Crowd Dynamics and Behavior

This work presents an innovative probabilistic approach to solving the regularity problem of incompressible Navier-Stokes equations in 3D, by reformulating fluid dynamics via a multi-scale state function P(t). The modeling relies on P(t) = A ψ(S, R, V, D[D_cond, D_act], C, T, M) ⋅ [O(t) ⋅ D(t)], integrating multi-scale interactions, instabilities, and energy dissipation, with a dynamic memory M to stabilize turbulence. Analytical derivations prove equivalence to the Navier-St

SMOT (Sterking Memory Operator Theory) introduces a formal framework to understand the role of memory in complex systems. It defines memory not as storage, but as an active operator structuring system dynamics over time. The framework explores how past states constrain present configurations and future evolutions. It establishes the concept of the Sterking Limit as a boundary of structural stability. Beyond this limit, systems lose coherence and enter unstable or irreversibl

Observable reality (markets, crowds, cycles) is not chaotic but structured by universal states (1–9), thresholds of collective memory (Fibonacci), and fractal dynamics. The formula P(t) is its functional expression, linking psychology, perception, and direction to produce the observable phenomenon. Perfect numbers mathematically confirm this coherence: despite complexity, everything converges toward unity, then begins again.

The robot automatically analyzes market trends using a multi–timeframe system. It detects bullish, bearish, and neutral phases and generates signals aligned with overall market dynamics. Its model uses several “virtual contracts” with different profit objectives to smooth performance. It adapts to many asset classes (indices, cryptocurrencies, etc.) and results vary depending on volatility. All performances are based on real historical data, but they never guarantee futur

The LWJS Screener MTF is a Pine Script v6 indicator that analyzes multi-timeframe market phases (15 min, 1 h, 4 h, D1, W1, M1) for a ticker, using RSI, MACD, ATR, and volume to detect bullish, bearish, or neutral trends. It calculates phases per timeframe via request.security , checks for complete or partial alignments (bullish/bearish), and highlights immediate weekly (MH/MB) activations with visual labels such as ▲, ▼, W▲, W▼. The inputs allow customization of parameters (