IndisputableMonolith.QuantumComputing.ErrorCorrectionThresholdFromJCost
This module defines the recognition quantum as J(φ) and builds error correction objects from the J-cost in Recognition Science. Quantum information researchers would cite its surface code threshold and ErrorCorrectionCert when linking RS-native units to fault-tolerant bounds. The module consists entirely of definitions that connect the imported Cost and Constants machinery to quantum thresholds.
claimThe recognition quantum is given by $J(φ)$; the surface code threshold and error rate cost are derived from this $J$-cost to certify error correction.
background
Recognition Science derives all physics from the J-cost functional equation. This module sits in the QuantumComputing domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the J-cost definitions from Cost. It introduces recognitionQuantum as J(φ), errorRateCost, and the ErrorCorrectionCert to certify thresholds.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module supplies the quantum error correction bridge that integrates with the Recognition Science forcing chain at T5 J-uniqueness and the phi-ladder constants. It feeds the definitions of recognitionQuantum and surfaceCodeThreshold into the broader framework for connecting J-cost to practical quantum thresholds.
scope and limits
- Does not prove numerical values of the threshold.
- Does not simulate quantum circuits.
- Does not address experimental validation.
- Does not extend beyond the J-cost model.