SynechismCore v23.0

Latent Neural ODEs with Aperiodic φ-Scaling for Chaotic Dynamical Systems

Author: Paul E. Harris IV · Independent Researcher, Mashantucket Pequot Nation
Status: Codebase locked, mathematically patched, and optimized for Hopper GPUs (v23.0.1). Pending full 10-seed empirical benchmark run.

Overview

SynechismCore is a Latent Neural ODE architecture that uses golden-ratio ($\varphi$) aperiodic time sampling and attractor regularization to model chaotic and regime-shifting dynamical systems. The core question this project answers empirically:

When do continuous latent dynamics provide a measurable advantage over discrete sequence models — and when do they not?

We report results honestly. The architecture's confirmed wins (KS-PDE, Lorenz bifurcation) are documented alongside its failures (Robotics actuator loss). The v23.0 architecture introduces three surgical components to directly address the failure modes identified in v22.

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🚀 What's New in v23.0 (Architecture Complete)

The v23 architecture is fully implemented and patched for mathematical correctness and hardware efficiency.

1. IrrationalShutter: Replaces adaptive dopri5 stepping with forced rk4 steps exactly on the $\varphi$-Weyl sequence grid. Goal: Eliminate resonance and phase-locking on high-chaos fractal attractors (e.g., Lorenz $\rho \ge 45$).
2. ElasticManifold: Couples a learned regime-shift event detector to the attractor radius constraint, allowing the topological boundary to dynamically "breathe" (expand via a GELU network). Goal: Recover the $0.52\times$ loss on discontinuous underdamped physics (Robotics).
3. LaminarBypass: A local-curvature heuristic that routes smooth dynamics through a computationally cheap, $\Delta t$-aware linear projection, reserving heavy ODE integration only for turbulent bursts. Goal: Drastically reduce wall-clock time.

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📊 Current Status: Confirmed Results vs Pending Claims

Confirmed v22 Results (Produced on Kaggle free-tier P100/T4):

• ✅ KS-PDE ($\nu$: 1.0→0.5): $1.43\times$ MAE win over Transformer across 5 seeds.
• ✅ Lorenz-63 Coherence: 19,940 continuous prediction steps before divergence ($15.8\times$ vs baselines).
• ✅ $\varphi$-Significance: Aperiodic sampling achieves $p=0.0000$ over uniform grids.
• ❌ Robotics ($\gamma$: 0.5→0.05): ODE loses badly ($0.52\times$) to Transformer due to fixed attractor sphere.
• ⚠️ Weather L96 / Finance: Statistically tied or marginally significant.

Pending v23 Benchmark (Awaiting H100 execution):

• ⏳ Claim 4 Ablation: Does $\varphi$ specifically beat $\sqrt{2}$ and $e$?
• ⏳ Robotics Recovery: Does ElasticManifold turn the $0.52\times$ loss into a win?
• ⏳ High-Chaos Lorenz: Does IrrationalShutter prevent topological collapse at $\rho=50$?
• ⏳ KS-PDE 10-Seed Validation: Does the $1.43\times$ headline hold under rigorous 10-seed Mann-Whitney U testing?

(Note: Empirical JSON results will be pushed to /results/v23/ upon run completion.)

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⚙️ Repository Structure

SynechismCore/
├── src/
│   ├── models.py             # v22 core: SynechismV20, all baselines
│   ├── v23_components.py     # ElasticManifold, IrrationalShutter, LaminarBypass
│   ├── hyperagent.py         # Event detector + discrete jump correction
│   ├── data.py               # 5 synthetic dynamical system generators
│   ├── train.py              # Training loop + evaluation module
│   ├── stats.py              # Corrected Mann-Whitney U significance testing
│   ├── chaotic_metrics.py    # VPT, sMAPE, nRMSE, fractal dimension
│   ├── quantum_lattice.py    # PhiLattice, FibonacciLattice, HaltonLattice
│   └── hyevo.py              # Evolutionary hyperparameter search
│
├── launch_h100.py            # H100-optimized full suite launcher (TF32 + torch.compile)
├── run_v23_benchmark.py      # v23 vs v22 head-to-head + coherence testing
├── run_phi_ablation.py       # φ vs √2 vs e ablation 
├── run_experiments.py        # Legacy v22 5-experiment benchmark
└── results/                  # JSON outputs go here

💻 Quick Start & Reproduction

1. Install Dependencies

pip install torch torchdiffeq scipy pandas matplotlib

(PyTorch 2.0+ required for torch.compile optimizations).

2. Sanity Check (~5 mins) Verify the pipeline works before renting heavy compute:

python launch_h100.py --quick

3. Run the Full v23 Benchmark Suite This executes the $\varphi$-ablation, v23 component tests, coherence tests, and KS-PDE multi-seed validation. Optimized for NVIDIA Hopper (H100) or Ampere (A100) GPUs.

# Start a persistent screen session
screen -S synechism

# Launch the full 10-seed suite
python launch_h100.py --seeds 0 1 2 3 4 5 6 7 8 9

🔬 Significance Testing Methodology All multi-model comparisons use the non-parametric Mann-Whitney U test over per-sample error distributions to preserve the i.i.d. assumption:

# Averages error over Time and Dimension FIRST
ode_errors = np.abs(ode_preds - true_values).mean(axis=(1, 2))   # Shape: (N,)
baseline_errors = np.abs(baseline_preds - true_values).mean(axis=(1, 2))
stat, p = scipy.stats.mannwhitneyu(ode_errors, baseline_errors, alternative='less')

This prevents the artificial inflation of $N$ (and subsequently hacked $p$-values) common in flattened time-series benchmarking.

📜 Citation

@misc{harris2026synechismcore,
  title     = {SynechismCore: Latent Neural ODEs with Aperiodic phi-Scaling for Chaotic Dynamical Systems},
  author    = {Harris IV, Paul E.},
  year      = {2026},
  note      = {Preprint. v23 benchmark pending.},
  url       = {https://github.com/pz33y/SynechismCore}
}

License: MIT