Redefinition of Cosmological Distances: Debugging the Hubble Tension and the Dark Energy Illusion (k-Foam Theory)

[Description] Modern cosmology relies heavily on redshift ($z$-values) as a primary observational tool for estimating cosmic distances. Within the standard framework, redshift is interpreted predominantly as a consequence of cosmic expansion. This working paper, developed within the k-Foam framework, explores an alternative interpretation in which the observed redshift may be decomposed into multiple contributing components. In this view, the measured redshift is treated as a compound quantity that may include both a component associated with large-scale spatial dynamics ($\Lambda_{real}$) and an additional contribution that could arise from geometric or topological effects related to propagation through a discrete $k=6$ spatial structure. The study investigates whether such a decomposition could offer a different perspective on distance estimation at cosmological scales, and whether certain observational tensions might be reinterpreted within this framework. Key Observations and Hypotheses: - On the Hubble tension: The discrepancy between early-universe and late-universe measurements of $H_0$ may reflect sensitivity to different contributing components of the observed redshift, rather than a direct inconsistency. - On accelerated expansion: The apparent acceleration inferred from Type Ia supernova observations may admit alternative interpretations if additional cumulative effects are present in the measured redshift. - On high-redshift galaxy observations: Certain early-epoch galaxy observations (e.g., those associated with the James Webb Space Telescope) that appear difficult to reconcile with standard timelines may be re-examined under modified distance interpretations. This work does not challenge the observational results of modern cosmology. Instead, it proposes a reinterpretation of how redshift measurements are decomposed and understood, within a speculative geometric framework based on discrete spatial structure. The framework is exploratory and remains unverified, but aims to highlight the possibility that aspects of cosmological inference may depend on underlying assumptions about the nature of space and propagation.