Closed-Form Complex-Domain Encoding vs Learned Neural Encoders for Time-Series Trajectory Data: Lossless Reconstruction, Output Determinism, Compute Efficiency, and Calibration-Free Forecasting

This revised deposit contains the Paper 5 manuscript (PDF and DOCX) along with the supplementary reproducibility archive. The manuscript files were added in this revised version of the deposit; the supplementary ZIP file remains unchanged from the original deposit. Manuscript targets IEEE Transactions on Neural Networks and Learning Systems (under preparation). Coverage. 4 pre-registered studies (Studies 63-66, Phase XI of the spiral-domain encoder validation campaign). 12 hypotheses, 5 SUPPORTED (42%), 7 honest bounded negatives substantively interpreted (two of which revealed stronger architectural findings than the literal hypotheses tested). Substantive findings. 7 orders of magnitude lower encode-decode RMSE than matched autoencoder (5.4e-8 vs 0.13); 32 orders of magnitude lower output variance than VAE (1.05e-32 vs 0.885); 117x faster inference vs transformer; 2,589x fewer parameters; 30x better small-data forecast RMSE; zero training epochs (instant cold-start); AR(1) near-optimal for spiral-encoded trajectories (learned heads make forecasting worse). Contents. Manuscript (PDF and DOCX of the paper itself); supplementary reproducibility archive containing: README.md (submission-package map and reproduction instructions); preregistrations/ (frozen pre-registration .md documents with literal-threshold decision rules); reports/ (per-study .md verdict reports against frozen rules + phase summaries); runners/ (deterministic Python runners under PYTHONHASHSEED=0); raw_data/ (per-study CSV outputs and JSON verdict blocks); figures/ (manuscript figures at 300 DPI + figure-build script); code/ (encoder source code). Reproducibility. Full validation pipeline is reproducible end-to-end under PYTHONHASHSEED=0 on a standard Python 3.9+ installation with NumPy 2.0+, SciPy, scikit-learn, and PyTorch 2.8+ (required for the autoencoder, variational autoencoder, and transformer baselines). For full reproducibility of the determinism measurements, configure torch.use_deterministic_algorithms(True) and run on CPU. Reference machine: Apple Silicon arm64 (M-series), macOS 14. Methodological discipline. Every hypothesis was pre-registered with externally anchored decision rules frozen prior to runner execution. Zero post-hoc threshold adjustments were applied. Honest bounded negatives are interpreted substantively rather than discarded. Related companion archives. Paper 1 (10.5281/zenodo.20129137), Paper 2 (10.5281/zenodo.20138786), Paper 3 (10.5281/zenodo.20139171), and the corresponding Papers 4, 6, 7, 8 archives in this same Zenodo collection (Paper 8 at 10.5281/zenodo.20466035).