Rotation Field of the Cosmic Microwave Background — Intrinsic Periodicity in ℓ-space (v2.0)

Summary This dataset (v2.0) isolates the intrinsic periodic structure in the CMB rotation field α(n̂), using the locked rotation map derived from Planck 2018 polarization data. The goal of v2.0 is not to re-detect birefringence, but to determine the origin of the periodic structure observed in Cℓ(αα) and classify whether it is physical or an analysis artifact. All analysis is performed on validated rotation field outputs from v1.0–v1.8. No recomputation from Q/U maps is performed, and all inputs are SHA-256 hash-locked. LOCKED INPUTS (read-only, inherited from prior versions) α(n̂) rotation field (SMICA/NILC consistent, uncalibrated EB proxy) — v1.4 Dipole + traceless quadrupole model — v1.5 Amplitude + deg/rad conversions — v1.6Harmonic persistence / model rejection — v1.8 METHOD (Δℓ-origin pipeline introduced in v2.0) Stage A: Finite multipole subtraction (remove ℓ ≤ Lcut)Tests whether periodicity is caused by leakage of low-ℓ power. Stage B: Mask apodization (0° to 3°)Tests whether periodicity is a pseudo-Cl mask artifact. Stage C: Spatial localization (N/S and E/W hemispheres)Tests whether periodicity is global or directional. Stage D: Model identification (AIC / BIC / AICc)Three models are compared:(1) A sin(2π ℓ / Δℓ + φ) + C(2) A sin(2π ℓ / Δℓ + φ) exp(−ℓ / ℓ_d) + C ← best model (damped sinusoid)(3) Chirped sinusoid (Δℓ varies slowly with ℓ)Correct parameter counting used: k = 4, 5, 5 respectively. RESULTS Two periodic features were identified and classified: Intrinsic periodicity: Δℓ ≈ 108 (± bootstrap CI)• Persists under apodization, finite-ℓ subtraction, and hemisphere tests; stable across detrending window variations and ℓ-band boundaries (Δℓ = 107.8–109.3 across all sensitivity variants). Full sensitivity results are archived in the zip at stageE/deltaL_sensitivity_v2.json. • Behavior is global, not directional• Best model: damped sinusoid in harmonic space Artifact periodicity: Δℓ ≈ 455• Appears only when very low multipoles (ℓ ≤ 4) are not removed• Disappears after removing those modes• Interpretation: low-ℓ leakage / mode coupling artifact Key discovery of v2.0:The CMB rotation field contains a global damped sinusoidal structure in harmonic space with Δℓ ≈ 108. CONSERVATIVE CLAIM This dataset makes an empirical claim:The intrinsic periodicity in α(ℓ) is best modeled by a damped sinusoid with Δℓ ≈ 108. This dataset does not propose a physical mechanism for the sinusoid. It reports the empirical behavior of the validated rotation field under controlled tests. FILES INCLUDED • README for v2.0• JSON summaries (pipeline, uncertainty, model selection)• CSV tables (Δℓ vs Lcut, hemisphere Δℓ and amplitude)• PNG figures (periodograms, sinusoid fit, hemisphere comparison)• SHA-256 manifest This release is part of an iterative research series in which analysis methods, masks, and calibration procedures were progressively refined. Later releases establish the physical calibration of the α(n̂) field. CITATION Condit, Amy. Rotation Field of the Cosmic Microwave Background — Intrinsic Periodicity in ℓ-space (v2.0).22 Blue — The Heartbeat of the Universe.DOI: 10.5281/zenodo.17574048 PUBLICATION RECORD PREDECESSOR PUBLICATION (Separate Record) Sep 20, 