The Topological Invariance Principle: Dark Energy as a Geometric Constraint of Spatial Flatness in Einstein-Cartan Cosmology

In the standard cosmological model, the strict spatial flatness of theobservable Universe (ΩK ≈ 0) is treated as an observational constraintrequiring fine-tuned initial conditions, while late-time acceleratedexpansion is attributed to a phenomenological cosmological constant Λ. In this Letter, we propose an alternative conceptual framework based onEinstein-Cartan gravity, governed by what we term the TopologicalInvariance Principle (TIP). We postulate that global spatial flatness (Ωₜotal = 1) is not a parametric coincidence, but a fundamental constantand a dynamic gauge law of spacetime. It is shown that to preserve thistopological invariance against the emergence of material curvature, thegeometric coupling induces a spacetime reaction: any primordial fractionalspin density Ωₛpin injected prior to recombination algebraically enforcesa strictly compensatory torsion debt Ω_τ, such thatΩ_τ^ (initial) = −Ωₛpin, peak. We demonstrate that Dark Energy naturallyemerges from this formalism — not as an exotic substance, but as theresidual and dynamic manifestation of this frozen geometric debt. Ascosmic expansion dilutes matter, the fractional torsion densitymechanically increases to maintain topological equilibrium, acting atleading order as an effective cosmological constant. This gauge model, whose numerical foundations and implications for dark matter are developedin companion papers (Foundation I & II), provides a natural geometricexplanation for cosmic acceleration, consistent with recent observations (Planck 2018, DESI 2024). ── Version notes (v2. 0) ──────────────────────────────────────────────Three targeted theoretical reinforcements, following a cross-auditagainst Foundation II (in preparation): 1. Sec. I — Poincaré Gauge Theory (PGT) scope: torsion is described as effectively algebraic in the low-density ECKS limit, and acquires propagating degrees of freedom via PGT at high density. This removes the objection that minimal ECKS cannot support vacuum torsion. 2. Sec. III — Torsion condensate: the freezing mechanism is formally grounded via a vacuum expectation value ⟨S_μ⟩ = s₀ δ_μ⁰ ≠ 0, with effective energy density ρ_Λᵉff = ½ mT² s₀². Full derivation is deferred to Foundation II. 3. Sec. IV — TIP postulate status: explicit statement that the TIP is a phenomenological postulate of the extended Einstein-Cartan framework, not a theorem of minimal ECKS. No numerical results were modified. All predictions of v1 are preserved.