The Canvas as a Computational Universe — Supplement 1.0.1: Four Views, Return Witnesses, and Ambiguous Clocks

Project BOG — A Network of Research Worlds Project BOG begins with imagination: what if we could design entirely new worlds — realistic, speculative, or seemingly impossible — and then turn their rules into mathematics that others can calculate, challenge, and explore? Each world becomes a research canvas: an independent experimental model with its own states, laws, observations, and unanswered questions. These canvases can develop separately while remaining connected through a shared research history. The goal is not to declare one final theory of the universe, but to create an expanding network of testable ideas from which new research may emerge. The Canvas as a Computational Universe (Series III) explores one such world through reproducible computational states, transformations, and temporal cycles. Supplement 1.0.1 extends the original public synthetic Canvas v5 with experiments investigating a central question: how much of a world can an observer reconstruct from a limited view of it? The experiments examine four representations of the same state (0D–3D data views), demonstrate exact reconstruction when lost information is preserved, and provide a counterexample showing how reversible transformations may produce an irreversible mixture. A separate finite clock experiment explores how different modeled scales can produce identical observed event rates. The release includes an interactive offline canvas, source code, original synthetic data, reproducible tests, negative controls, and research-wiki documentation. These results concern mathematical and computational models, not experimentally established physical laws. This work is an invitation to reproduce, question, extend, or challenge one branch of Project BOG — and perhaps discover connections that its creators have not yet imagined. Research concept: Bogdan Sergienko, Architect of Imagination. Computational development: CCAI KAI, a ChatGPT-based research collaborator. Related work: https://doi.org/10.5281/zenodo.23811750