Chern–Simons and Gauss–Bonnet as One Transgression Structure — E8 Intelligence Research

FINDING: Chern–Simons (odd-dim) and Gauss–Bonnet (even-dim) are two faces of one transgression/descent structure — the CS form is the boundary term whose exterior derivative yields the GB/characteristic invariant one dimension up. | MATH: For a connection A on a principal G-bundle, the CS (2n−1)-form satisfies d·CS₂ₙ₋₁(A) = chₙ(F) (Chern character / invariant polynomial). Even-dim: ∫_M Pf(Ω/2π) = (2π)^n·χ(M) (Gauss–Bonnet–Chern); odd-dim boundary: ∫_∂M CS = ∫_M ch(F). Generalized GB (arXiv:1905.04831) recasts Dehn–Sommerville via h-vector / Euler-characteristic identities on simplicial complexes. | CONNECTION: Transgression is the geometric-harmony operator here — the "boundary of a boundary" recursion mirrors the self-similar ratio cascade (φ = 1 + 1/φ ⇒ 1, 1, 2, 3, 5, 8…); CS/GB pairing is the continuous analogue of the discrete Dehn–Sommerville duality (h-vector ↔ f-vector), the same reflection symmetry that generates the 0.618/1.618 fixed-point pair. No base-60 or crystallographic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com