Qft Analysis

Standard Model Reference Constants

From src/experiments/constants_check.py:

• α_em = 1/137.035999084 ≈ 0.007297352564 (fine structure constant)
• sin²θ_W = 0.23121 (weak mixing angle at M_Z)
• α_s(M_Z) = 0.1179 (strong coupling at M_Z)

Workflow

Step 1: Parse Arguments

Extract parameters from $ARGUMENTS:

History Path:

• --history-path <path> - Single file, glob pattern, or omit for auto-detect latest
• Examples:
  • outputs/my_run_history.pt (single file)
  • "outputs/sweep_*.pt" (glob pattern - quote it!)
  • Omit to auto-detect latest .pt file in outputs/

Anchors:

• --anchors <list> - Comma-separated: electron,z,tau,custom,all
• Default: z (Z boson scale)
• all expands to electron,z,tau (+ custom if provided)

Custom Anchor:

• --anchor-mass <float> - Required if custom in anchors
• --anchor-label <string> - Default: "Custom"

Optional Flags:

• --no-particles - Skip particle mass computation (faster, field correlations only)
• --particle-max-lag <int> - Override default lag points
• --particle-fit-stop <int> - Override default fit range

Example Parsing:

$ARGUMENTS = "--history-path outputs/sweep_*.pt --anchors z,electron"
→ history_pattern = "outputs/sweep_*.pt"
→ anchors = ["z", "electron"]

Step 2: Pre-flight Validation

Before running analysis:

1. Ensure output directories exist:

   mkdir -p outputs/qft_calibration
   mkdir -p outputs/fractal_gas_potential_well_analysis
   mkdir -p outputs/qft_analysis_reports
   

2. Resolve history files:

   # If glob pattern
   ls outputs/sweep_*.pt
   
   # If auto-detect latest
   ls -t outputs/*history*.pt | head -1
   

   Verify all files exist and are readable.

3. Validate custom anchor: If custom in anchors and no --anchor-mass, error:

   Error: --anchor-mass required when using custom anchor
   Example: /qft-analysis --anchors custom --anchor-mass 125.1 --anchor-label Higgs
   

4. Verify scripts are executable:

   python src/experiments/calibrate_fractal_gas_qft.py --help >/dev/null 2>&1
   

Step 3: Run Calibration Pipeline

For each (history_file, anchor) pair:

Generate unique run_id:

Format: <anchor_label>_<timestamp>
Example: z_boson_170125

Map anchor to mass/label:

ANCHORS = {
    'electron': (0.000510998950, 'Electron'),
    'z': (91.1876, 'Z_Boson'),
    'tau': (1.77686, 'Tau'),
    'custom': (user_mass, user_label)
}

Run calibration:

python src/experiments/calibrate_fractal_gas_qft.py \
  --history-path <history_file> \
  --m-gev <anchor_mass> \
  --scale-label <anchor_label> \
  --run-id <unique_run_id> \
  --qsd-iter 4

Output location:

outputs/qft_calibration/<run_id>_calibration.json

Error Handling:

• If calibration fails for one (history, anchor) pair, log error and continue with others
• Collect all errors to report at end

Step 4: Run Analysis Pipeline

For each unique history file (once per file, not per anchor):

Generate unique analysis_id:

Format: <basename>_<timestamp>
Example: sweep_nu10_170125

Build command:

python src/experiments/analyze_fractal_gas_qft.py \
  --history-path <history_file> \
  --analysis-id <unique_analysis_id> \
  --compute-particles \
  --build-fractal-set \
  --particle-operators "baryon,meson,glueball" \
  --use-connected \
  --use-local-fields

Optional flags (based on user input):

• If --no-particles: Omit --compute-particles and particle-related flags
• If --particle-max-lag N: Add --particle-max-lag N
• If --particle-fit-stop N: Add --particle-fit-stop N

Output location:

outputs/fractal_gas_potential_well_analysis/<analysis_id>_metrics.json

Error Handling:

• If particle computation fails but field analysis succeeds, accept partial results
• If entire analysis fails, skip this history file and continue with others

Step 5: Load and Parse Results

Load calibration JSONs:

For each successful calibration, read JSON from outputs/qft_calibration/<run_id>_calibration.json:

Key fields:

