DOI: 10.5281/zenodo.17561313
title: Rotation Field of the Cosmic Microwave Background — Phase Model Validation (v1.43)

description: Phase Model Validation (v1.43)

 

This dataset archives the validation stage of the Phase Model analysis of the CMB polarization rotation field α(ℓ). The goal of this release is focused and audit-oriented:

 

Confirm that the large-scale parity anisotropy in the rotation field α(ℓ) is real and does not depend on calibration, transfer choice, or MASTER normalization.

 

A locked α(n̂) map (units: radians) and a fixed apodized polarization mask (NSIDE=512, f_sky≈0.467) are used to compute MASTER-corrected C_L^{αα} for L = 2…10 (dipole removed).

 

The scalar parity statistic is:

 

T_obs = Σ_even C_L^{αα} − Σ_odd C_L^{αα}

 

165,000 masked null simulations using identical mask, apodization, pixel window, and MASTER geometry yield:

 

exceedances = 0 / 165,000

empirical add-one estimate: p = 6.06 × 10⁻⁶

Gaussian-equivalent one-sided significance: 4.38σ

 

Calibration-independence is demonstrated by constructing a simulation-derived MASTER coupling matrix M_LL′ (L=2…10), inverting it, and applying it to the observed pseudo-spectrum. The scale-invariant parity statistic A = (E−O)/(E+O) and a scaled T match the MASTER result to ≤ 0.26% relative difference, showing that the detection does not depend on calibration or transfer construction.

 

No physical interpretation (e.g., axion or φ–γ coupling) is assumed in this version. This is a validation-only release.

 

Contents:

• phase_model_v1_release_20251108_201510.zip (full reproducibility archive)

• README_v1.43.md (methods and reproduction instructions)

 

Reproducibility archive contains:

• null_ensemble_lowL_.npz (array of T_null values only)

• simulation-derived MASTER coupling matrix M_hat_.npz

• parity_minimaster_*.json (numeric comparison report)

• locked α-map (SHA-256 recorded)

• polarization mask (SHA-256 recorded)

• MANIFEST with SHA-256 of all files

• run-all notebook for reproduction

 

Version history (22 Blue Series):

 

• Separate publication (Sep 20, 2025): “Evidence for Harmonic Phase Alignments in Planck 2018 CMB Polarization Data.” First publication; identifies coherent multi-harmonic structure (Δℓ ≈ 320) in polarization phases.

• v1.0 (Oct 10, 2025): First quantitative detection of scale-dependent, anisotropic cosmic birefringence (8.5σ isotropic + 4–5σ directional).

• v1.1 (Oct 20, 2025): Adds full statistical validation and reproducibility materials (TB/EB diagnostics, covariance checks).

• v1.2 (Oct 21, 2025): Introduces two-harmonic extension (Δℓ ≈ 180 and 360 periodicity).

• v1.3 (Oct 28, 2025): Completes verification and robustness tests (calibration, simulation, injection/recovery).

• Dataverse mirror (Oct 29, 2025): Harvard Dataverse v2 (DOI 10.7910/DVN/PTDG20) mirrors the archive.

• v1.4 (Nov 1, 2025): MASTER-calibrated rotation field α(ℓ); low-L map and transfer verified.

• v1.41 (Nov 1, 2025): Extended calibration and robustness evaluation (SMICA/NILC, HM splits).

• v1.42 (Nov 7, 2025): Dependence-aware empirical joint significance (parity + high-ℓ harmonics) using 165,000 null realizations; add-one p ≈ 6.06×10⁻⁶ (~4.38σ one-sided).

• v1.43 (Nov 8, 2025): Phase Model validation — calibration-invariant parity result. Simulation-derived MASTER coupling reproduces parity statistic to ≤0.26% relative difference; null exceedances remain 0/165,000.

Part of the 22 Blue research archive:

“22 Blue — The Heartbeat of the Universe”