IndisputableMonolith.Information.QuantumChannelCapacityFromPhi
The module defines the φ-ladder finite-N correction factor for quantum channel capacity at input-symbol-count N. Information theorists working in Recognition Science cite these objects when adjusting capacity bounds for small symbol counts. The module consists of a core definition together with lemmas on positivity, ordering, and bounds.
claimThe φ-ladder finite-N correction factor for quantum channel capacity at input-symbol-count $N$ is denoted correction$(N)$.
background
The module resides in the Information domain and imports the fundamental RS time quantum τ₀ = 1 tick from Constants. It introduces the correction factor drawn from the φ-ladder together with auxiliary statements on its sign and monotonicity. The local setting applies the self-similar fixed point of phi to finite-N quantum information quantities.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the finite-N correction that enters quantum channel capacity calculations inside Recognition Science. It links the phi-ladder fixed point to information bounds and supports the sibling certification object QuantumChannelCapacityCert.
scope and limits
- Does not derive the full quantum channel capacity expression.
- Does not treat the infinite-N limit.
- Does not incorporate explicit noise models.