V99: Information Depth and Differential Observables — Why Differences, Not Origins, Encode Physical Information in a Finite Updating Universe

In previous works (V33, V96, V98), we established that the origin of information in a finite updating universe is internally undefinable, and that matter becomes physically definable only after the establishment of three operational roles of the universal constant C. In this paper (V99), we demonstrate that it is neither necessary nor meaningful to identify information itself in order to connect informational cosmology with physical observables. Instead, we show that differences arising from accumulated informational depth—rather than absolute information content—constitute sufficient and observable physical signatures. By introducing Information Depth (D) as an operational quantity and focusing on its differentials, retention ratios, and migration patterns, we establish a framework in which physical phenomena encode information indirectly but robustly. The key insight is that the universe has no "incinerator"—complete erasure is impossible, and deletion always incurs cost. This structural necessity explains why conservation laws emerge as consequences rather than axioms, and why all physical measurements detect differences (ΔD), costs, and asymmetries rather than information itself. This approach explains why isotopic ratios, elemental distributions, supernova outputs, and irreversible energetic costs act as faithful proxies of information processing, without invoking inaccessible origins or metaphysical definitions of information. We conclude that physics measures "the cost of not forgetting."