bandwidth_linear
plain-language theorem explainer
Recognition bandwidth scales linearly with the enclosed area in the Recognition Science model. Researchers deriving information processing rates from holographic bounds would cite this result when rescaling from microscopic to macroscopic areas. The proof proceeds by unfolding the bandwidth definition and applying ring normalization to the resulting expression.
Claim. Let $A$ be an area and $c > 0$ a positive real scalar. Then the recognition bandwidth of the scaled area $cA$ equals $c$ times the recognition bandwidth of $A$.
background
Recognition bandwidth is defined in this module as the maximum rate at which recognition events can be processed within a holographically bounded region. It is expressed as the holographic capacity divided by the product of the recognition cost per bit $k_R = ln(phi)$ and the eight-tick cadence period $8 tau_0$, yielding a quantity proportional to the boundary area $A$ over the Planck area scale.
proof idea
The proof is a one-line wrapper that unfolds the bandwidth definition and applies the ring tactic to verify the linear scaling algebraically.
why it matters
This result fills a basic scaling property in the recognition bandwidth definitions, supporting the holographic capacity recovery section of the module. It aligns with the 8-tick cadence and area proportionality from the holographic bound in the unified forcing chain. Though currently unused by other declarations, it closes a prerequisite for the monotone and positive bandwidth siblings.
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