cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.5517/ccdc.csd.cc1pxdbb
title: CCDC 1576422: Experimental Crystal Structure Determination

description: Related Article: Z.W. Schroeder, L.K. Hiscock, L.N. Dawe|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|905|doi:10.1107/S205322961701381X
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdcc
title: CCDC 1576423: Experimental Crystal Structure Determination

description: Related Article: Z.W. Schroeder, L.K. Hiscock, L.N. Dawe|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|905|doi:10.1107/S205322961701381X
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxddd
title: CCDC 1576424: Experimental Crystal Structure Determination

description: Related Article: Z.W. Schroeder, L.K. Hiscock, L.N. Dawe|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|905|doi:10.1107/S205322961701381X
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pllb6
title: CCDC 1566998: Experimental Crystal Structure Determination

description: Related Article: Arnab Mandal, Sanchari Dasgupta, Sumi Ganguly, Antonio Bauzá, Antonio Frontera, Debasis Das|2017|Dalton Trans.|46|15257|doi:10.1039/C7DT03040A
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1p8tsk
title: CCDC 1557619: Experimental Crystal Structure Determination

description: Related Article: Sam C. K. Hau, Thomas C. W. Mak|2017|Dalton Trans.|46|14098|doi:10.1039/C7DT03406G
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdff
title: CCDC 1576425: Experimental Crystal Structure Determination

description: Related Article: Ming Zhang,  Jianlin Yang,  Qing Xu,  Chao Dong,  Li-Biao Han,  Ruwei Shen|2018|Adv.Synth.Catal.|360|334|doi:10.1002/adsc.201701368
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdpp
title: CSD 1576433: Experimental Crystal Structure Determination

description: Related Article: Unithrattil, Sanjith|2017|CSD Communication|||
description: Related Article: Sanjith Unithrattil, Paulraj Arunkumar, Yoon Hwa Kim, Ha Jun Kim, Ngoc Hung Vu, Jaeyeong Heo, Woon Jin Chung, Won Bin Im|2017|Inorg.Chem.|56|15130|doi:10.1021/acs.inorgchem.7b02456
description: An entry from the Inorganic Crystal Structure Database, the world’s repository for inorganic crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the joint CCDC and FIZ Karlsruhe Access Structures service and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdqq
title: CCDC 1576434: Experimental Crystal Structure Determination

description: Related Article: E. Żesławska, W. Nitek, H. Marona, A. Gunia-Krzyżak|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|953|doi:10.1107/S2053229617013845
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdrr
title: CCDC 1576435: Experimental Crystal Structure Determination

description: Related Article: E. Żesławska, W. Nitek, H. Marona, A. Gunia-Krzyżak|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|953|doi:10.1107/S2053229617013845
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdss
title: CCDC 1576436: Experimental Crystal Structure Determination

description: Related Article: E. Żesławska, W. Nitek, H. Marona, A. Gunia-Krzyżak|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|953|doi:10.1107/S2053229617013845
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfmn
title: CCDC 1576462: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfnp
title: CCDC 1576463: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfpq
title: CCDC 1576464: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5281/zenodo.17410764
title: Two-Harmonic Extension of Scale-Dependent Cosmic Birefringence in Planck 2018 Polarization Data

description:  

Description (for Zenodo v1.2 – DOI 10.5281/zenodo.17410764)

 

 

Two-Harmonic Extension of Scale-Dependent Cosmic Birefringence in Planck 2018 Polarization Data

 

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.

 

We designate this feature “22 Blue” — the Heartbeat of the Universe — to reflect its distinctive mid-multipole structure and dipole signature.

 

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.


 

Citation

 

Condit, A. (2025). Two-Harmonic Extension of Scale-Dependent Cosmic Birefringence in Planck 2018 Polarization Data (Version 1.2) [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.17410764
DOI: 10.5517/ccdc.csd.cc1pxfqr
title: CCDC 1576465: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfrs
title: CCDC 1576466: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfst
title: CCDC 1576467: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxftv
title: CCDC 1576468: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfvw
title: CCDC 1576469: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfhj
title: CSD 1576458: Experimental Crystal Structure Determination

description: Related Article: Ailijiang Abudurusuli, Kui Wu, Shilie Pan|2018|New J.Chem.|42|3350|doi:10.1039/C7NJ04288D
description: An entry from the Inorganic Crystal Structure Database, the world’s repository for inorganic crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the joint CCDC and FIZ Karlsruhe Access Structures service and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfwx
title: CCDC 1576470: Experimental Crystal Structure Determination

