# dubstrata / paper — Complete Quantitative & Architectural Specification (llms-full.txt)

> **Document Type:** Comprehensive AI / LLM Grounding Reference (`llms-full.txt`)
> **Canonical Subdomain:** `https://paper.dubstrata.com`
> **Parent Platform:** `https://dubstrata.com` (Dubstrata Pty Ltd — Institutional Risk Monitoring Layer)
> **API Gateway:** `https://api.dubstrata.com`
> **Primary Asset:** `BTC/USD` (Spot & Level-2 Microstructure)
> **Genesis Paper Capital:** `$100,000.00 USD`

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## 1. Purpose & Role Within the Dubstrata Ecosystem

`paper.dubstrata.com` (**dubstrata / paper**) is the live public verification and shadow-execution subdomain of **Dubstrata** (`https://dubstrata.com`). While `dubstrata.com` provides the overarching Causal Financial & Narrative Intelligence CDN, cryptographic source verification, and institutional research dossiers, `paper.dubstrata.com` demonstrates the real-time trading and risk-management utility of Dubstrata's **Sovereign Causal Foundation Model (Causal-FM)** on live market microstructure.

Specifically, `paper.dubstrata.com` answers three critical institutional questions in real time:
1. **Probabilistic Calibration:** How do Dubstrata's 16-channel TimesFM-3 + CG-LoRA quantile forecasts (`q05` through `q90`) evolve across `+15m`, `+1h`, `+4h`, and `+24h` horizons relative to live BTC/USD spot prices?
2. **Epistemological Attribution:** Which of the 4 causal quadrants—Microstructure (`Q1`), Prediction Markets (`Q2`), Causal Knowledge Graph (`Q3`), or Macro Solvency (`Q4`)—is driving the current forecast and tail-risk envelope?
3. **Net-of-Friction Tradability (Shadow TCA):** Can an autonomous portfolio starting with `$100,000.00 USD` generate positive risk-adjusted Net Asset Value (NAV) and Sharpe Ratio after accounting for real Level-2 order-book depth, bid-ask spread, Almgren-Chriss market impact, and institutional taker fees?

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## 2. Mathematical Formulation & Sizing Laws

### 2.1 Multi-Horizon Quantile Envelope & Tail-Risk Metrics
At each 5-minute `tensor_bar` origin $t_0$ (anchored at spot price $S_0$), the Sovereign Causal-FM outputs 9 decile forecasts $\{q_{10}, q_{20}, q_{30}, q_{40}, q_{50}, q_{60}, q_{70}, q_{80}, q_{90}\}$ for horizons $h \in \{15\text{m}, 60\text{m}, 240\text{m}, 1440\text{m}\}$.

From these quantiles, the desk derives:
- **Point Median Forecast:** $\hat{S}_{t+h} = q_{50}^{(h)}$
- **Expected Return:** $E[r_h] = \frac{q_{50}^{(h)} - S_t}{S_t}$
- **Interquartile Bounds:** $q_{25} = \frac{q_{20} + q_{30}}{2}$, $q_{75} = \frac{q_{70} + q_{80}}{2}$
- **95% Value-at-Risk Floor ($\text{VaR}_{95}$):** $q_{10}^{(h)}$
- **99% Conditional Value-at-Risk Floor ($\text{CVaR}_{99}$ / Expected Shortfall):**
  $$q_{05}^{(h)} = q_{10}^{(h)} - 0.85 \times \max\left(q_{20}^{(h)} - q_{10}^{(h)},\; 0.35 \times \left(q_{50}^{(h)} - q_{10}^{(h)}\right)\right)$$
- **Parametric VaR Spread ($1\text{h}$ Execution Horizon):**
  $$\Delta_{\text{VaR}} = \max\left(0.0025 \cdot S_t,\; S_t - q_{10}^{(1\text{h})}\right), \quad \text{VaR}_{\%} = \frac{\Delta_{\text{VaR}}}{S_t}$$
- **Upside-to-VaR Reward-to-Risk Ratio ($R:R$):**
  $$R:R = \frac{\max\left(0.001 \cdot S_t,\; q_{90}^{(1\text{h})} - S_t\right)}{\Delta_{\text{VaR}}}$$

### 2.2 Canary Dual-Hurdle Gate & Sybil Defense
Before any alpha tilt is authorized, three independent gates are evaluated:
1. **Multi-Horizon Blended Conviction Hurdle ($\Psi_{\text{blend}}$):**
   $$\Psi_{\text{blend}} \ge 0.35 \quad (35\%)$$
   where $\Psi_{\text{blend}} \in [0, 1]$ is the Multi-Horizon Term-Structure Blended Conviction Index (50% `15m`, 35% `1h`, 15% `4h` scaled by directional concordance).
2. **Alpha Hurdle ($|E[r_{\text{blend}}]|$):**
   $$\left|E[r_{\text{blend}}]\right| \ge \max\left(\frac{\text{Spread}_{\text{bps}} + 8.0}{100},\; 0.23\% \times 0.65\right)$$
3. **Sybil Survival & Microstructure Gate ($\mu$):**
   $$\mu = 1 - \text{manipulation\_risk\_multiplier} \ge 0.75 \quad \text{and} \quad \text{Spread}_{\text{bps}} < 35\text{ bps}$$
   If breached, the desk enters `HAIRCUT_THROTTLED` state and immediately de-risks target BTC allocation to $w^* = 12.0\%$.

