quantumChannelCapacityCert
This definition packages the three properties of the phi-based correction into a single certificate structure for quantum channel capacity. Information theorists studying finite-N corrections would cite it to invoke positivity, monotonicity, and the 1/N bound simultaneously. The construction is a direct record that supplies the three supporting lemmas to the structure fields.
claimLet correction denote the phi-suppressed finite-N correction to quantum channel capacity. The certificate is the structure asserting that for every positive integer $N$, correction$(N) > 0$, correction$(N+1) < $ correction$(N)$, and correction$(N) ≤ 1/N$.
background
The module derives a correction to the quantum (entanglement-assisted) channel capacity that scales as log₂(1 + 1/(φ N)) per input symbol, extending the classical Shannon bound already formalized via J-cost. The correction function is defined from the golden ratio φ supplied by Constants.phi. The certificate structure QuantumChannelCapacityCert collects exactly the three properties required for rigorous use of this correction: positivity for all positive N, strict decrease as N increases, and the bound by 1/N.
proof idea
The definition is a one-line wrapper that directly supplies the three upstream theorems correction_pos, correction_strictly_decreasing, and correction_le_inv to the corresponding fields of the QuantumChannelCapacityCert structure.
why it matters in Recognition Science
This certificate completes the formal packaging of the phi-ladder correction for quantum channel capacity, supporting the module's structural prediction that the entanglement-assisted-to-classical ratio carries a distinguishable 1/N term. It draws on the phi constant from the unified forcing chain (T6) and the J-cost framework. No downstream uses are recorded yet, leaving the certificate available for applications in finite-block quantum information bounds.
scope and limits
- Does not derive the explicit functional form of the correction.
- Does not evaluate numerical capacities for concrete channels.
- Does not address entanglement measures beyond the correction term.
- Does not prove the classical limit as N tends to infinity.
formal statement (Lean)
81def quantumChannelCapacityCert : QuantumChannelCapacityCert where
82 correction_pos := @correction_pos
proof body
Definition body.
83 strictly_decreasing := correction_strictly_decreasing
84 bounded_by_inv := @correction_le_inv
85
86end
87end QuantumChannelCapacityFromPhi
88end Information
89end IndisputableMonolith