This note develops a metric–measure framework for weighted discrete flows, suggesting new insights into geometry.
We develop a discrete metric–measure framework in which informational depth acts as a unified structural variable, simultaneously modifying distance, measure, conductance, and diffusion. The resulting weighted discrete flows are shown to satisfy stability, coercivity, and non-collapse properties under refinement. The note provides a mathematically controlled formulation of informational weighting as geometry.
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Pablo González Ferreiro (2026) studied this question.
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