gap45
plain-language theorem explainer
gap45 defines the real number 10^45 as the Gap-45 threshold. This constant approximates the Planck-to-biological timescale ratio and marks the point where environmental coupling drives decoherence in Recognition Science models. Researchers deriving quantum-to-classical transitions or error-correction bounds would cite the value. The definition is a direct constant assignment.
Claim. The Gap-45 threshold is the real number $10^{45}$.
background
Gap-45 is introduced in the QFT.Decoherence module as the boundary separating the quantum regime (coherent superposition preserved) from the classical regime (entanglement with the environment). The module sets this threshold at 10^45 to represent the approximate ratio of Planck time to a characteristic biological timescale of order 1 s. Decoherence is then expressed as occurring when the number of coupled environmental modes pushes the interaction count across this gap, using the scaling factor phi from the Recognition Science phi-ladder.
proof idea
The definition is a direct constant assignment of the literal 10^45 to the real-valued identifier gap45.
why it matters
This definition anchors the decoherence timescale derivations in the QF-009 section of the Recognition Science framework. It supplies the numerical cutoff used by sibling declarations such as decoherenceTime and decoherence_decreases_with_modes to connect discrete structure to observable loss of coherence. The value supports the broader claim that coherence persists only below the Planck-to-biological gap and opens patent routes for threshold-based qubit design.
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