2025 (v1.0) — Harmonic Phase Alignments in Planck 2018 CMB — DOI:10.5281/zenodo.17167268 MAIN RESEARCH SERIES Concept DOI:10.5281/zenodo.17317397 Oct 10, 2025 (v1.0) — Scale-Dependent Anisotropic Birefringence: Initial Detection — DOI:10.5281/zenodo.17317398 Oct 20, 2025 (v1.1) — Scale-Dependent Anisotropic Birefringence: Validation Dataset — DOI:10.5281/zenodo.17396428 Oct 21, 2025 (v1.2) — Two-Harmonic Extension — DOI:10.5281/zenodo.17410764 Oct 28, 2025 (v1.3) — Two-Harmonic Dipole Verification — DOI:10.5281/zenodo.17468988 Nov 1, 2025 (v1.4) — MASTER-Calibrated Dipole — DOI:10.5281/zenodo.17500791 Nov 1, 2025 (v1.41) — Extended MASTER Calibration and Robustness — DOI:10.5281/zenodo.17508908 Nov 7, 2025 (v1.42) — Dependence-Aware Joint Validation — DOI:10.5281/zenodo.17553829 Nov 8, 2025 (v1.43) — Phase Model Validation — DOI:10.5281/zenodo.17561313 Nov 8, 2025 (v1.44) — Axis + Frequency + Half-Mission Validation — DOI:10.5281/zenodo.17561768 Nov 9, 2025 (v1.5) — Multipole Structure and Model Selection — DOI:10.5281/zenodo.17562965 Nov 9, 2025 (v1.6) — Phenomenology and Physical Interpretation — DOI:10.5281/zenodo.17566197 Nov 9, 2025 (v1.7) — Prediction and Experiment Overlays — DOI:10.5281/zenodo.17566870 Nov 9, 2025 (v1.8) — Model Rejection and Δℓ Persistence — DOI:10.5281/zenodo.17567241 Nov 10, 2025 (v2.0) — Intrinsic Periodicity in ℓ-Space — DOI:10.5281/zenodo.17574048 Nov 10, 2025 (v2.1) — Physical Origin of Δℓ Modulation — DOI:10.5281/zenodo.17577086 Nov 11, 2025 (v2.2) — Universe-Model Evaluation — DOI:10.5281/zenodo.17585419 Nov 12, 2025 (v2.3) — Domain Geometry and Topological Inference — DOI:10.5281/zenodo.17594157 Nov 13, 2025 (v2.4) — Real-Space Correlation of the Birefringence Field — DOI:10.5281/zenodo.17597537 Nov 13, 2025 (v2.5) — Spectral Surgery on the Δℓ ≈ 109 Harmonic — DOI:10.5281/zenodo.17604982 Nov 14, 2025 (v2.6) — Angular Locality of the Δℓ = 109 Standing Wave — DOI:10.5281/zenodo.17613348 Nov 15, 2025 (v2.7) — Sky-Local Origin of the Δℓ ≈ 109 Standing Wave — DOI:10.5281/zenodo.17620029 Nov 15, 2025 (v2.8) — Domain Topology of the Δℓ ≈ 109 Standing Wave — DOI:10.5281/zenodo.17620605 Nov 16, 2025 (v2.9) — Dual-Domain Coherence and Boundary Geometry — DOI:10.5281/zenodo.17621871 Nov 17, 2025 (v2.10) — Boundary Sequence Structure on the Dual-Domain Loop — DOI:10.5281/zenodo.17635811 Nov 19, 2025 (v2.11) — Boundary Standing-Wave and Phase-Structure Analysis — DOI:10.5281/zenodo.17648033 Nov 21, 2025 (v2.12) — Boundary Universality and Standing-Wave Fingerprints — DOI:10.5281/zenodo.17676377 Nov 23, 2025 (v2.13) — Interior Propagation and Boundary-Driven Structure — DOI:10.5281/zenodo.17693540 Jun 18, 2026 (v2.29) — Rotation Field of the Cosmic Microwave Background — Interior Propagation Audit & Harmonic Normalization — DOI:10.5281/zenodo.20753037 Jun 19, 2026 (v2.30) — Calibrated Interior Propagation Validation — DOI: 10.5281/zenodo.20755330 Jun 20, 2026 (v2.31) — Rotation Field of the Cosmic Microwave Background — Physical Origin of Boundary-to-Interior Propagation — DOI: 10.5281/zenodo.20777435 Jun 21, 2026 (v2.32) — Rotation Field of the Cosmic Microwave Background — Antipodal Specificity, Boundary Ordering, and Cross-Scale Spectral Organization — DOI: 10.5281/zenodo.20787307 22 Blue - The Heartbeat of the Universe