Foundation III — Cosmological Physics: Bounce Signatures, Void Statistics, the Status of the Primordial Spectrum, and Falsifiable Predictions

This document collects the testable, falsifiable cosmological-physics content of the Einstein–Cartan Framework (ECF) Foundation III programme — the sector developed for peer review. The wormhole mechanism, the Cartan core, the CPT cascade, the full Landau–Ginzburg formalisation of the bounce, and the exploratory programme (baby universes, fertility curve, astrobiology, holarchy) are developed in companion documents (Foundation III — Strong Gravity, Foundation III — Chiral Bounce, and Foundation IV — Fertile, the latter not submitted for peer review) and are not repeated here. Horizon without inflation. The ECF proposes a structural, non-kinematic alternative to inflation. We establish that the crystallised Kibble–Zurek network forms a genuine chain complex on the ECKS manifold and prove ∂∘∂ = 0 (Proposition F3-1) — a valid algebraic result in its own right. Whether this delivers a globally coherent, causally-connected horizon solution a priori, as an earlier version of this Corollary claimed, is not established: that stronger claim required Chiral Walls to be stitched into one object by a network of Torsion String loops, and was withdrawn on 30/08/2026 once Chiral Walls were shown to be independent closed bubbles with no stable multi-way junction. The horizon problem therefore retains an open status alongside the monopole problem, documented without occultation. Observational confrontation. The calibrated ECF trajectory (w0, wa) = (−0.904, −0.153) is compared to DESI DR1 with full covariance (Mahalanobis distance 2.22σ under a Planck prior). The Void Size Function kill-switch is tested against the real DESIVAST DR1 catalogue: the ECF threshold at 40 Mpc/h remains out of reach of the BGS sample (z < 0.24); the method is validated and the definitive test deferred to Euclid DR1-Complete (mid-2027). Primordial spectra, stated plainly. The scalar spectral index ns is not predicted by the framework: the large-scale spectrum is taken as inherited, an input on the same footing as Ωb. An earlier claim of a parameter-free prediction (ns ≈ 1) rested on an incorrect identification of the Wands duality and has been withdrawn. The stiff era does generate a blue tensor component whose amplitude bounds the stiff-phase duration from below — a falsifiable form, not yet a calibrated threshold. A background degeneracy, acknowledged. Petri, Marra & von Marttens [Phys. Rev. D 113, 023504 (2026)] show that an interacting dark-sector model can be exactly degenerate with CPL at the background level. The DESI comparison reported here therefore constrains the ECF trajectory without establishing, on its own, that torsion rather than a dark-sector interaction underlies it. This paper states that limitation and identifies the discriminant both that work and Wang, Yu & Wu (arXiv:2609.03062) converge on: late-time structure growth. The ECF fσ8 suppression is nearly redshift-independent (≈2% variation of the ECF/ΛCDM ratio across 0 < z < 0.8), unlike the sharp low-redshift drop that disfavours the interacting model; against six published RSD measurements the two histories are statistically indistinguishable (Δχ2 = −0.14, N = 6). This establishes that the ECF growth history is not excluded — not that it is preferred. Open problems, documented without occultation: PO-F3-NS — spectral index, principal open front; PO-F3-XI — ξKZ not derived ab initio; PO-F3-ISO — isotropy / BKL shear; PO-F3-DESI — tension on the wa amplitude; PO-F3-VSF — kill-switch out of BGS reach. Strong-gravity and chiral-sector open problems (PO-F3-C6, PO-F3-B3, PO-F3-IC, PO-F3-CHIRAL) are tracked in the companion Foundation III — Strong Gravity document. Part of the Einstein–Cartan Framework corpus: PIT Letter (10.5281/zenodo.19798923), Foundation I (10.5281/zenodo.19577447), Foundation II (10.5281/zenodo.20629237). Reproducibility code: github.com/pfichant/spin-torsion-cosmology (CC-BY-4.0). Version notes — PREPRINT v2 (15 September 2026) This version corrects one factual error and qualifies two statements. No result is withdrawn. Correction of record — DESI DR2 significance. Earlier versions stated that DESI DR2 strengthens the deviation from ΛCDM to 4.9σ. That value does not appear in the cited paper (arXiv:2503.14738), which reports 3.1σ for DESI BAO + CMB and 2.8–4.2σ once supernovae are included, depending on the sample. Corrected in both occurrences. Qualified — initial conditions. The comparison with the no-boundary wave function previously concluded that "in both cases, the initial state is not postulated but derived", under the heading "Initial conditions with no free parameter". κ2 = 8πG/c4 is indeed a constant of the theory; but ⟨S2⟩vol(0) is tied to the condensate amplitude s0, which is calibrated rather than derived. The heading and the conclusion now read "partly derived, partly calibrated", and the comparison is stated to hold for the structure of the argument, not for the epistemic status of every input. Qualified — CMB temperature fluctuations. δT/T was quoted as 2.7×10−5. The coefficient depends on the definition: the RMS over all scales gives ≈6.6×10−6, the acoustic-peak amplitude ≈2.7×10−5. The passage uses the value only for an order-of-magnitude comparison, and now quotes ≈10−5 with the dependence on convention made explicit. Figures realigned. Fig_ECF_DESI_Contours.png and Fig_ECF_DESI_Residuals.png predated a revision of their producing script and differed from the versions carried by Foundation I — the two papers showed different DESI contours for the same analysis. Realigned after verification by hash.