capacity_at_10_percent
plain-language theorem explainer
The definition supplies the Shannon capacity value for a binary symmetric channel at 10 percent crossover probability by direct substitution into the binary entropy expression. Researchers modeling information transmission under Recognition Science's eight-tick redundancy would reference this constant when bounding reliable rates. The implementation is a one-line wrapper that invokes binarySymmetricCapacity on the fixed argument 0.1.
Claim. The capacity of a binary symmetric channel with crossover probability 0.1 equals $1 - H(0.1)$, where the binary entropy is $H(p) = -p log_2 p - (1-p) log_2 (1-p)$.
background
The Information.ErrorCorrectionBounds module derives error correction bounds from the eight-tick structure. Shannon's channel capacity theorem states that the maximum reliable transmission rate for a channel with noise probability p is C = 1 - H(p), where H is the binary entropy. The upstream binarySymmetricCapacity implements this as 1 + p * (Real.log p / Real.log 2) + (1-p) * (Real.log (1-p) / Real.log 2). The module links the formula to 8-tick phases that supply natural redundancy for error correction.
proof idea
This definition is a one-line wrapper that applies binarySymmetricCapacity to the argument 0.1.
why it matters
This definition supplies a concrete numerical anchor for error correction analysis in the Recognition Science framework, showing that a 10 percent error rate still permits reliable transmission at roughly 53 percent of raw capacity. It illustrates the module's application of Shannon capacity inside the eight-tick redundancy mechanism. No downstream uses are recorded, yet the constant supports the broader derivation of bounds from the eight-tick octave.
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