We are pioneering the application of cutting-edge mathematical frameworks to financial markets. Inspired by Deterministic Deep Representation Learning via Geometric Invariants, we have successfully adapted its core principles from image analysis to financial time series.

Insight:
Instead of treating markets as purely stochastic, we model them as deterministic dynamical systems. Using the Koopman operator for linear representation of nonlinear dynamics, a log-prime Hilbert space for natural orthogonality, and geometric invariants for scale-invariant feature extraction, we build a deterministic, interpretable, and efficient framework for market analysis.

Key Achievements (Proof of Concept):
• Regime Detection: Achieved 70–94% confidence in classifying trending vs. mean-reverting regimes across diverse instruments (including SPY, QQQ, EURUSD, and BTC-USD).
• Predictive Signals: Developed trading signals with 35–54% direction accuracy above random using invariant-based strategies.
• Arithmetic Structure Discovery: Uncovered subtle prime-harmonic coherence (~0.04–0.20) in market returns, a pattern missed by traditional stochastic models.
• Compression-Accuracy Trade-off: Demonstrated smooth trade-offs between feature compression and predictive accuracy—mirroring results in image-based applications.

Why This Matters:
This framework is:
• Deterministic: No iterative training, ensuring reproducibility and transparency.
• Interpretable: Features like Hurst exponent, spectral moments, and prime coherence have clear financial meanings.
• Efficient: Runs in a single pass, making it suitable for real-time and edge applications.

Forward Testing:
The algorithm is currently under forward testing in live market conditions. We are excited to monitor its performance and refine its application across asset classes and timeframes.

This research represents a meaningful step toward more transparent, efficient, and mathematically rigorous financial analytics – bridging advanced geometry, operator theory, and quantitative finance.
https://doi.org/10.5281/zenodo.17535844

We look forward to sharing more updates as this innovative approach evolves.