R_t ≈ K × M_t × (1-L_t) × C_t × D_t

M* = M_now × (R*/R_now)         # Required multiple
(1-L*) = (1-L_now) × (R*/R_now) # Required deleveraging level
C* = C_now × (R*/R_now)         # Required cost improvement → implied AISC*
D* = D_now × (R*/R_now)         # Required dilution discount

cd skills/backsolve-miner-vs-metal-ratio-with-fundamentals
pip install pandas numpy yfinance matplotlib  # First-time use
python scripts/fundamental_analyzer.py --quick

python scripts/fundamental_analyzer.py \
  --metal-symbol SI=F \
  --miner-universe etf:SIL \
  --region-profile us_sec \
  --start-date 2015-01-01 \
  --output result.json

python scripts/visualize_factors.py --quick --output output/

The visualization dashboard includes four panels:
1. **Ratio Time Series**: Historical trend + quantile intervals (bottom/top)
2. **Factor Radar Chart**: Overview of the health status of the four factors
3. **Factor Score Bar Chart**: Scores for cost, leverage, multiple, and dilution
4. **Scenario Heatmap**: Combination analysis of multiple expansion × silver price changes

**Co-rise Scenario Simulation**

```bash
python scripts/scenario_path_simulator.py --quick --output output/

Core Formula: **Mining stock return = (1 + silver price return) × (R₁/R₀) - 1**

Custom Parameters:
```bash
python scripts/scenario_path_simulator.py \
  --silver-monthly 5 \      # Silver price monthly return 5%
  --ratio-start 1.10 \      # Ratio starting point
  --ratio-end 1.20 \        # Ratio ending point
  --months 6 \              # Simulate 6 months
  --heatmap                 # Generate return heatmap simultaneously

{
  "now": {
    "metal_price": 94.4,
    "miner_price": 103.4,
    "ratio": 1.13,
    "ratio_percentile": 0.111
  },
  "thresholds": {
    "bottom_ratio": 1.20,
    "top_ratio": 1.70,
    "median_ratio": 1.51
  },
  "fundamentals_weighted": {
    "aisc_usd_per_oz": 28.0,
    "net_debt_to_ev": 0.25,
    "ev_to_ebitda": 6.4,
    "shares_yoy_change": 0.12
  },
  "factors_now": {
    "cost_factor_C": 0.7034,
    "leverage_factor_1_minus_L": 0.75,
    "multiple_M": 6.4,
    "dilution_discount_D": 0.89
  },
  "backsolve_to_top": {
    "multiple_only_need": 9.1,
    "deleverage_only_need_1_minus_L": 1.12,
    "cost_only_implied_aisc": 15.6,
    "dilution_only_need_D": 1.26
  }
}

backsolve-miner-vs-metal-ratio-with-fundamentals/
├── SKILL.md                           # This file (router)
├── skill.yaml                         # Frontend display metadata
├── manifest.json                      # Skill metadata
├── workflows/
│   ├── analyze.md                     # Full analysis workflow
│   └── data-fetch.md                  # Data crawling workflow
├── references/
│   ├── input-schema.md                # Complete input parameter definition
│   ├── data-sources.md                # Data source description
│   ├── fundamental-factors.md         # Calculation logic of the four factors
│   └── backsolve-math.md              # Backsolve mathematical formulas
├── templates/
│   ├── output-json.md                 # JSON output template
│   └── output-markdown.md             # Markdown report template
├── scripts/
│   ├── fundamental_analyzer.py        # Main calculation script
│   ├── visualize_factors.py           # Visualization dashboard script
│   └── scenario_path_simulator.py     # Co-rise scenario simulator
└── examples/
    └── sample-output.json             # Sample output

{
  "skill": "backsolve_miner_vs_metal_ratio_with_fundamentals",
  "inputs": {
    "metal_symbol": "SI=F",
    "miner_universe": {"type": "etf_holdings", "etf_ticker": "SIL"},
    "region_profile": "us_sec"
  },
  "now": {
    "metal_price": 94.4,
    "miner_price": 103.4,
    "ratio": 1.13,
    "ratio_percentile": 0.111
  },
  "thresholds": {
    "bottom_ratio": 1.20,
    "top_ratio": 1.70,
    "median_ratio": 1.51
  },
  "fundamentals_weighted": {
    "aisc_usd_per_oz": 28.0,
    "net_debt_to_ev": 0.25,
    "ev_to_ebitda": 6.4,
    "shares_yoy_change": 0.12
  },
  "factors_now": {
    "cost_factor_C": 0.7034,
    "leverage_factor_1_minus_L": 0.75,
    "multiple_M": 6.4,
    "dilution_discount_D": 0.89
  },
  "backsolve_to_top": {
    "multiple_only_need": 9.1,
    "deleverage_only_need_1_minus_L": 1.12,
    "cost_only_implied_aisc": 15.6,
    "dilution_only_need_D": 1.26,
    "two_factor_grid_examples": [
      {"multiple_up": 1.20, "metal_down": -0.15, "hits_top": true},
      {"deleverage": -0.10, "multiple_up": 1.15, "hits_top": true}
    ]
  },
  "event_study": {
    "bottom_events": [
      {
        "date": "2026-01-02",
        "ratio": 1.13,
        "aisc": 29.1,
        "net_debt_to_ev": 0.27,
        "ev_to_ebitda": 5.8,
        "shares_yoy": 0.14,
        "dominant_driver": "multiple_compression"
      }
    ]
  },
  "summary": "The ratio is at a historical bottom, mainly driven by multiple compression...",
  "notes": [
    "AISC was calculated using hybrid method, some values are proxy estimates for certain companies",
    "Recommended cross-validation: COT positions, ETF flows, USD/real interest rates"
  ]
}