Foundation II: The Chiral Universe and the Three Fossils of the Bounce — Baryogenesis, the Geometric Dark Sector, and Cosmic Alignment within an Einstein-Cartan Framework, Extended Version

Foundation II develops the three observable fossil signatures of the primordial spin-torsion bounce, giving geometric accounts of the cosmological dark sector — no new particles, no ad hoc scalar fields. Each result carries its status (derived, calibrated, conditional, open); no open problem is closed by rewording.

The three fossils.

• Chiral baryogenesis (t ~ 10⁻¹¹ s): η ≈ 5.9×10⁻¹⁰, within 3.5% of the Planck-inferred value, from a 5:1 ratio set by 20:4 torsion degrees of freedom. Semi-derived: the pre-dilution asymmetry is normalised on the observed value, so this agreement is not an independent test.
• Geometric dark matter (t ~ 1 s): χ˜²_med = 0.80 for the adopted pseudo-isothermal halo profile against 1.29 for an NFW profile refitted under the same protocol, on 171 of the 175 SPARC galaxies, with two parameters per galaxy. A goodness of fit of the adopted profile, not a torsion-specific test; the profile is not yet derived from the torsion (PO-ECF-HALO).
• Cosmic alignment: the Big Ring and the Giant Arc, read only conditionally as Torsion Vortex Rings (exploratory consistency check; not required for the core argument).

Topological zoology. Micro-Knots (M = 3.74×10²⁴ kg, the horizon mass at the electroweak crossing), Macro-Knots (a conditional heavy-seed channel, M ~ 10⁵–10⁶ M_☉, set by the Jeans mass at the Great-Annihilation horizon; collapse efficiency and abundance not derived), Chiral Walls (void boundaries) and the Torsion Fluid (dark-energy condensate). ⚠️ The 1D sector is carried as an open problem (PO-F2-8): torsion strings have no established Lagrangian foundation in the present field content, S^μ being a real axial vector with no internal phase.

Version notes — PREPRINT v5 (October 2026), supersedes PREPRINT v4 (15 September 2026). Propagation of the second audit and of the October corrections. The authoritative list is the Version register and erratum deposited with this version; in case of discrepancy, the text of the paper prevails.

Correction of record — void-statistics figure. In v4 the points labelled “Observations (SDSS BOSS Catalog)” were simulated (analytic curve plus noise, fixed seed) and the “Fit Statistics” box was hard-coded. The figure is replaced by an illustrative mock slice; no simulated data are presented as observations.

Correction of record — NGC 6503. The v4 data file (24 points) did not match the SPARC file (31 points). The refit on the actual SPARC data gives χ²_ν = 1.68, not 0.97, and the rotation curve is redone. The MCMC figure, previously drawn from a synthetic normal distribution, is now drawn from the actual chain (deterministic emcee).

Correction of record — annihilation energetics. For M₂ = 10⁴ M_☉, 2M₂c² = 3.6×10⁵⁸ erg, not 4×10⁵⁶ erg. The GRB/FRB “calibration” η_ann ~ 0.1–0.5 rested on that error and is withdrawn; η_ann is open.

Correction of record — DESI. The Mahalanobis distance of the ECF point to DESI DR1 is 2.03σ (Planck prior) and 6.98σ (SH0ES prior), full covariance, 12 observables; the earlier 2.22σ/7.32σ used a 13-observable block including two rows DESI DR1 does not publish. The ECF is not favoured over ΛCDM by those data alone (Δχ² = +6.21 and +38.59). (w₀, w_a) = (−0.904, −0.153) is a calibrated point without error bar; ξ = 1.645 is calibrated on the DESI preference, hence not independent of DESI.

Correction of record — BAO. The BOSS error at z = 0.61 combines statistical and systematic errors (0.166 / 0.206 / 0.251). The BAO target at z = 1.48 is 30.21 ± 0.79 (eBOSS DR16 QSO consensus); χ²_BAO = 12.11 against 1.79 for ΛCDM. r_drag is not identified with r_s (open problem).

Values and statuses changed. Background Ω_m = ω_m/h² ≃ 0.267 (0.315 kept only as the Planck reference); age t₀ = 13.33 Gyr, compatible with the globular-cluster age, and the age-tension narrative is abandoned; recombination at 368.4 kyr with the spin term (371.3 kyr in ΛCDM), replacing 343,000 yr. The global Δχ² = −39.5 of Foundation I is historical and not recomputed. S₈ = 0.766 is a KiDS-1000 target, not an ECF output. The Micro-Knot → Macro-Knot chain is withdrawn; the bounce equations are qualified per regime; the instrument timeline is updated.

Reference audit. Fifty-six references corrected and some forty passages rewritten where a source did not say what was attributed to it.

Compilation verified: 173 pages · 0 LaTeX errors · 0 missing figures. Run of the reproducibility pipeline on 28/10/2026: 116 of 116 scripts completed.

Part of the Einstein–Cartan Framework corpus: PIT Letter (10.5281/zenodo.19798923), Foundation I (10.5281/zenodo.19577447), Foundation III — Cosmological Physics (10.5281/zenodo.22359982), Architecture (10.5281/zenodo.22778507). Reproducibility code: github.com/pfichant/spin-torsion-cosmology (CC-BY-4.0).