IndisputableMonolith.Information.ShannonAsJCostLimit
This module introduces the classical Shannon channel capacity as the high-N limit of the Recognition Science J-cost formulation. Researchers recovering standard information bounds inside the monolith would cite the definitions when passing to the classical regime. The module supplies the base capacity expression together with a finite-N correction term whose vanishing is proved downstream.
claimThe classical Shannon channel capacity is $C = \log_2 N$ (in bits), recovered exactly as the limit of the RS cost-based capacity when the number of states $N \to \infty$.
background
The module sits in the Information domain and imports Constants, where the fundamental RS time quantum is defined as $\tau_0 = 1$ tick, together with the Cost module that supplies the J-cost structure. It introduces the classical capacity expression alongside the RS correction $\mathrm{correction_{RS}}(N) = \log_2(1 + 1/(\phi N))$. The setting prepares the high-N limit argument that recovers ordinary Shannon theory from the Recognition Science monolith.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the base objects for the ShannonHighNLimit theorem, which proves that the RS finite-N correction tends to zero as $N \to \infty$ and thereby recovers the classical Shannon capacity exactly. It corresponds to the Track E5 deepening of Plan v5.
scope and limits
- Does not prove the high-N limit itself.
- Does not derive the correction term from the J-cost equation.
- Does not address forcing-chain steps T0-T8 or the Recognition Composition Law.
- Does not connect to the phi-ladder mass formula or Berry threshold.