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GQ2.Phase140.LIndep

l-independence of the T-cocycle count #

The (140) witness μ of prop_8_9 is fixed once, at a reference scalar l₀ (docs/orchestration/p16d6-concrete-spec.md §1: μ := Nat.card (TCocycle (En.radData l₀ h₀) …)), but the phase140_of_nonsingular field needs hμ (l h) : ∀ ρ, Nat.card (TCocycle (En.radData l h) …) = μ at the current scalar l. Combined with the ρ-independence of the Prop. 8.9 assembly (tcocycle_mu_indep), that requires the count to be independent of l as well.

This is nearly definitional: the enrichment datum En.radData l h varies with l only in its cover C := RF.scalarCover l h and its square form q := En.q l h, but

So the two count objects coincide. Pure std-3, no source input — the genuinely l-dependent piece of the witness is G0 = gaussSum (En.qbar l h) (part of the Prop. 8.9 assembly; see docs/orchestration/p16d6c-handoff.md).

theorem GQ2.SectionEight.tcocycle_card_l_indep {H E : Type} [Group H] [TopologicalSpace H] [DiscreteTopology H] [Finite H] [CommGroup E] [TopologicalSpace E] [DiscreteTopology E] [Finite E] {Γ : Type} [Group Γ] [TopologicalSpace Γ] {Y : Type} [Group Y] [Finite Y] {T : MarkedTarget H E Y} {Blk : SectionSeven.MinimalBlock T.LY} (RF : RecursionFrame T Blk) (b : Γ →ₜ* boundarySubgroup) (F : BoundaryFrame H E) (En : RF.Enrichment) (l : RF.DR) (h : l RF.zeroDR) (l' : RF.DR) (h' : l' RF.zeroDR) (ρ : BoundaryLifts b F RF.TC) :
Nat.card (CentralObstruction.TCocycle (En.radData l h) (RF.rhoPrime b F (En.radData l h) ρ)) = Nat.card (CentralObstruction.TCocycle (En.radData l' h') (RF.rhoPrime b F (En.radData l' h') ρ))

l-independence of the T-cocycle count (the Prop. 8.9 assembly, c3): for a fixed boundary lift ρ, the crossed count #Z¹_{Γ,ρ}(T) computed against the enrichment datum En.radData l h does not depend on the scalar l — the datum's M/T layers (and hence TCocycle and rhoPrime) are the same for every l. Feeds the (140) field: pin μ at a reference l₀, transport to the current l here, then apply the Prop. 8.9 assembly's ρ-independence.