tau_planck
plain-language theorem explainer
Recognition Science anchors the Planck time at 5.4 × 10^{-44} seconds to fix the lower bound of the Gap-45 ratio between quantum and classical regimes. Modelers of decoherence timescales cite this constant when scaling from the fundamental tick through environmental mode coupling to biological intervals. The definition consists of a direct noncomputable real-number assignment with no derivation steps.
Claim. $τ_P = 5.4 × 10^{-44}$ seconds, where $τ_P$ is the Planck time that sets the scale for the Gap-45 threshold separating coherent quantum behavior from decoherence.
background
The QFT.Decoherence module treats Gap-45 as the ratio ≈10^{45} between Planck-scale and biological timescales. Quantum coherence persists below this threshold; above it, entanglement with the environment produces classical behavior. The module expresses decoherence time as τ_decoherence ≈ τ_0 × φ^{-N}, where τ_0 is the fundamental tick and N counts coupled environmental modes. This definition supplies the numerical value of τ_P that realizes the lower end of that ratio.
proof idea
The declaration is a direct noncomputable constant assignment of the floating-point literal 5.4e-44 to a real number.
why it matters
The constant feeds the sibling definition tau_bio, which records the logarithmic gap log₁₀(tau_bio / tau_planck) ≈ 43.3 and thereby closes the Gap-45 mechanism. It supplies the concrete scale required by the module's decoherence formula and the patent claims for threshold-based quantum error correction. The placement aligns with the Recognition Science forcing chain by fixing the Planck tick that precedes the phi-ladder and eight-tick octave.
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