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Dataset . 2025
License: CC BY
Data sources: Datacite
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Rotation Field of the Cosmic Microwave Background — Angular Locality of the Δℓ = 109 Standing Wave (v2.6)

Authors: Condit, Amy;

Rotation Field of the Cosmic Microwave Background — Angular Locality of the Δℓ = 109 Standing Wave (v2.6)

Abstract

Summary Version 2.6 of the 22 Blue project tests the angular locality of the locked Δℓ ~ 109 standing wave in the CMB rotation field. Previous releases (v2.4 and v2.5) established that the 3.3° real-space peak in ξ(θ) is the visible imprint of the Δℓ harmonic identified in v2.0–v2.1. Version 2.6 answers a deeper structural question: Is the Δℓ = 109 mode generated uniformly across all angular separations, or does it originate specifically from the narrow 3.3° region? This release performs θ-domain isolation and exclusion tests using only the locked residual Cℓ(αα) spectrum and Legendre transforms, with no maps and no healpy. The baseline ξ(θ) is reconstructed from the frozen ℓ = 100–1500 spectrum using: ξ(θ) = Σ_ℓ [(2ℓ + 1) / (4π)] C_ℓ P_ℓ(cos θ). The peak occurs at: θ_peak ~ 3.353°, ξ_peak ~ 1.55 × 10³. Gaussian windows centered at 3.3° (σ = 0.15°, 0.30°, 0.60°) isolate the θ-region believed to drive the signal. After applying W(θ), the windowed correlation function ξ_win(θ) is projected back into ℓ-space using the inverse Legendre integral: C_ℓ^(win) = 2π ∫ ξ_win(θ) P_ℓ(cos θ) sin θ dθ. Each reconstructed spectrum is compared to the fixed Δℓ = 109 standing-wave template: T_ℓ = cos(2πℓ / 109). The template-projection amplitude A_proj = Σ_ℓ [C_ℓ T_ℓ] / Σ_ℓ [T_ℓ²] is used as the stable, linear measure of harmonic strength. The ratio A_win / A_base quantifies harmonic survival. Results: Gaussian isolation preserves most of the Δℓ = 109 mode: σ = 0.15° → 0.723, σ = 0.30° → 0.832, σ = 0.60° → 0.884. Removing only the band 3.0°–3.6° destroys ~85% of the Δℓ power: A_excl / A_base = 0.155. This demonstrates that the 3.3° region is the high-leverage source of the Δℓ = 109 standing wave. The harmonic is θ-localized, not θ-uniform. Map-locality preparation To prepare for sky-locality tests in v2.7, the locked α(n̂) map was downsampled from NSIDE = 512 to NSIDE = 16, and a neighbor-variance boundary proxy was constructed: proxy(p) = mean[(α_neighbor − α_p)²]. This field is not analyzed in v2.6 but will be used in v2.7 to correlate local boundary strength with local harmonic amplitude. Findings • The Δℓ = 109 mode is strongly θ-localized around 3.3°. • The narrow 3.3° band carries the majority of the harmonic coherence. • Removing this band collapses the Δℓ signal by ~85%. • A full sky-locality grid (NSIDE = 16) is prepared for v2.7. • All locked inputs remain unchanged; no α reconstruction and no Δℓ fitting were performed. Citation Condit, Amy (2025). *Rotation Field of the Cosmic Microwave Background — Angular Locality of the Δℓ ~ 109 Standing Wave (v2.6).* *22 Blue — The Heartbeat of the Universe.* Zenodo. https://doi.org/10.5281/zenodo.17613348 Derived from Condit, Amy (2025). *Rotation Field of the Cosmic Microwave Background — Spectral Surgery on the Δℓ ~ 109 Harmonic (v2.5).* *22 Blue — The Heartbeat of the Universe.* Zenodo. https://doi.org/10.5281/zenodo.17604982 Version History (22 Blue Dataset Series) Separate publication — Sep 20 2025 • Evidence for harmonic phase alignments in Planck 2018 CMB polarization data (Δℓ ~ 320) v1.0 — Oct 10 2025 • First quantitative detection of anisotropic cosmic birefringence v1.1 — Oct 20 2025 • Statistical validation and reproducibility v1.2 — Oct 21 2025 • Two-harmonic extension v1.3 — Oct 28 2025 • Robustness tests and injections Dataverse Mirror — Oct 29 2025 • DOI: 10.7910/DVN/PTDG20 v1.4 — Nov 1 2025 • MASTER-calibrated α(ℓ) v1.41–1.44 — Nov 1–8 2025 • SMICA/NILC + HM splits; parity and axis checks v1.5 — Nov 9 2025 • Model selection; Δℓ ~ 454.7 v1.6 — Nov 9 2025 • Phenomenology and interpretation v1.7 — Nov 9 2025 • Forward prediction of α(n̂) and EB(ℓ) v1.8 — Nov 9 2025 • Harmonic persistence and rejection tests v2.0 — Nov 10 2025 • Intrinsic Δℓ ~ 108 discovered v2.1 — Nov 10 2025 • Physical interpretation; ξ(θ) at 3.3° v2.2 — Nov 11 2025 • Universe-model evaluation v2.3 — Nov 12 2025 • Domain geometry inference v2.4 — Nov 13 2025 • Direct real-space ξ(θ) confirmation v2.5 — Nov 13 2025 • Spectral surgery: Δℓ ~ 109 necessary, nearly sufficient, and phase-coherent v2.6 — Nov 14 2025 • Angular locality: isolation vs exclusion of the 3.3° region; Δℓ = 109 shown to be θ-local 22 Blue — The Heartbeat of the Universe Twitter/X: @Project22Blue

Keywords

Parity Violation, Harmonic Analysis, Anisotropy, Planck 2018, Cosmic Birefringence, Cosmological Dipole, CMB Polarization, 22 Blue

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average