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: Γₑff = γₗoss · G² · 1 + β·A² · f (dₒrbit) · L (δdetune) Four factors: (1) Base rate γₗoss·G², decay requires irreversible sector coupling; Γₑff = 0 when γₗoss = 0, regardless of all other factors. (2) Asymmetry term 1 + β·A², coupling asymmetry A ~ |βJ − 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 (dₒrbit) = 1 − e^−α (dₒrbit − 2), saturation form reflecting finite Q5 combinatorial depth; f (2) = 0 at the minimal orbit of T36–T37. (4) Lorentzian detuning suppression L (δdetune) = 1/ (1 + (δdetune/γc) 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 (Γₑff = 0 when γₗoss = 0) ; resonance maximum at δdetune = 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 (γₗoss, G, α, β, γc) 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.