DOI: 10.5281/zenodo.17561768
title: Rotation Field of the Cosmic Microwave Background — Axis + Frequency + Half-Mission Validation (v1.44)

description:  

This release extends the prior validation of the CMB polarization rotation field α(ℓ) by testing whether the anisotropic (directional) signal remains stable under all transformations external to the rotation-field reconstruction:

• different component–separation pipelines (SMICA, NILC)• different frequency channels (Planck 100 / 143 / 217 GHz)• independent detector splits (Half-Mission 1, Half-Mission 2, and HM× cross-maps)

No new α-map is generated in this version.α(n̂) is not recomputed — the exact same locked low-ℓ FITS file from v1.43 is used unchanged.

This version does not alter the statistical detection from v1.43.It only tests whether the anisotropy remains consistent when the data source changes.

---

### What is held fixed in v1.44

• Locked α(n̂) FITS map (dipole removed, low-ℓ structure) — identical file as v1.43  • Apodized polarization mask (NSIDE = 512, f_sky ≈ 0.467)  • ℓ bandpass: L = 2…10  • Parity statistic from v1.43 (p = 6.06 × 10⁻⁶, 165,000 null simulations)

All input files are hash-verified (SHA-256).  α(n̂) is not recomputed — only validated.

---

### Results (v1.44)

• The best-fit axis of α(n̂) is stable under bootstrap resampling.  • The parity asymmetry    A = (E − O) / (E + O)   remains consistently high for: – SMICA / NILC   – 100 / 143 / 217 GHz   – Half-Mission 1, Half-Mission 2, and HM× cross-maps (HM× suppresses noise bias)

• The anisotropic rotation field remains stable under: – component-separation method   – frequency channel   – detector splitting

Axis proximity to other large-scale CMB directions (dipole, hemispherical asymmetry, quadrupole–octopole) is provided for reference only.  No joint alignment significance is claimed.

v1.44 does not change the empirical p-value from v1.43.

---

### Reproduction instructions (minimal)

1. Download the attached archive (`v1_44_staging_…zip`).2. Open: `run_v144_axis_frequency_validation.ipynb`3. Run cells sequentially — outputs are written into timestamped directories.

Dependencies: healpy, numpy, matplotlib, astropy  `requirements.txt` included.

---

### Archive contents

• Summary figure (axis + frequency + half-mission validation)  • CSV + JSON parity tables (all frequency and HM splits)  • Bootstrap uncertainty tables  • MANIFEST with SHA-256 for every file  • Timestamped output directories  • README_v1.44.txt  

The locked α-map and mask are stored in v1.43, not duplicated here, to prevent version confusion.

---

### Version history (22 Blue Series)

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

• 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).

• 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),   165,000 null realizations; add-one p ≈ 6.06×10⁻⁶ (~4.38σ).

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

• v1.44 (this release):   Axis + frequency + half-mission validation using the same locked α(n̂).   The anisotropic rotation field remains stable under component separation, frequency choice, and detector splits.

---

### Conservative claim

v1.44 validates robustness.  It does not introduce physical interpretation.

---

Part of the “22 Blue — The Heartbeat of the Universe” research archive.