surfaceCodeThreshold
plain-language theorem explainer
Recognition Science predicts the surface code fault tolerance threshold as the recognition quantum divided by ten. Quantum computing researchers cite this when comparing to the empirical threshold near one percent. It is a direct definition performing that division.
Claim. The RS surface code threshold equals $J(φ)/10$, with $J(φ)$ the recognition quantum.
background
This sits in the Quantum Error Correction Threshold from J-Cost module. The recognition quantum equals phi minus three halves and represents J(φ). Upstream the empirical surface code threshold is defined as 0.01, below which arbitrarily long computation is possible as stated in its doc-comment: 'Surface code threshold: p_threshold ≈ 1%. Below this error rate, arbitrarily long computation is possible. Above it, errors accumulate faster than correction.'
proof idea
The declaration is a one-line definition that divides the recognition quantum by ten.
why it matters
It provides the RS-predicted threshold that populates the ErrorCorrectionCert structure and supports the surfaceCodeThreshold_pos theorem. This fills the Recognition Science prediction for the surface code threshold at J(φ)/10 ≈ 1.18%, aligning with the empirical one percent and the 0.5-2% band noted in the module. The falsifier is any implementation exceeding two percent or below 0.1 percent.
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