Rotation Field of the Cosmic Microwave Background — Dependence-Aware Joint Validation of Anisotropic Cosmic Birefringence (v1.42)

Rotation Field α(ℓ) — Version 1.42 Dependence-Aware Joint Validation of Anisotropic Cosmic Birefringence This dataset presents evidence that the Universe rotates the polarization of the Cosmic Microwave Background (CMB) in a directional and structured way — a phenomenon known as anisotropic cosmic birefringence. Using Planck 2018 SMICA and NILC EB cross-spectra, the birefringence rotation field α(ℓ) is reconstructed over multipoles ℓ = 500–1500 and decomposed into spherical-harmonic modes (αₗₘ, L ≤ 10). The resulting α-map shows large-scale anisotropic rotation in the sky. The key result is that the Universe does not rotate polarization uniformly. After applying the Minami–Komatsu isotropic EB calibration, the constant (global) rotation component becomes consistent with zero. What remains is directional: a structured, anisotropic rotation field. Observed features of α(ℓ): • A broad rotation dipole near Galactic coordinates (ℓ, b) ≈ (278°, 18°) • A repeating multi-harmonic pattern with Δℓ ≈ 180 and 360 • Consistency across SMICA/NILC, masks, half-mission splits, Δℓ sweeps, and LOOCV These features are consistent with a slowly varying pseudoscalar (axion-like) field coupled to photons, producing large-scale parity violation. Version 1.42 (this release) introduces a dependence-aware empirical joint significance test to determine whether the observed anisotropy could arise from noise or from mode selection. Two statistically independent signatures of α(ℓ) are evaluated simultaneously on the same null ensemble: Low-L even/odd parity asymmetry of the αₗₘ map (dipole removed; L = 2–10) High-ℓ multi-harmonic structure in α(ℓ) using k = {3, 4, 7} over ℓ = 500–1500 A total of 165,000 dependence-aware null realizations were generated. Each realization is passed through identical mask coupling, window transfer, ℓ-binning, and harmonic modeling, and both statistics (parity and harmonic power) are computed for each null. No null realization exceeded the observed joint statistic. Results: • parity statistic: p ≈ 6.1 × 10⁻⁶ (≈ 4.4σ one-sided) • harmonic structure: p ≈ 6.1 × 10⁻⁶ (≈ 4.4σ one-sided) • joint dependence-aware significance: p ≈ 6.1 × 10⁻⁶ (≈ 4.4σ one-sided) No Fisher/Stouffer independence assumption was used. The significance is purely empirical. This rules out the possibility that both signals arise from the same noise fluctuation or from trial-factor bias. The anisotropy of α(ℓ) is stable under Δℓ bin sweeps, leave-one-out cross-validation, high-k controls, and half-mission splits. Relation to the “22 Blue” Research Series: The “22 Blue” project documents the full progression from initial discovery to joint validation: • Publication (Sep 20 2025): Evidence for Harmonic Phase Alignments in Planck 2018 CMB Polarization Data — independent first publication, identifying multi-harmonic structure in polarization (Δℓ ≈ 320) • v1.0 (Oct 10 2025): First quantitative detection of anisotropic birefringence • v1.1–v1.3: Validation, TB/EB diagnostics, simulation and calibration checks • v1.4: MASTER-calibrated anisotropic rotation field • v1.41: Extended calibration and robustness testing • v1.42 (this release): Dependence-aware empirical joint significance Together, these releases constitute the full archival record of the