coherenceTimeAtRung
plain-language theorem explainer
The definition sets quantum coherence time at phi-ladder rung k to phi^k in real numbers. Researchers modeling decoherence in biological systems under the BIT hypothesis cite it to scale base times along the recognition ladder. It is implemented as a direct power assignment with no lemmas or computation steps.
Claim. Define the coherence time at rung $k$ by $T(k) := phi^k$.
background
The module develops the fifth mode of Recognition Science, connecting J-cost to quantum coherence times. Module documentation states that the BIT hypothesis predicts decoherence times at φ-ladder rungs with the relation coherence time at rung k equal to τ_0 times φ^k, where τ_0 ≈ 7.3 × 10^{-15} s; this definition normalizes τ_0 to 1 so that only the scaling factor φ^k remains. The phi constant is taken from the imported Constants module and satisfies the self-similar fixed-point equation of the forcing chain.
proof idea
The definition is a direct one-line assignment of the expression phi ^ k.
why it matters
This supplies the scaling function certified by the downstream CoherenceTimeCert structure and used in the coherenceTimeRatio theorem. Module documentation positions it as the key claim supporting predictions for biological rung 12, where φ^12 yields microsecond-range times. It realizes the phi-ladder scaling from T6 and the eight-tick octave from T7, linking J-cost to observable coherence durations.
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