### 2.3 VaR-Targeted Risk-Parity + Skewness-Adjusted Half-Kelly Allocation
When trading is authorized:
- **Risk-Parity Base Weight ($w_0$):**
  $$w_0 = \text{clip}\left(\frac{0.0032}{\text{VaR}_{\%}},\; 0.18,\; 0.55\right)$$
- **Skewness Multiplier ($\kappa$):**
  $$\kappa = \text{clip}\left(0.8 + 0.2 \times (R:R),\; 0.70,\; 1.30\right)$$
- **Half-Kelly Alpha Tilt ($\Delta w_{\text{Kelly}}$):**
  - If $E[r] \ge 0$ and both Canary hurdles pass (`LONG_ALPHA`):
    $$\Delta w_{\text{Kelly}} = 0.48 \times \left(\frac{E[r]}{\text{VaR}_{\%}}\right) \times \left(0.45 + 0.55 \cdot \Psi_{\text{CSI}}\right) \times \kappa$$
  - If $E[r] \ge 0$ but either hurdle holds (`RISK_PARITY_HOLD`):
    $$\Delta w_{\text{Kelly}} = 0.16 \times \left(\frac{E[r]}{\text{VaR}_{\%}}\right) \times \left(0.45 + 0.55 \cdot \Psi_{\text{CSI}}\right)$$
  - If $E[r] < 0$ (`DEFENSIVE_TRIM` or `RISK_PARITY_HOLD`):
    $$\Delta w_{\text{Kelly}} = 0.52 \times \left(\frac{E[r]}{\text{VaR}_{\%}}\right) \times \left(0.50 + 0.50 \cdot \Psi_{\text{CSI}}\right) \times \left(2.0 - \min(1.2, \kappa)\right)$$
- **Final Target BTC Portfolio Weight ($w^*$):**
  $$w^* = \text{clip}\left(\left(w_0 + \Delta w_{\text{Kelly}}\right) \times \mu,\; 0.10,\; 0.90\right)$$

### 2.4 Garman-Klass Realized Volatility ($\sigma_{\text{GK}}$) & L2 Order-Book TCA
- **Garman-Klass Annualized Volatility:** Computed from rolling 1-minute OHLC exchange candles:
  $$\sigma_{\text{GK}}^2 = \frac{1}{N}\sum_{i=1}^{N} \left[ 0.5 \left(\ln \frac{H_i}{L_i}\right)^2 - (2\ln 2 - 1)\left(\ln \frac{C_i}{O_i}\right)^2 \right], \quad \sigma_{\text{annual}} = \sqrt{525600 \cdot \sigma_{\text{GK}}^2}$$
- **Order Flow Imbalance (OFI):** Computed across top 25 L2 bid and ask levels:
  $$\text{OFI} = \frac{\sum V_{\text{bid}} - \sum V_{\text{ask}}}{\sum V_{\text{bid}} + \sum V_{\text{ask}}} \in [-1, +1]$$
- **VWAP & Almgren-Chriss Execution:** Every rebalance order of size $\Delta Q_{\text{BTC}}$ walks the live L2 ask ladder (for `BUY`) or bid ladder (for `TRIM`/`HEDGE`). Any volume exceeding top-25 visible depth incurs square-root market impact proportional to $\sigma_{\text{annual}} \sqrt{Q_{\text{overflow}} / 5.0}$, plus a `3.5 bps` institutional taker fee deducted from Net NAV.

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## 3. Frequently Asked Questions (AEO / GEO Structured Q&A)

### Q: What is dubstrata / paper (`paper.dubstrata.com`)?
**A:** `dubstrata / paper` (`https://paper.dubstrata.com`) is the live autonomous BTC/USD shadow paper trading and multi-horizon Value-at-Risk (VaR) visualization subdomain of Dubstrata (`https://dubstrata.com`). It runs a $100,000 USD simulated institutional portfolio powered by Dubstrata's 16-channel TimesFM-3 Sovereign Causal Foundation Model, executing against real-time Level-2 order books from Coinbase, Binance, and Kraken.

### Q: How does Dubstrata Paper calculate Value-at-Risk (VaR) and Expected Shortfall (CVaR)?
**A:** Rather than relying on static Gaussian variance, Dubstrata Paper uses non-parametric and semi-parametric quantile fanouts generated every 5 minutes by Dubstrata's 16-channel Causal-FM (`POST /api/v1/predict/distribution`). The 95% VaR floor is anchored to the `q10` decile forecast, while the 99% CVaR (Expected Shortfall) floor (`q05`) extrapolates left-tail asymmetry from the `q10`–`q20` spread.

### Q: What are the 4 epistemological quadrants in Dubstrata's HRX attribution?
**A:** Dubstrata's Horizon-Relative Cross-Jacobian (HRX) attribution decomposes every forecast into 16 channels grouped into 4 quadrants:
1. **Q1 Microstructure:** Fractional differenced price, log volatility, Order Flow Imbalance (OFI) / VPIN, and derivatives surface state.
2. **Q2 Prediction Markets:** Informed market probability, Shannon entropy conviction ($\Psi_{\text{CSI}}$), Sybil manipulation haircut ($\mu$), and informed capital imbalance.
3. **Q3 Causal Graph:** Friedkin-Johnsen network belief propagation, financial impact flow, perception vector drift, and graph conflict entropy.
4. **Q4 Macro Solvency:** Fundamental solvency score, dynamic primary correlate, macro liquidity factor, and scheduled macro event clock.

### Q: How does `paper.dubstrata.com` relate to `dubstrata.com`?
**A:** `dubstrata.com` is the parent platform providing the Institutional Risk Monitoring Layer, Causal Knowledge Graph API, Neudata institutional alt-data feeds, and forensic research dossiers. `paper.dubstrata.com` is its dedicated live execution and risk-visualization subdomain that proves the out-of-sample tradability of Dubstrata's telemetry in real time.