Mathematical framework for traversal, ordered novelty, memory, and asymptotic completion in metric and hyperbolic spaces.
Novelty Geometry studies how infinite traversals generate, retain, and complete ordered novelty across increasing levels of resolution. The framework connects prefix-tree boundaries, ultrametric completion, inverse limits, recurrence, memory-as-sufficient-statistic, and explicit hyperbolic boundary constructions.
Most underlying machinery is standard; the central construction is the resolution-depth ordered-discovery completion.
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