Two-Harmonic Extension of Scale-Dependent Cosmic Birefringence in Planck 2018 Polarization Data (v1.2)

Summary This dataset extends the findings of “Scale-Dependent and Anisotropic Cosmic Birefringence: 8.5 σ Isotropic and 4–5 σ Directional Rotation in Planck Polarization Data” (Condit 2025, v1.0; DOI 10.5281/zenodo.17317397). The analysis builds directly upon the validated α(ℓ) measurements derived from Planck 2018 SMICA and NILC component-separated polarization maps (fₛₖᵧ ≈ 0.467), introducing a two-harmonic model that captures oscillatory structure in the birefringence spectrum. Using bootstrap and Monte Carlo resampling (N = 1500), we fit α(ℓ) as the superposition of two coherent sinusoidal modes. The best-fit solution yields: Fundamental and overtone periods: Δℓ ≈ 180 and 360 Amplitudes: A₁ = 0.467° (Δℓ = 180), B₁ = 0.147° (Δℓ = 360) Phases: φ₁ ≈ –85°, φ₂ ≈ +32° Model comparison: ΔAICc ≈ –6.8 × 10³ (favoring the two-harmonic model) These results demonstrate statistically robust periodic modulation of the birefringence angle across multipoles ℓ = 400–1600, consistent with a coherent cosmological signal rather than instrumental systematics. Files included data/alpha_bands_expanded.csv — final per-band α and σ values data/alpha_bootstrap_REAL.csv — bootstrap distributions for fitted parameters data/alpha_period_scan_REAL.csv — χ²/dof scan across trial periods figures/alpha_two_harmonics_PUBLICATION.png / .svg — publication-quality plots of the best-fit model figures/alpha_bootstrap_period_hist.png and alpha_bootstrap_phi_hist.png — bootstrap histograms code/fit_alpha_twoharmonic_publication.py — Python script reproducing the two-harmonic fit meta/citation_chain.json — links to prior Zenodo versions and supporting datasets Version notes v1.0 (2025-10-10): Original discovery of 8.5 σ isotropic and 4–5 σ anisotropic cosmic birefringence. v1.1 (2025-10-18): Replication and validation dataset (Monte Carlo & half-mission cross-spectra). v1.2 (2025-10-21): Two-harmonic α(ℓ) extension and bootstrap analysis confirming coherent periodicity. 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