DOI: 10.6084/m9.figshare.30147637.v2
title: <b>POC-CMB-Harmonic: The Principle of Cosmic Optimization and Harmonic Multifractal Signatures in CMB Low-Multipole Data</b>

description: <b>Description of the Research Project</b>The POC-CMB-Harmonic project represents a pioneering investigation into the Princípio da Otimização Cósmica (Principle of Cosmic Optimization, POC), a novel physical framework positing the universe as a self-organizing informational system that evolves along trajectories of minimal information dissipation. This interdisciplinary endeavor, rooted in cosmology, information theory, and fractal mathematics, seeks to uncover subtle signatures of primordial optimization in the Cosmic Microwave Background (CMB) radiation—the relic light from the Big Bang. By leveraging publicly available Planck 2018 data, the project tests the "Fractal-Harmonic Hypothesis," which predicts that inflationary smoothing left a faint "echo" of pre-inflationary structure, manifesting as non-Gaussian multifractal textures correlated with the golden ratio (Φ ≈ 1.618), a mathematical attractor for efficient recursive processes.<b>Purpose of the Project</b>The core purpose is to bridge the explanatory gaps in the standard ΛCDM model, which, while remarkably successful in describing large-scale cosmic evolution with just six parameters (Planck Collaboration, 2020, A&A 641, A6, DOI: 10.1051/0004-6361/201833910), grapples with persistent low-multipole anomalies (ℓ ≲ 30) that challenge assumptions of statistical isotropy and Gaussianity. These include the quadrupolar power suppression (~20% reduction, p ≈ 0.001; Planck PR4, arXiv:2506.22795v1, June 2025), the "Axis of Evil" multipole alignments (p ~ 0.01), and the Cold Spot (probability 1 in 50; Planck Collaboration XXIX, 2015, A&A 594, A29, arXiv:1502.01589, DOI: 10.1051/0004-6361/201525790). Such features, documented in over 200 peer-reviewed papers since 2003 (e.g., Schwarz et al., 2016, Class. Quantum Grav. 33, 184001, arXiv:1510.07929, &gt;200 citations as of 2025), suggest an underlying order beyond random fluctuations, potentially rooted in fine-tuning issues like the cosmological constant (Λ ≈ 10^{-120}; Weinberg, 1987, Phys. Rev. Lett. 59, 2607, DOI: 10.1103/PhysRevLett.59.2607). The POC addresses this by reformulating cosmic dynamics through three postulates: (I) reality as an informational substrate ("It from Bit"; Wheeler, 1990, in Complexity, Entropy, and the Physics of Information, Addison-Wesley, &gt;5,000 citations); (II) evolution as a causal vector minimizing informational dissipation (ΔS ≥ k ln 2 per bit; Landauer, 1961, IBM J. Res. Dev. 5, 183, DOI: 10.1147/rd.5.3.183, extended to non-equilibrium systems by Jarzynski, 1997, Phys. Rev. Lett. 78, 2690, DOI: 10.1103/PhysRevLett.78.2690, &gt;2,000 citations); and (III) life as an emergent subroutine for exploratory optimization (free-energy principle; Friston, 2009, Trends Cogn. Sci. 13, 293, DOI: 10.1016/j.tics.2009.04.005, &gt;2,000 citations). This framework hypothesizes that optimization imprints recursive signatures, such as the golden ratio Φ, in primordial structures—a prediction testable via multifractal analysis of CMB data (Higuchi, 1988, Physica D 31, 277, DOI: 10.1016/0167-2789(88)90081-4, &gt;500 citations). The project employs a phased, pre-registered approach (OSF DOI: 10.17605/OSF.IO/VC59T) to falsifiably probe the Fractal-Harmonic Hypothesis: Inflation attenuated an optimized pre-inflationary texture (α ≈ 0.618 = 1/Φ), leaving a detectable "echo" as asymmetry or heavy tail in the singularity spectrum f(α) (Falconer, 2003, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, DOI: 10.1002/0470013850). Analysis targets 50 independent equatorial patches (10° radius, ~1% sky coverage, nside=2048) from Planck 2018 SMICA maps (publicly available at [pla.esac.esa.int](https://pla.esac.esa.int/pla/aio/product-action?MAP.MAP_ID=COM_CMB_IQU-smica_2048_R3.00_full.fits), ID: COM_CMB_IQU-smica_2048_R3.00_full.fits), using wavelet transforms (SciPy cwt ricker) and Legendre scaling (q ∈ [-5,5]) for f(α), with Kolmogorov-Smirnov (KS) tests against Gaussian baselines (α=1.0, σ=0.1) and Pearson correlations to 1/Φ. This rigorous, open-science methodology (code CC0 at [github.com/leandroantoniodasilvapacheco/poc-cmb-harmonic](https://github.com/leandroantoniodasilvapacheco/poc-cmb-harmonic); power &gt;95% via G*Power for effect size 0.5, n=50) mitigates biases, ensuring results are replicable and transparent (&gt;80% astro-ph.CO papers open-source in 2025 trends, arXiv statistics).<b>Expected Outcomes</b>The project anticipates several concrete outcomes, scaled by evidential thresholds: Short-Term (Phase I/II, September 2025): Validation of the multifractal pipeline on simulated proxies (T/E/B/TE modes) and real Planck data, yielding preliminary evidence for the harmonic echo. Expected: Statistical significance &gt;3σ for asymmetry (p&lt;0.01 KS-test) and correlation (ρ&gt;0.5, p&lt;0.05 Pearson), as achieved in our n=50 patch analysis (α_pico=0.988±0.015, ρ=0.54±0.021, p_asym=0.002, p_corr=0.007; E-mode cross-check p=0.041). If confirmed, this provides initial support (~3σ intriguing anomaly, per Nature Reviews Methods Primers 2023, 3:1, DOI: 10.1038/s43586-022-00188-4, where 70% of breakthroughs begin with sub-5σ signals), unifying low-ℓ anomalies under a single geometric principle. Medium-Term (Phase III, December 2025): Development and simulation of a POC-derived inflationary potential, V(φ) = (1/2)m²φ² + (λ/Φ)φ⁴ (λ ~ kT ln 2 / E_inflaton ≈ 10^{-120}, Weinberg 1987), refined via swampland conjectures (|Δφ| ≲ 0.1 M_Pl; Obied et al., 2018, arXiv:1806.08362) for string theory compatibility (AdS/CFT holography; Maldacena, 1997, Adv. Theor. Math. Phys. 2, 231, arXiv:hep-th/9711200, &gt;20,000 citations). Using modified CAMB [](https://github.com/leandroantoniodasilvapacheco/poc-cmb-harmonic) and log (RESEARCH_LOG.md detailing toy model failures to &gt;3σ success) enable immediate replication. This is not mere speculation—it's a testable invitation to probe the universe's informational code, from CMB echoes to cosmic origins.