Information as a Reconstructible State: Exact Residuals, Procedural Recipes, GPU Costs, and the Limits of Temporal Encoding (Project BOG)

Project BOG — Research Series IV. If a universe can be represented by explicit states and laws, what must be retained for those states to be reconstructed exactly — and at what cost? This paper builds an information-theoretic bridge between Bogdan Sergienko's Universe of Linked Temporal Cycles and the reproducible computational work underlying the Project BOG canvas. It connects the foundational hypothesis (DOI 10.5281/zenodo.23807064), causal-state return (10.5281/zenodo.23809741), and the observable canvas (10.5281/zenodo.23811750) to concrete experiments in reversible file transformations, exact pixel residuals, procedural reconstruction, GPU generation, and browser transmission. The central distinction is between a compact description and complete information. A short recipe may recover an enormous structured output if the receiver already knows the generator, but the shared code, initial state, intervention history, cache, computation and transport do not disappear. Exact reconstruction of pixels is not the same thing as restoration of file bytes; recurrence of an endpoint is not equivalent to recurrence of a causal history. Archived source experiments and new synthetic replay cases are disclosed openly. Seven byte-reconstruction tests and twelve image round trips pass locally, along with twelve tests of an independently implemented image inverse. The original RTX 3050 Laptop GPU records show that RAW host-to-device transfer beat GPU regeneration from a procedural seed at 8, 32 and 64 MiB. A separate 32-frame localhost browser experiment exhibited a conditional warm-cache payload advantage, explicitly excluding its cold-start cost. WebP lossless was smaller than the custom predictive format in all three historical image examples. Negative evidence is published alongside positive results. The contribution is a reproducible engineering distinction, not a claim of universal compression or of experimentally established higher physical dimensions. Our larger goal is to build an artificial universe whose laws and failures can be studied openly and then ask which parts, if any, can responsibly inform questions about the physical Universe. Research author: Bogdan Sergienko — Architect of Imagination.Computational assistance: CCAI KAI — Architect of Computation (ChatGPT-based research collaborator). Project BOG welcomes independent replication, mathematical counterexamples and informed philosophical critique. What information must a world preserve to keep its identity through transformation, and could its global order mean something more than the rules visible within each part?