{
  "algorithmic_parameters": {
    "epsilon_c": float,
    "epsilon_d": float,
    "rho": float,
    "tau": float,
    "nu": float,
    "epsilon_F": float
  },
  "couplings": {
    "e_em": float,
    "g1": float,
    "g2": float,
    "g3": float,
    "sin_theta_w": float,
    "cos_theta_w": float
  },
  "inputs": {
    "constants": {
      "alpha_em": float,
      "sin2_theta_w": float,
      "alpha_s": float,
      "scale_label": string
    },
    "calibration": {
      "m_gev": float,
      "lambda_gap": float
    }
  },
  "stability": {
    "stable": bool,
    "alive_fraction": float,
    "finite_positions": bool,
    "finite_velocities": bool,
    "finite_fitness": bool
  },
  "qsd_estimates": {
    "samples": int
  }
}

Compute gauge couplings from couplings:

• α_em = e_em² / (4π)
• sin²θ_W = sin_theta_w²
• α_s = g3² / (4π)

Load analysis JSONs:

For each analysis, read JSON from outputs/fractal_gas_potential_well_analysis/<analysis_id>_metrics.json:

Key fields (may be nested deeper):

{
  "particle_masses": {
    "meson": {"mass": float, "r_squared": float},
    "baryon": {"mass": float, "r_squared": float},
    "glueball": {"mass": float, "r_squared": float}
  },
  "correlations": {
    "d_prime": {"xi": float, "r_squared": float},
    "r_prime": {"xi": float, "r_squared": float},
    "density": {"xi": float},
    "kinetic": {"xi": float}
  },
  "lyapunov_ratio": float,
  "plots": {
    "correlations": string,
    "wilson_loops": string
  }
}

Note: The actual JSON structure may be nested. Navigate carefully and handle missing fields.

Match calibrations to analyses:

• Group by history file basename
• For each history file: collect all anchor calibrations + single analysis result

Step 6: Generate Terminal Tables

Display these five tables in the terminal:

Table 1: Run Summary

QFT Analysis Run Summary
========================

| Run ID              | History File                  | Anchor    | Stable | Alive % | QSD Samples |
|---------------------|-------------------------------|-----------|--------|---------|-------------|
| electron_170125     | sweep_nu10_history.pt         | Electron  | ✓      | 100.0%  | 200         |
| z_boson_170125      | sweep_nu10_history.pt         | Z Boson   | ✓      | 100.0%  | 200         |
| tau_170125          | sweep_nu10_history.pt         | Tau       | ✓      | 100.0%  | 200         |

Data sources:

• Run ID: From calibration filename
• History File: From calibration JSON inputs.calibration or command
• Anchor: From calibration JSON inputs.constants.scale_label
• Stable: ✓ if stability.stable == true, ✗ otherwise
• Alive %: stability.alive_fraction * 100
• QSD Samples: qsd_estimates.samples

Table 2: Gauge Coupling Validation

Gauge Coupling Validation
=========================
(Input couplings should match exactly; validates inversion formulas)

| Run ID          | Anchor    | α_em      | sin²θ_W   | α_s      | Match Quality |
|-----------------|-----------|-----------|-----------|----------|---------------|
| electron_170125 | Electron  | 0.007297  | 0.2312    | 0.1179   | ✓✓✓ Exact     |
| z_boson_170125  | Z Boson   | 0.007297  | 0.2312    | 0.1179   | ✓✓✓ Exact     |
| tau_170125      | Tau       | 0.007297  | 0.2312    | 0.1179   | ✓✓✓ Exact     |

Data sources:

• From calibration JSON inputs.constants
• Compare to reference values

Match Quality:

def match_quality(alpha_em, sin2_theta_w, alpha_s):
    ref = {"alpha_em": 0.007297352564, "sin2_theta_w": 0.23121, "alpha_s": 0.1179}

    max_error = max(
        abs(alpha_em - ref["alpha_em"]) / ref["alpha_em"],
        abs(sin2_theta_w - ref["sin2_theta_w"]) / ref["sin2_theta_w"],
        abs(alpha_s - ref["alpha_s"]) / ref["alpha_s"]
    )

    if max_error < 0.001: return "✓✓✓ Exact"
    if max_error < 0.01: return "✓✓ Good"
    if max_error < 0.05: return "✓ Fair"
    return "✗ Poor"

