bandwidth_pos'
plain-language theorem explainer
The theorem establishes that recognition bandwidth is strictly positive whenever the boundary area A is positive. Researchers bounding ledger throughput under holographic constraints in Recognition Science would cite this when deriving rate ceilings from the area formula. The proof is a direct one-line application of the companion result bandwidth_pos.
Claim. If the boundary area satisfies $A > 0$, then the recognition bandwidth $R_ {max}(A) = A / (4 ell_P^2 ln phi · 8 tau_0) > 0$.
background
The module introduces recognition bandwidth as the maximum rate of recognition events inside a holographically bounded region. It is defined by the formula R_max = A / (4 ℓ_P² · ln(φ) · 8 τ₀), where A is boundary area, ℓ_P the Planck length, φ the golden ratio, and τ₀ the fundamental tick. This expression combines the holographic bound on information capacity, the per-bit recognition cost k_R = ln(φ), the eight-tick cadence, and the ILG parameters C_lag = φ^{-5} and α = (1 - 1/φ)/2.
proof idea
This is a one-line wrapper that applies the theorem bandwidth_pos to the hypothesis hA.
why it matters
The result supplies the first key claim listed in the module: recognition bandwidth is strictly positive. It supports downstream calculations of maximum ledger throughput that connect the holographic bound, the eight-tick octave, and the recognition cost per bit inside the Recognition Science forcing chain. No open scaffolding remains for this positivity statement.
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