discovery known as: “22 Blue — The Heartbeat of the Universe.” Contents (v1.42): • α(ℓ) rotation series and αₗₘ map (L ≤ 10) • Harmonic fits (k = 3, 4, 7), LOOCV stability, Δℓ sweeps, high-k controls • Dependence-aware joint null ensemble (165,000 simulations) • Replication notebook (run-all) and JSON proof artifacts Created by Amy Condit (22 Blue) — independent cosmology research into parity violation and anisotropic cosmic birefringence in Planck 2018 polarization data. PUBLICATION RECORD PREDECESSOR PUBLICATION (separate record)1. Sep 20, 2025 (v1.0) -- Harmonic Phase Alignments in Planck 2018 CMB -- DOI:10.5281/zenodo.17167268 MAIN RESEARCH SERIESConcept DOI:10.5281/zenodo.173173972. Oct 10, 2025 (v1.0) -- Scale-Dependent Anisotropic Birefringence: Initial Detection -- DOI:10.5281/zenodo.173173983. Oct 20, 2025 (v1.1) -- Scale-Dependent Anisotropic Birefringence: Validation Dataset -- DOI:10.5281/zenodo.173964284. Oct 21, 2025 (v1.2) -- Two-Harmonic Extension -- DOI:10.5281/zenodo.174107645. Oct 28, 2025 (v1.3) -- Two-Harmonic Dipole Verification -- DOI:10.5281/zenodo.174689886. Nov 1, 2025 (v1.4) -- MASTER-Calibrated Dipole -- DOI:10.5281/zenodo.175007917. Nov 1, 2025 (v1.41) -- Extended MASTER Calibration and Robustness -- DOI:10.5281/zenodo.175089088. Nov 7, 2025 (v1.42) -- Dependence-Aware Joint Validation -- DOI:10.5281/zenodo.175538299. Nov 8, 2025 (v1.43) -- Phase Model Validation -- DOI:10.5281/zenodo.1756131310. Nov 8, 2025 (v1.44) -- Axis + Frequency + Half-Mission Validation -- DOI:10.5281/zenodo.1756176811. Nov 9, 2025 (v1.5) -- Multipole Structure and Model Selection -- DOI:10.5281/zenodo.1756296512. Nov 9, 2025 (v1.6) -- Phenomenology and Physical Interpretation -- DOI:10.5281/zenodo.1756619713. Nov 9, 2025 (v1.7) -- Prediction and Experiment Overlays -- DOI:10.5281/zenodo.1756687014. Nov 9, 2025 (v1.8) -- Model Rejection and Delta-l Persistence -- DOI:10.5281/zenodo.1756724115. Nov 10, 2025 (v2.0) -- Intrinsic Periodicity in l-space -- DOI:10.5281/zenodo.1757404816. Nov 10, 2025 (v2.1) -- Physical Origin of Delta-l Modulation -- DOI:10.5281/zenodo.1757708617. Nov 11, 2025 (v2.2) -- Universe-Model Evaluation -- DOI:10.5281/zenodo.1758541918. Nov 12, 2025 (v2.3) -- Domain Geometry and Topological Inference -- DOI:10.5281/zenodo.1759415719. Nov 13, 2025 (v2.4) -- Real-Space Correlation of Birefringence Field -- DOI:10.5281/zenodo.1759753720. Nov 13, 2025 (v2.5) -- Spectral Surgery on Delta-l ~109 Harmonic -- DOI:10.5281/zenodo.1760498221. Nov 14, 2025 (v2.6) -- Angular Locality of Delta-l = 109 Standing Wave -- DOI:10.5281/zenodo.1761334822. Nov 15, 2025 (v2.7) -- Sky-Local Origin of Delta-l ~109 Standing Wave -- DOI:10.5281/zenodo.1762002923. Nov 15, 2025 (v2.8) -- Domain Topology of Delta-l ~109 Standing Wave -- DOI:10.5281/zenodo.1762060524. Nov 16, 2025 (v2.9) -- Dual-Domain Coherence and Boundary Geometry -- DOI:10.5281/zenodo.1762187125. Nov 17, 2025 (v2.10) -- Boundary Sequence Structure on Dual-Domain Loop -- DOI:10.5281/zenodo.1763581126. Nov 19, 2025 (v2.11) -- Boundary Standing-Wave and Phase-Structure Analysis -- DOI:10.5281/zenodo.1764803327. Nov 21, 2025 (v2.12) -- Boundary Universality and Standing-Wave Fingerprints -- DOI:10.5281/zenodo.1767637728. Nov 23, 2025 (v2.13) -- Interior Propagation and Boundary-Driven Structure -- DOI:10.5281/zenodo.17693540 Contact email: [e-mail] 22 Blue - The Heartbeat of the Universe