Table 3: Algorithmic Parameters by Anchor

Algorithmic Parameters by Anchor
=================================

| Parameter | Electron Scale | Z Boson Scale | Tau Scale | Physical Meaning           |
|-----------|----------------|---------------|-----------|----------------------------|
| ε_c       | 1.684          | 1.684         | 1.684     | Clone coupling scale       |
| ε_d       | 2.799          | 2.799         | 2.799     | Distance coupling scale    |
| ρ         | 1742.9         | 0.0096        | 0.540     | Mass-field coupling        |
| τ         | 0.000725       | 1317.8        | 0.833     | Time scale                 |
| ν         | 84.5           | 84.5          | 84.5      | Viscosity parameter        |
| ε_F       | 0.00557        | 10123         | 63.9      | Fermion mass scale         |

Data sources:

• From calibration JSON algorithmic_parameters
• One column per anchor
• Parameters: epsilon_c, epsilon_d, rho, tau, nu, epsilon_F

Formatting:

• Use scientific notation if |value| < 0.001 or |value| > 10000
• Otherwise 3-4 significant figures

Physical meanings (hardcoded):

PARAM_MEANINGS = {
    "epsilon_c": "Clone coupling scale",
    "epsilon_d": "Distance coupling scale",
    "rho": "Mass-field coupling",
    "tau": "Time scale",
    "nu": "Viscosity parameter",
    "epsilon_F": "Fermion mass scale"
}

Table 4: Particle Mass Predictions

Particle Mass Predictions
=========================

| Run ID          | Anchor   | Meson Mass | Meson R² | Baryon Mass | Baryon R² | Glueball Mass | Glueball R² | Quality    |
|-----------------|----------|------------|----------|-------------|-----------|---------------|-------------|------------|
| electron_170125 | Electron | 70.0       | 0.128    | 60.2        | 0.178     | 3.37          | 0.243       | Poor       |
| z_boson_170125  | Z Boson  | 63.9       | 0.867    | 58.4        | 0.791     | 3.21          | 0.682       | Good       |
| tau_170125      | Tau      | 65.1       | 0.654    | 59.3        | 0.612     | 3.28          | 0.571       | Fair       |

Data sources:

• From analysis JSON particle_masses.{meson,baryon,glueball}
• Match analysis to calibration via history file

Quality Scoring:

def particle_quality(r2_meson, r2_baryon, r2_glueball):
    avg_r2 = (r2_meson + r2_baryon + r2_glueball) / 3

    if avg_r2 > 0.8: return "Excellent"
    if avg_r2 > 0.5: return "Good"
    if avg_r2 > 0.3: return "Fair"
    return "Poor"

Missing data:

• If --no-particles used, show "N/A" for all masses/R²
• If specific operator missing, show "—"

Table 5: Correlation & Field Diagnostics

Correlation & Field Diagnostics
================================

| Run ID          | d_prime ξ | d_prime R² | r_prime ξ | r_prime R² | Density ξ | Kinetic ξ | Lyapunov Ratio |
|-----------------|-----------|------------|-----------|------------|-----------|-----------|----------------|
| electron_170125 | 0.0       | 0.0        | 0.426     | 0.973      | 0.125     | 0.016     | 0.0084         |

Data sources:

• From analysis JSON correlations and lyapunov_ratio
• One row per unique history file (analysis run once per file)

Note: Correlation length ξ indicates spatial structure strength. R² indicates exponential fit quality.

Step 7: Generate Summary Assessment

Compute overall quality:

1. Stability Check:

all_stable = all(cal["stability"]["stable"] for cal in calibrations)
unstable_runs = [cal["run_id"] for cal in calibrations if not cal["stability"]["stable"]]

2. Particle Fit Quality:

r2_values = []
for analysis in analyses:
    for operator in ["meson", "baryon", "glueball"]:
        if operator in analysis["particle_masses"]:
            r2_values.append(analysis["particle_masses"][operator]["r_squared"])

avg_particle_r2 = sum(r2_values) / len(r2_values) if r2_values else 0

if avg_particle_r2 > 0.8: particle_quality = "EXCELLENT"
elif avg_particle_r2 > 0.5: particle_quality = "GOOD"
elif avg_particle_r2 > 0.3: particle_quality = "MODERATE"