phi
plain-language theorem explainer
Defines a local alias for the golden ratio φ drawn from the CPM constants bundle. Researchers deriving decoherence timescales in Recognition Science would reference this when expressing τ_decoherence ≈ τ_0 × φ^(-N) for systems crossing the Gap-45 threshold. The definition is a direct one-line alias with no additional computation or proof obligations.
Claim. $φ$ denotes the golden ratio as supplied by the Constants structure, satisfying the self-similar fixed-point equation $φ = 1 + 1/φ$.
background
The module QF-009 derives quantum decoherence timescales from the Gap-45 threshold, the approximate ratio 10^45 separating Planck-scale ticks from biological timescales. Quantum coherence persists below this threshold; above it, entanglement with environmental modes drives decoherence via the scaling τ_decoherence ≈ τ_0 × φ^(-N), where N counts coupled modes. The upstream Constants structure bundles the core Recognition Science parameters (Knet, Cproj, Ceng, Cdisp) together with non-negativity constraints, supplying the shared numerical value of φ used throughout the framework.
proof idea
One-line wrapper that aliases the phi field from the upstream Constants structure.
why it matters
Supplies the scaling factor required by the Gap-45 decoherence formula inside the QFT module. It directly instantiates the self-similar fixed point (T6) that propagates through the forcing chain and appears in the mass ladder and octave structure. No downstream uses are recorded yet, leaving the alias available for any later theorem that invokes φ^(-N) scaling in decoherence or error-correction contexts.
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