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

v2 update (2026-06-01): Reproducibility ZIP added back to the latest version alongside the manuscript files, so that downloading from the concept DOI gives all materials in one place rather than requiring navigation to v1. 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) ; rawdata/ (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. usedeterministicₐlgorithms (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).