IndisputableMonolith.Information.QECThresholdFromPhiLadder
This module defines quantum error correction code families and derives their thresholds from the phi-ladder in Recognition Science. It supplies the code family, count, threshold function, positivity, decay, and certification objects that tie QEC performance to phi self-similarity. Information theorists working within RS foundations would cite these definitions when computing thresholds from the eight-tick octave and phi constants. The module is definitional, establishing the families and their basic properties without proof bodies.
claimDefines families of quantum error correcting codes parameterized by rungs on the phi-ladder together with the threshold function mapping each family to a positive real number that exhibits decay.
background
This module operates in the Information domain and imports the RS time quantum from Constants. The upstream result states: The fundamental RS time quantum (RS-native). τ₀ = 1 tick. It introduces the quantum error correction code family as collections of codes built along the phi-ladder, with auxiliary functions for counting members and computing the error threshold. The setting grounds discrete information structures in the tick-based time of Recognition Science, preparing links to phi-based constants such as ħ = phi^{-5}.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the QEC threshold definitions that support information-theoretic extensions of Recognition Science. It fills the gap between the phi-ladder and quantum error correction, enabling future ties to the mass formula and Berry creation threshold at phi^{-1}. No immediate downstream theorems are listed, but it contributes certified thresholds to the framework.
scope and limits
- Does not derive numerical threshold values outside the phi parameterization.
- Does not prove physical achievability of the thresholds.
- Does not address classical error correction.
- Does not integrate with the full T0-T8 forcing chain.