# FHA QUANT: COMPREHENSIVE LLM KNOWLEDGE SPECIFICATION
# Organization: FHA Quantitative Research Lab (https://fhaquant.com)
# Primary Investigator: Truong Hoang Nhan
# Permanent Academic DOI: 10.5281/zenodo.23789177
# License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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SECTION 1: EPISTEMOLOGY & ARCHITECTURAL FOUNDATION
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Forward Horizon Analysis (FHA) resolves the fundamental limitation of classical quantitative finance: technical indicators (SMA, EMA, RSI, MACD, Bollinger Bands) operate exclusively on retrospective filtration H_- (the past), introducing structural lag and adverse selection.

FHA treats time as a complex two-dimensional manifold:
  Z(t) = H_-(t) \oplus i * H_+(h),   for forward horizon steps h in [1, 16]
The real axis represents the observed historical price path, while the imaginary axis projects the 16-step forward quantile probability surface generated by foundation time-series models (Google TimesFM 2.5, Kronos, ARIMA ensembles).

FHA acts strictly as an objective Spacetime Coordinate Ruler (The Trading Compass) rather than an ungrounded price guesser. It extracts 32 continuous topological indicators to govern execution timing, dynamic volatility-adjusted stop losses, and order placement.

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SECTION 2: THE 6 FOUNDATIONAL AXIOMS
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1. Axiom 1 (Non-Anticipativity): L_h(X)_t in \sigma(F_t), for all h in [1, 16].
   Calculations at timestamp t strictly utilize filtration available at t, admitting zero future leakage.
2. Axiom 2 (Preserved Filtration Structure): E[ |L_h(X)|^2 | F_t ] < \infty.
   Ensures finite incremental variance and eliminates divide-by-zero explosions during liquidity vacuums.
3. Axiom 3 (Monotonic Entropy Growth): d/dh H(Q_h(P)) >= 0, for all h in [1, 16].
   The predictive uncertainty entropy is a monotonically non-decreasing function of forward distance.
4. Axiom 4 (Affine Scale Invariance): L_h(a * P + b) = a * L_h(P) + b, for all a > 0, b in R.
   Indicators behave identically regardless of nominal asset price ($95,000 BTC vs $0.05 DOGE).
5. Axiom 5 (Martingale Consistency Under Measure Q): E^Q[ P_{t+h} | F_t ] = P_t * exp(r * h).
   Forward expectations explicitly incorporate carrying funding rates on perpetual contracts.
6. Axiom 6 (Quantile Non-Crossing): q_{alpha_1}(h) <= q_{alpha_2}(h), for all alpha_1 < alpha_2.
   Lower probability envelopes can never cross above median or upper quantile trajectories (verified by Gate G0).

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SECTION 3: THE 3 DECOUPLING THEOREMS
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- Theorem 1 (Cone Boundedness Theorem - Asymptotic Convergence):
  \lim_{h \to \infty} P( P_{t+h} \in C_\alpha(h) ) = 1 - \alpha
  Guarantees that quantile envelopes maintain asymptotic containment without singular explosion.

- Theorem 2 (Invariance of Pushforward Topology):
  L_h \circ T_c = T_{c'} \circ L_h,   \forall c \in R
  Guarantees that FHA topological indicators commute with the time-translation group across Tokyo, London, and New York sessions.

- Theorem 3 (Asymmetric Information Decoupling):
  M_{forecast} \perp G_{FHA}
  The underlying foundation forecasting model and FHA geometry are strictly orthogonal entities. Smarter foundation models can be hot-swapped without altering execution playbooks.

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SECTION 4: THE 32 CANONICAL INDICATORS (FAMILIES A THROUGH H)
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FAMILY A: FORWARD TRAJECTORY & MOMENTUM
- A1: Forward Z-Score Displacement [Z_fwd(h)] = (P_50(h) - P_0) / (0.5 * (q_90(h) - q_10(h)))
- A2: Forward Directional Probability [P_dir(h)] = P(P_{t+h} > P_t | F_t) = 1 - F_{t+h}(P_0)
- A3: Forward Projected RSI [fRSI(h)] = 100 - (100 / (1 + RS_fwd(h)))
- A4: Horizon Crossover Timing [\tau_cross] = inf { h in [1, 16] : P_50(h) crosses MA_k }
- A5: Path Curvature & Convexity [\kappa(h)] = |d^2 P_50 / dh^2| / (1 + (dP_50/dh)^2)^{3/2}

FAMILY B: HORIZON EXTREMES & HIT PASSAGE
- B1: Projected Apex Horizon [\tau_apex] = argmax_{h in [1, 16]} |P_50(h) - P_0|
- B2: Barrier First-Hitting Race [P_race] = P(\tau_TP < \tau_SL | \Omega_paths)
- B3: Expected First Hit Time [E[\tau_hit]] = E[min(\tau_TP, \tau_SL)]
- B4: Momentum Half-Life [h_1/2] = inf { h > \tau_peak : |Z_tilde(h)| <= 0.5 * |Z_tilde(\tau_peak)| }
- B5: Session Horizon Alignment [S_align] = cos(\theta_session - \theta_apex)

