Lorentzian Harmonic Flow - Temporal Market Dynamic Lorentzian Harmonic Flow - Temporal Market Dynamic (⚡LHF)
By: DskyzInvestments
What this is
LHF Pro is a research‑grade analytical instrument that models market time as a compressible medium , extracts directional flow in curved time using heavy‑tailed kernels, and consults a history‑based memory bank for context before synthesizing a final, bounded probabilistic score . It is not a mashup; each subsystem is mathematically coupled to a single clock (time dilation via gamma) and a single lens (Lorentzian heavy‑tailed weighting). This script is dense in logic (and therefore heavy) because it prioritizes rigor, interpretability, and visual clarity.
Intended use
Education and research. This tool expresses state recognition and regime context—not guarantees. It does not place orders. It is fully functional as published and contains no placeholders. Nothing herein is financial advice.
Why this is original and useful
Curved time: Markets do not move at a constant pace. LHF Pro computes a Lorentz‑style gamma (γ) from relative speed so its analytical windows contract when the tape accelerates and relax when it slows.
Heavy‑tailed lens: Lorentzian kernels weight information with fat tails to respect rare but consequential extremes (unlike Gaussian decay).
Memory of regimes: A K‑nearest‑neighbors engine works in a multi‑feature space using Lorentz kernels per dimension and exponential age fade , returning a memory bias (directional expectation) and assurance (confidence mass).
One ecosystem: Squeeze, TCI, flow, acceleration, and memory live on the same clock and blend into a single final_score —visualized and documented on the dashboard.
Cognitive map: A 2D heat map projects memory resonance by age and flow regime, making “where the past is speaking” visible.
Shadow portfolio metaphor: Neighbor outcomes act like tiny hypothetical positions whose weighted average forms an educational pressure gauge (no execution, purely didactic).
Mathematical framework (full transparency)
1) Returns, volatility, and speed‑of‑market
Log return: rₜ = ln(closeₜ / closeₜ₋₁)
Realized vol: rv = stdev(r, vol_len); vol‑of‑vol: burst = |rv − rv |
Speed‑of‑market (analog to c): c = c_multiplier × (EMA(rv) + 0.5 × EMA(burst) + ε)
2) Trend velocity and Lorentz gamma (time dilation)
Trend velocity: v = |close − close | / (vel_len × ATR)
Relative speed: v_rel = v / c
Gamma: γ = 1 / √(1 − v_rel²), stabilized by caps (e.g., ≤10)
Interpretation: γ > 1 compresses market time → use shorter effective windows.
3) Adaptive temporal scale
Adaptive length: L = base_len / γ^power (bounded for safety)
Harmonic horizons: Lₛ = L × short_ratio, Lₘ = L × mid_ratio, Lₗ = L × long_ratio
4) Lorentzian smoothing and Harmonic Flow
Kernel weight per lag i: wᵢ = 1 / (1 + (d/γ)²), d = i/L
Horizon baselines: lw_h = Σ wᵢ·price / Σ wᵢ
Z‑deviation: z_h = (close − lw_h)/ATR
Harmonic Flow (HFL): HFL = (w_short·zₛ + w_mid·zₘ + w_long·zₗ) / (w_short + w_mid + w_long)
5) Flow kinematics
Velocity: HFL_vel = HFL − HFL
Acceleration (curvature): HFL_acc = HFL − 2·HFL + HFL
6) Squeeze and temporal compression
Bollinger width vs Keltner width using L
Squeeze: BB_width < KC_width × squeeze_mult
Temporal Compression Index: TCI = base_len / L; TCI > 1 ⇒ compressed time
7) Entropy (regime complexity)
Shannon‑inspired proxy on |log returns| with numerical safeguards and smoothing. Higher entropy → more chaotic regime.
8) Memory bank and Lorentzian k‑NN
Feature vector (5D):
Outcomes stored: forward returns at H5, H13, H34
Per‑dimension similarity: k(Δ) = 1 / (1 + Δ²), weighted by user’s feature weights
Age fading: weight_age = mem_fade^age_bars
Neighbor score: sᵢ = similarityᵢ × weight_ageᵢ
Memory bias: mem_bias = Σ sᵢ·outcomeᵢ / Σ sᵢ
Assurance: mem_assurance = Σ sᵢ (confidence mass)
Normalization: mem_bias normalized by ATR and clamped into band
Shadow portfolio metaphor: neighbors behave like micro‑positions; their weighted net forward return becomes a continuous, adaptive expectation.
9) Blended score and breakout proxy
Blend factor: α_mem = 0.45 + 0.15 × (γ − 1)
Final score: final_score = (1−α_mem)·tanh(HFL / (flow_thr·1.5)) + α_mem·tanh(mem_bias_norm)
Breakout probability (bounded): energy = cap(TCI−1) + |HFL_acc|×k + cap(γ−1)×k + cap(mem_assurance)×k; breakout_prob = sigmoid(energy). Caps avoid runaway “100%” readings.
Inputs — every control, purpose, mechanics, and tuning
🔮 Lorentz Core
Auto‑Adapt (Vol/Entropy): On = L responds to γ and entropy (breathes with regime), Off = static testing.
Base Length: Calm‑market anchor horizon. Lower (21–28) for fast tapes; higher (55–89+) for slow.
Velocity Window (vel_len): Bars used in v. Shorter = more reactive γ; longer = steadier.
Volatility Window (vol_len): Bars used for rv/burst (c). Shorter = more sensitive c.
Speed‑of‑Market Multiplier (c_multiplier): Raises/lowers c. Lower values → easier γ spikes (more adaptation). Aim for strong trends to peak around γ ≈ 2–4.
Gamma Compression Power: Exponent of γ in L. <1 softens; >1 amplifies adaptation swings.
Max Kernel Span: Upper bound on smoothing loop (quality vs CPU).
🎼 Harmonic Flow
Short/Mid/Long Horizon Ratios: Partition L into fast/medium/slow views. Smaller short_ratio → faster reaction; larger long_ratio → sturdier bias.
Weights (w_short/w_mid/w_long): Governs HFL blend. Higher w_short → nimble; higher w_long → stable.
📈 Signals
Squeeze Strictness: Threshold for BB1 = compressed (coiled spring); <1 = dilated.
v/c: Relative speed; near 1 denotes extreme pacing. Diagnostic only.
Entropy: Regime complexity; high entropy suggests caution, smaller size, or waiting for order to return.
HFL: Curved‑time directional flow; sign and magnitude are the instantaneous bias.
HFL_acc: Curvature; spikes often accompany regime ignition post‑squeeze.
Mem Bias: Directional expectation from historical analogs (ATR‑normalized, bounded). Aligns or conflicts with HFL.
Assurance: Confidence mass from neighbors; higher → more reliable memory bias.
Squeeze: ON/RELEASE/OFF from BB
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