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
TCocycle D ρreadsDonly throughD.T(u γ ∈ D.T; the crossed condition is aboutρand conjugation, not the cover), and(En.radData l h).T = RF.TBsubfor everyl;- the lower map
RF.rhoPrime b F (En.radData l h) rfl ρ = (piBCiso …).symm ∘ ρdepends on the datum only throughD.M = RF.MB(viapiBCiso), again constant inl.
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).
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) hμ field: pin μ at a reference l₀, transport to the current
l here, then apply the Prop. 8.9 assembly's ρ-independence.