"""CC0. Reproduce the exact global-class/measure diagram in Figure 12.1.""" from pathlib import Path root=Path(__file__).resolve().parents[1] out=root/'public/assets/global-jet-measure.svg' out.parent.mkdir(parents=True,exist_ok=True) out.write_text(''' A global secondary class and the sign of its measured index The two-jet projection on Borel spaces is a homotopy equivalence with contractible two-dimensional principal fiber. The invariant forms omega and beta give the pullback of the normalized Godbillon-Vey class as beta wedge d beta, equal to minus Omega, where Omega is the positive volume two nu. For a geometric K zero cycle y over the two-jet space, its positive measure trace is minus the evaluation of its geometric character against Omega. The proof uses an added even m-plane, an odd base dimension d, even normal rank r equal to three plus m minus d, and the signs epsilon d epsilon r equal to epsilon three plus m equal to minus epsilon m. The remaining comparison with the inverse two-step Thom map is explicitly open. Original mathematical diagram, CC0. Proposition 12.2 and Theorem 12.4. Human source: Alain Connes, transverse fundamental class, Section 7, Lemma 7.8. The global class and the measured geometric sign Y₂ = (J₂⁺(S¹))Γ dω = β ∧ ω, Ω = 2ν > 0 [β ∧ dβ]Γ = −[Ω]Γ Invariant form → bar total cocycle Y = (S¹)Γ GVY = B*(h₁c₁) π*GVY = −[Ω]Γ h₁ ↦ β, c₁ ↦ dβ π G₂ ≅ ℝ² fiber homotopy equivalence A geometric cycle over Y₂ y ∈ 𝒢₀(Z, Γ), Ω = 2dy ∧ dp ∧ dq/p³ T₂*(μZ y) = −⟨CZ(y), [Ω]Γ⟩ TZ has three positive real line quotients. Â(τZ) = Td(τZ,ℂ) = 1 on the Borel space. All discrete Γ; compact relative support. The normal reduction d odd, m even, D = 3 + m r = D − d even, εk = (−1)ᵏ⁽ᵏ⁻¹⁾/² εd εr = εD = −εm Outward normal: +c₁(L)/2 exponent. Positive even Bott trace factor: +1. Still required: compare the lifted proper cycle with (m₀Φ₂)⁻¹μ(x). The two statements above do not alone prove the full cyclic/GV geometric pairing. Proof locators: Lemma 12.1; Proposition 12.2; Lemma 12.3; Theorem 12.4. Connes, §7. ''',encoding='utf-8') print(out.resolve())