Pattern Recognition in Discrete Twisted Lattices: Data, Code, and Sensitivity Analysis (v1.0.0)

Overview

This repository contains the full simulation data, code, and analysis for the study "Pattern Recognition in Discrete Twisted Lattices." This work documents the scaling behavior of discrete photonic lattices with anti-periodic boundary conditions, specifically investigating the $\lfloor L/2 \rfloor$ dependence of critical curvature $K_c$.

This Zenodo release serves as the permanent, citable archive for the data, code, and sensitivity analysis supporting the manuscript.

Key Evolution of Understanding

This project documents a shift from observing "perfect" constants to identifying numerical artifacts and conditional stability:

1. Initial Illusion: Coarse scans suggested universal constants ($\alpha \approx 0.19$ for Klein Bottle, $\alpha \approx 0.12$ for Twisted Torus).
2. Artifact Discovery: High-resolution binary search ($10^{-8}$) revealed these were grid artifacts.
3. Metric Harmonization: Switching to a unified Euclidean metric eliminated the hypothesized $\sqrt{2}$ ratio between topologies.
4. The "Smooth Twist" Falsification: Replacing the hard discontinuous twist with smooth variants (Cosine, Linear Ramp) caused the system to become oscillatory at $K=0$, eliminating the stable phase and the $\lfloor L/2 \rfloor$ scaling pattern entirely.

Current Findings (High-Resolution, Hard Twist)

• Conditional Stability: The $\lfloor L/2 \rfloor$ scaling pattern and stable phase ($K_c > 0$) appear strictly dependent on the use of a hard, discontinuous anti-periodic boundary condition.
• Universal Constant (Hard Boundary): Under the specific CME implementation with hard boundaries and Euclidean metric, the scaling product $P = K_c \times \lfloor L/2 \rfloor$ stabilizes at $P \approx 1.11072$ for both Klein Bottle and Twisted Torus up to $L=128$.
• Open Question: Why does the hard boundary create a stable phase while smooth perturbations induce immediate oscillation? We seek an analytical derivation for this conditional existence.

Dataset Contents

• Raw Data (CSV):
  • v1_coarse/: Original data (historical context, contains grid artifacts).
  • v2_highres/: High-resolution data (binary search, $10^{-8}$ tolerance) for Klein Bottle and Twisted Torus (Euclidean & Manhattan).
  • v3_sensitivity/: Smooth Twist sensitivity analysis (Linear Ramp, Weak Cosine) showing system oscillation.
• Scripts:
  • Core simulation scripts (High-res & Extended scale).
  • Sensitivity & Falsification scripts (smooth_twist_test.py, smooth_twist_sensitivity_test.py).
• Documentation:
  • Full manuscript (Pattern Recognition in Discrete Twisted Lattices.md).
  • Non-tech companion guide.
  • History log (HISTORY.md) tracking the evolution of findings.

Methodology Note

This research was assisted by Large Language Models (LLMs) for text generation, formatting, literature search, and code scaffolding. All conceptual frameworks, ethical arguments, and editorial decisions are the author's own. The LLM bias toward "smooth binary" solutions was noted as a challenge requiring constant human intervention to preserve non-binary analytical approaches.

Citation

Cite this dataset as:

Jacoby, K. (2026). Pattern Recognition in Discrete Twisted Lattices: Data, Code, and Sensitivity Analysis [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.20522335

Cite the manuscript as:

Jacoby, K. (2026). Pattern Recognition in Discrete Twisted Lattices. PhilArchive. https://philpapers.org/rec/JACPRI-4

License

GNU Affero General Public License v3.0 (AGPL-3.0)