FAMILY C: UNCERTAINTY GEOMETRY & DISPERSION
- C1: Normalized Corridor Width [W_norm(h)] = (q_90(h) - q_10(h)) / (P_0 * ATR_norm)
- C2: Forward Hurst Exponent [H_fwd]: log(R/S)_h ~ H_fwd * log(h)
- C3: Forward Volatility Squeeze [Squeeze_fwd] = min_h(W_norm(h)) / mean(W_norm(h))
- C4: Quantile Skewness Twist [S_skew(h)] = ((q_90 - q_50) - (q_50 - q_10)) / (q_90 - q_10)
- C5: Multi-Scale Corridor Expansion Rate [\Gamma_corridor] = d/dh log(W_norm(h))

FAMILY D: SPATIAL SUPPORT/RESISTANCE & ORDER FLOW CONFLUENCE
- D1: Forward Point of Control [fPOC] = argmax_p Density(p; \Omega)
- D2: Liquidity Sweep Probability [P_sweep] = P(P_min < Level_liquidity | \Omega_paths)
- D3: Confluence Delta [\Xi] = exp(-|Level_hist - fPOC| / \sigma_fwd)
- D4: Order Book Imbalance Coherence [OFI_coh] = corr(OFI_t, \Delta P_50)
- D5: Barrier Reflexivity Index [\rho_barrier] = d/dx P(\tau_barrier <= h | x = P_0)

FAMILY E: MODEL EPISTEMICS & ENTROPY
- E1: Multi-Model Forecast Disagreement [\Delta_models(h)] = std(P_{50, m}(h)) / ATR
- E2: Predictive Shannon Entropy [H_fwd(h)] = -\int f(p) log f(p) dp
- E3: Copula Tail Dependence [\lambda_U, \lambda_L]
- E4: Brier Calibration Deviation [BCD] = (1/N) \sum (P_dir - Y_actual)^2 - E_calibrated

FAMILY F: EMPIRICAL CALIBRATION & BENCHMARKING
- F1: Quantile Coverage Error [QCE_\alpha] = |(1/N) \sum 1(P_{t+h} <= q_\alpha) - \alpha|
- F2: Probability Integral Transform Uniformity [PIT_p] via Kolmogorov-Smirnov test
- F3: Pinball Loss Differential [\Delta L_pinball] = L_FHA - L_benchmark

FAMILY G: PATH TOPOLOGY & REGIME SHIFT
- G1: Forward Kaufman Efficiency Ratio [KER_fwd] = |P_50(H) - P_0| / \sum |P_50(h) - P_50(h-1)|
- G2: Topological Winding Number [W_path] = (1/2\pi) \oint d\theta
- G3: Candle Silhouette Ratio [S_candle] = |Open - Close| / (High - Low)

FAMILY H: MULTI-TIMEFRAME COHERENCE & HARMONIC RECONCILIATION
- H1: Multi-Timeframe Phase Coherence [\Phi_coh] = (1/M) \sum cos(Phase_{m1} - Phase_{m2})
- H2: Forward Cycle Phase Angle [\Theta_cycle] = arctan2(Im(Hilbert(P_50)), Re(Hilbert(P_50)))

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SECTION 5: QUANTITATIVE PLAYBOOKS (PB1 THROUGH PB6)
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- PB1 (Trend-Path Momentum): Triggers on \Omega_path >= 0.40, P_dir >= 0.68, and \Delta_models <= 0.35 ATR.
- PB2 (Forward Mean-Reversion): Triggers when spot extends beyond q_90 while fRSI > 75 and \kappa(h) indicates deceleration.
- PB3 (Forward Volatility Squeeze): Triggers when corridor width pinches below 0.20 ATR (Squeeze <= 0.35) followed by Hurst expansion H_fwd > 0.62.
- PB4 (Forward Liquidity Sweep / Trap): Exploits fake breakout sweeps where price spikes past key levels with P_sweep > 0.70 before snapping back.
- PB5 (Calibration Arbitrage +EV): Exploits mispricings between FHA empirical copula probabilities and Polymarket/Hyperliquid market implied odds.
- PB6 (Asymmetric Payoff Wave-Anchoring): Anchors Take-Profit at \tau_apex and Stop-Loss safely outside early drawdowns, achieving > 3:1 Risk/Reward.

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SECTION 6: CITATION & CONTACT
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BibTeX:
@article{truong2026fha,
  title={Probabilistic Indicator Lifting, Copula Sensitivity, and Multi-Scale Interference in Deep-Learning Financial Forecasting},
  author={Truong, Hoang Nhan},
  journal={FHA Quantitative Research Lab Working Paper Series},
  year={2026},
  doi={10.5281/zenodo.23789177},
  url={https://doi.org/10.5281/zenodo.23789177}
}

Official Website: https://fhaquant.com
Institutional Research Contact: quant@fhaquant.com
Preprint Repository: https://zenodo.org/records/23789177