description: Related Article: Chad T. Palumbo, Dominik P. Halter, Vamsee K. Voora, Guo P. Chen, Alan K. Chan, Megan E. Fieser, Joseph W. Ziller, Wolfgang Hieringer, Filipp Furche, Karsten Meyer, William J. Evans|2018|Inorg.Chem.|57|2823|doi:10.1021/acs.inorgchem.7b03236
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfdf
title: CSD 1576455: Experimental Crystal Structure Determination

description: Related Article: Ailijiang Abudurusuli, Kui Wu, Shilie Pan|2018|New J.Chem.|42|3350|doi:10.1039/C7NJ04288D
description: An entry from the Inorganic Crystal Structure Database, the world’s repository for inorganic crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the joint CCDC and FIZ Karlsruhe Access Structures service and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxffg
title: CSD 1576456: Experimental Crystal Structure Determination

description: Related Article: Ailijiang Abudurusuli, Kui Wu, Shilie Pan|2018|New J.Chem.|42|3350|doi:10.1039/C7NJ04288D
description: An entry from the Inorganic Crystal Structure Database, the world’s repository for inorganic crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the joint CCDC and FIZ Karlsruhe Access Structures service and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfgh
title: CSD 1576457: Experimental Crystal Structure Determination

description: Related Article: Ailijiang Abudurusuli, Kui Wu, Shilie Pan|2018|New J.Chem.|42|3350|doi:10.1039/C7NJ04288D
description: An entry from the Inorganic Crystal Structure Database, the world’s repository for inorganic crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the joint CCDC and FIZ Karlsruhe Access Structures service and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxdvv
title: CCDC 1576438: Experimental Crystal Structure Determination

description: Related Article: N.N.Golovnev, M.S.Molokeev, I.V.Sterkhova|2019|Zh.Neorg.Khim.|64|1146|doi:10.1134/S0036023619090134
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfbc
title: CCDC 1576453: Experimental Crystal Structure Determination

description: Related Article: Tia L. Walker,  Ian S. Taschner,  Sharath Chandra M,  Michael J. Taschner,  James T. Engle,  Briana R. Schrage,  Christopher J. Ziegler,  Xinfeng Gao,  and Steven E. Wheeler|2018|J.Org.Chem.|83|10025|doi:10.1021/acs.joc.8b01382
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxc0z
title: CCDC 1576381: Experimental Crystal Structure Determination

description: Related Article: Okky Dwichandra Putra, Daiki Umeda, Yuda Prasetya Nugraha, Kazuya Nango, Etsuo Yonemochi, Hidehiro Uekusa|2018|Cryst.Growth Des.|18|373|doi:10.1021/acs.cgd.7b01371
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfxy
title: CCDC 1576471: Experimental Crystal Structure Determination

description: Related Article: N. Lu, J.-H. Zheng, Y.-J. Lu, H.-F. Chiang, C.-W. Chu, J.S. Thrasher, Y.-S. Wen, L.-K. Liu|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|930|doi:10.1107/S2053229617013857
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxfyz
title: CCDC 1576472: Experimental Crystal Structure Determination

description: Related Article: N. Lu, J.-H. Zheng, Y.-J. Lu, H.-F. Chiang, C.-W. Chu, J.S. Thrasher, Y.-S. Wen, L.-K. Liu|2017|Acta Crystallogr.,Sect.C:Cryst.Struct.Chem.|73|930|doi:10.1107/S2053229617013857
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1plnhf
title: CCDC 1567065: Experimental Crystal Structure Determination

description: Related Article: Zhi-Hui Zhang, Ganna A. Senchyk, Yi Liu, Tyler Spano-Franco, Jennifer E. S. Szymanowski, Peter C. Burns|2017|Inorg.Chem.|56|13249|doi:10.1021/acs.inorgchem.7b02019
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxg13
title: CCDC 1576475: Experimental Crystal Structure Determination

description: Related Article: Philip A. Smith, Tyler L. Spano, Peter C. Burns|2018|Z.Krist.Cryst.Mater.|233|507|doi:10.1515/zkri-2017-2139
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
DOI: 10.5517/ccdc.csd.cc1pxg24
title: CCDC 1576476: Experimental Crystal Structure Determination

description: Related Article: Philip A. Smith, Tyler L. Spano, Peter C. Burns|2018|Z.Krist.Cryst.Mater.|233|507|doi:10.1515/zkri-2017-2139
description: An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.