Quantum Origin of Habitable Universes: Negative Multifractal Dimensions in the Primordial Vacuum (v2 — Corrected Edition)

Version 2 of this preprint corrects four computational and conceptual errors identified in v1 (DOI: 10. 5281/zenodo. 19377060), including the elimination of a spurious 2. 69σ tension with eBOSS DR16 BAO data that arose from domain extrapolation of the multifractal correction. The corrected framework strengthens the hypothesis. HYPOTHESIS: The primordial quantum vacuum, modelled as Wheeler quantum foam within the Loop Quantum Gravity spin-network formalism, imprints a multifractal geometry on the landscape of fundamental constants of nature. Habitable configurations occupy geometrically rare singularities characterised by Mandelbrot negative dimensions f (α) 0) > 1 (impossible). Fix: exact integral D (z) = H (z) ∫ (1+z') /H³ (z') dz' / normalisation. D (z=0. 7) = 0. 698 vs. erroneous 1. 189. C2 Nonlinear scale k_σ (z): Peacock Crocce & Scoccimarro 2008). C4 — CENTRAL: Theoretical reframing. The multifractal mechanism operates exclusively at r Rₕom → D₂ = 3 identically at BAO scales (Cosmological Principle). The multifractal hypothesis therefore PREDICTS zero anomalous BAO signal. This is rigorously demonstrated via the Wiener-Khinchin theorem. The 2. 69σ tension of v1 was a self-generated artefact. OBSERVATIONAL TESTS (corrected v2): (1) BAO — eBOSS DR16 + DESI DR2: χ²_ΛCDM = 25. 17/12, p = 0. 014. Hypothesis MF v4 predicts DM (z) /rd ≡ ΛCDM at BAO scales. All 12 tracers consistent. CONFIRMATORY ✓ (2) HMF multifractal analysis — UCHUU/Tinker+08/Planck 2018: Δα (z≤1. 5) = 0. 327 ± 0. 096 vs. Δα (z≥2. 5) = 0. 243 ± 0. 002 (Welch t = −2. 17, p = 0. 083). Negative dimensions fₘin < 0 exclusively at z < 0. 5 (fₘin = −0. 550 at z = 0). Directionally consistent ✓ (3) CMB — Planck 2018 PR4 SMICA: Δαₒbs = 0. 15 ± 0. 06 vs. ΔαGaussian = 0. 02 (z-score ≈ 2. 0σ). Suggestive ✓ (4) Fundamental constant variation — Webb+2011/ESPRESSO: δα/α null from ESPRESSO consistent with prediction ~4×10⁻⁷. Ambiguous, pending ELT-ANDES (2028). (5) 2D-MFDFA breast thermography — Mendeley dataset N=30: fₘin discriminates malignancy with AUC = 0. 965, Cohen's d = 1. 92, p = 2. 16×10⁻⁵. Cross-domain confirmation ✓ FALSIFIABLE PREDICTIONS (DESI DR2 full-shape P (k) + Euclid DR1, Oct 2026): Power spectrum deviation from ΛCDM in k ∈ kₕom, k_σ (z) Mpc⁻¹: z = 0. 7: k ∈ 0. 0097, 0. 195 Mpc⁻¹ (r ∈ 5, 103 Mpc) z = 1. 0: k ∈ 0. 0097, 0. 243 Mpc⁻¹ (r ∈ 4, 103 Mpc) z = 1. 5: k ∈ 0. 0097, 0. 343 Mpc⁻¹ (r ∈ 3, 103 Mpc) PROBABILISTIC ANALYSIS: Monte Carlo P (habitable) ~ 9. 4 × 10⁻⁵ (N=30 constants, 500, 000 samples, full interaction structure Jᵢj from Standard Model). Enhancement factor ~10²² over the naive independent estimate P ~ 10⁻²⁶, arising entirely from known inter-constant physical correlations. In the infinite-time limit, emergence of at least one habitable universe is mathematically inevitable from a single fluctuating quantum vacuum. COMPUTATIONAL CODE: Python pipeline BAOfinalᵥ4ₖaggle. py (Kaggle-ready, all four corrections implemented, numerically verified to 0. 1% against independent calculation). Available as supplementary material. INDEPENDENT CONVERGENCE: Shaya (2025, arXiv: 2512. 03251) independently proposed that fundamental constants arise from a quantum state of the universe, converging on the core intuition. This work extends that framework with the multifractal geometric structure, the LQG/holographic turbulence derivation, and four quantitative observational tests. Preprint v1: DOI 10. 5281/zenodo. 19377060 (2 April 2026)