Restricted Hub-Star Phase Reconstruction: A Conditional Research Record on Ternary Resets and Noise Scaling

Abstract

Archival research record — NOT peer reviewed. Mathematical novelty: INCONCLUSIVE. This unrefereed research record studies a deliberately restricted symmetric binary hub-star Kuramoto network with known coupling and exact reset phases. Under these assumptions, a ternary initialization yields an internally checked second-jet encoding for one designated binary leaf edge. A normalized fixed-horizon comparison of noisy raw-hub-phase readings gives a model-specific Omega(sigma^2 N^4) lower bound under the stated assumptions. An upper raw-phase sample-complexity estimate remains an analytic proof outline and is NOT independently established as a complete theorem. The novelty assessment is INCONCLUSIVE; substantial overlap exists with established work on oscillator-network inference and partial observation. The work makes no claim of priority, independent peer review, broad hardware applicability, general weighted/frequency-unknown network reconstruction, or certified practical performance. The original 2026-10-16 audit concluded HOLD pending author authorization or external review. On 2026-10-17 the author authorized dissemination only as a transparently qualified archival record. The unchanged audit and its reproducibility material are included. The repository contains the 4-page English research record, TeX source, frozen audit ZIP, metadata, reproducibility notes and SHA-256 integrity checker. GitHub and Zenodo copies should be interpreted as the same archival version. Research Inquiries — Yonezu Research Lab Contact: yonezaemon1+research@gmail.com GitHub: https://github.com/yonezaemon1-hub/no28-hub-star-phase-reconstruction