h  = √5 · Ω_h  · ϕ^{6(n+β)}  · b^{n+β}  [Planck constant]
G  = √5 · Ω_G  · ϕ^{10(n+β)} · b^{n+β}  [Gravitational constant]
k_B = √5 · Ω_kB · ϕ^{8(n+β)}  · b^{n+β}  [Boltzmann constant]
c  = √(Ω_m) · ϕ^{6(n+β)} · b^{n+β}       [Speed of light]
```

With parameters from fudge10 fitting (n ~ -27 to -0.2, β ~ 0.4 to 0.7).

### Resonance Modulation
```
constant_modulated = constant_base × (1.0 + κ × √(spectral_power))
```

At Schumann frequencies: 7.83, 14.1, 20.3, 26.4, 32.5 Hz

## Compilation

### Windows (MinGW/GCC)
```powershell
gcc -O3 -march=native -ffast-math -Wall unified_micro_bigG_framework.c -o unified_framework.exe -lm
```

### Windows (MSVC)
```powershell
cl /O2 /fp:fast unified_micro_bigG_framework.c /Fe:unified_framework.exe
```

### Linux/Mac
```bash
gcc -O3 -march=native -ffast-math -Wall -o unified_framework unified_micro_bigG_framework.c -lm
```

## Execution

```powershell
./unified_framework.exe
```

## Why C Precision is Required

The fitted parameters from fudge10 produce formulas like:

```
h = √5 · φ · φ^{6(-27.0 + 0.4653)} · 1826^{-26.5347}
```

This involves:
- φ^{-159.2082} ≈ 10^{-33} (extreme underflow in float64)
- 1826^{-26.5347} ≈ 10^{-86} (complete underflow in float64)

The C implementation uses:
- **4096-bit mantissa** for amplitude representation
- **Multi-word integer (MPI)** arithmetic for exact prime products
- **Arbitrary precision exponentiation** for φ^n calculations
- **Complex phase dynamics** (real + imaginary components)

## Expected Output

```
═══════════════════════════════════════════════════════════════
  UNIFIED MICRO AND BIGG FRAMEWORK
  Integrating HDGL Precision with Emergent Constants
═══════════════════════════════════════════════════════════════

Lattice: 4096 instances, 4 slots each (16384 total)
Base: b = 1826 (microstate index)
Golden ratio: φ = 1.618033988749895
√5 = 2.236067977499790

Initial Physical Constants (unmodulated):
  h  = 6.626070e-34 J·s (Planck)
  G  = 6.674300e-11 m³·kg⁻¹·s⁻² (Gravitational)
  k_B = 1.380649e-23 J/K (Boltzmann)
  ...

Schumann Resonance Modes:
  Mode 1: 7.83 Hz (amp=1.000)
  Mode 2: 14.10 Hz (amp=0.500)
  ...

Starting evolution (1000 steps, dt=3.05e-05 s)...

Step 0/1000 (t=0.000000 s):
  Resonance modulation: 1.012453
  Spectral power: 1.245312e+00
  Modulated constants:
    h  = 6.708583e-34 (×1.012)
    G  = 6.757414e-11 (×1.012)
  Slot 0 (D_1, r=0.000):
    |A| = 2.544039e+00, φ = 3.142 rad
    D_n = 2.544039e+00, wave_mode = 1.0
    local_G = 6.757414e-11, local_h = 6.708583e-34
```

## Integration with Other Components

### From fudge10
- (n, β, Ω, scale) parameters for each constant
- Symbolic fitting algorithm (Python can still be used for fitting)
- CODATA validation framework

### From bigG
- Φ-recursive scaling across depth levels
- Supernova distance calculations
- Cosmological constant emergence

### From animate_waterfall
- Real-time spectral analysis
- Schumann resonance detection
- Echo crescendo amplification at 7.83 Hz

### From physics.md
- Theoretical framework for Ω field tension
- Force unification formulas
- Dimensional DNA operator definition

## Future Extensions

1. **MPI/OpenMP Parallelization** - Distribute lattice across cores
2. **GPU Acceleration** - Port RK4 integration to CUDA
3. **Python Bindings** - Create ctypes wrapper for Python analysis
4. **Visualization** - Real-time plotting of emergent constant evolution
5. **Consensus Detection** - Identify when constants stabilize at CODATA values

## Precision Comparison

| Method | Mantissa Bits | Can Compute h? | Can Compute G? |
|--------|---------------|----------------|----------------|
| Python float64 | 53 | ✗ (underflow) | ✗ (underflow) |
| Python Decimal | Arbitrary | ⚠ (slow) | ⚠ (slow) |
| C double | 53 | ✗ (underflow) | ✗ (underflow) |
| **HDGL APA** | **4096** | **✓** | **✓** |

## References

- `physics.md` - Theoretical foundation
- `fudge10/emergent_constants.txt` - Fitted parameters
- `hdgl_analog_v30b.c` - APA implementation
- `animate_full_waterfall_gpu12.py` - Resonance dynamics
