Effective Decoherence Rate Structure

This Theorem identifies the structural form of the effective decoherence rate arising from the irreversible coupling established in T50. The rate is not a free parameter but is determined by three structural inputs from the Q5 transport chain: Γ_eff = γ_loss · G² · [1 + β·A²] · f(d_orbit) · L(δ_detune) Four factors: (1) Base rate γ_loss·G², decay requires irreversible sector coupling; Γ_eff = 0 when γ_loss = 0, regardless of all other factors. (2) Asymmetry term [1 + β·A²], coupling asymmetry A ~ |β_J − β| = |μν'c'b − b'c| from T33; operationally A ~ |g₁ − g₀|/√(g₁² + g₀²) from T8; quadratic dependence consistent with simulation showing decay enhancement scales as (g₁ − g₀)². (3) Orbit depth term f(d_orbit) = 1 − e−α(d_orbit − 2), saturation form reflecting finite Q5 combinatorial depth; f(2) = 0 at the minimal orbit of T36–T37. (4) Lorentzian detuning suppression L(δ_detune) = 1/(1 + (δ_detune/γ_c)²), detuning suppresses coupling efficiency, not a decay channel. Three structural statements: scrambling is necessary but not sufficient for decoherence; asymmetry amplifies scrambling; irreversible coupling converts scrambling into decay. Three corollaries: zero-loss limit (Γ_eff = 0 when γ_loss = 0); resonance maximum at δ_detune = 0; symmetric coupling limit (A = 0 returns base rate). Status: Asymmetry identification A ~ |μν'c'b − b'c| from T33 solid. f(2) = 0 at minimal orbit solid within T36–T37. Three qualitative boxed statements solid from T50 and factor structure. Overall structural form model-level, functional forms of f and L are natural leading-order models, not uniquely forced. Five structural constants (γ_loss, G, α, β, γ_c) were identified qualitatively; explicit values from the T17 kernel geometry are open. All results inherit T8, T17, T33, T35, T36, T37, T50 conditionality. Dependencies: T8, T11, T29, T33, T35, T36, T37, T50.