Data & Datasets

All observational data, MCMC results, and generated datasets from the two-paper spin-torsion cosmology research program, organized by which paper each dataset supports.

Open Data Explorer GitHub Repo

Interactive Data Explorer

Browse 15 embedded datasets including real MCMC chain samples, convergence diagnostics, parameter results, birefringence measurements, galaxy spin counts, and the full branch results matrix. Features: sortable tables, column statistics, 6 equation calculators, and a node-tree visualization of the research program.

Explore Data

How this data supports the two papers. Every claim in the research program is backed by reproducible data. The datasets below map onto the paper arc as follows:

Paper 1 (Framework + Reckoning): 236,622 MCMC posterior samples across 4 dataset combinations (Planck+BAO, Planck+BAO+SN, Full Tension, Planck Only). Cobaya v3.6.1 + CAMB v1.6.5. Key finding: ΔN_eff ≈ 0. Also: 14 structural barriers documented in the branch results matrix, each closing a distinct mechanism class. The bounce evidence audit (16 claims) tracks the evidence hierarchy. ALP birefringence measurements from Planck HFI + ACT DR6 and MCMC posteriors (9,720 samples, 3 model configurations) are now included in §11.5.
Paper 2 (The Decisive Test): f_NL derivation verification (8 steps), Bayesian discrimination results (600K+ Monte Carlo), SPHEREx/MegaMapper forecast parameters.

MCMC Verification Results Paper 1

Independent MCMC verification using Cobaya v3.6.1 with stock CAMB v1.6.5 (no custom modifications). The spin-torsion extension maps onto a single effective parameter, \(\Delta N_{\rm eff}\), which parameterizes any additional dark radiation from torsion-induced four-fermion interactions.

236k+

Total samples

across 4 datasets

MCMC chains

independent runs

< 0.005

\(\hat{R}-1\)

convergence achieved

\(\approx 0\)

\(\Delta N_{\rm eff}\)

all datasets

Key finding: \(\Delta N_{\rm eff} \approx 0\) in all dataset combinations. The spin-torsion extension does not produce detectable dark radiation and does not resolve cosmological tensions.

Cross-Dataset Parameter Comparison

Parameter	Full Tension	Planck+BAO+SN	Planck 2018 ΛCDM
\(H_0\)	67.68 ± 1.06	67.79 ± 1.09	67.36 ± 0.54
\(\Delta N_{\rm eff}\)	−0.020 ± 0.169	+0.065 ± 0.17	0 (fixed)
\(\sigma_8\)	0.803 ± 0.008	0.812 ± 0.009	0.811 ± 0.006
\(S_8\)	0.814 ± 0.008	0.831 ± 0.018	0.832 ± 0.013
\(\Omega_m\)	0.308 ± 0.005	0.312 ± 0.006	0.315 ± 0.007

Source: reproducibility/cosmology/paper1_clean_restart_sync/. Uncertainties are 68% CL (1σ).

Correction: The earlier claim of \(H_0 = 69.2 \pm 0.8\) km/s/Mpc was an artifact of including the SH0ES prior. Without it, the framework recovers standard ΛCDM values. The spin-torsion extension alone does not resolve cosmological tensions.

Dataset Status

Four MCMC dataset combinations probe the spin-torsion extension under progressively richer data constraints.

FROZEN

Full Tension

Planck + BAO + SN + SH0ES + DES Y3 + KiDS-1000

176,840 samples

\(\hat{R}-1 < 0.001\)

FROZEN

Planck+BAO+SN

Planck + DESI BAO + Pantheon+

132,949 samples

\(\hat{R}-1 < 0.003\)

EXPLORATORY

Planck+BAO

Planck + DESI BAO only

463 samples

Insufficient for convergence; not used in final analysis

EXPLORATORY

Planck Only

Planck 2018 NPIPE only

452 samples

Insufficient for convergence; not used in final analysis

\(H_0\) Measurements Comparison

Comparison of Hubble constant measurements from different probes and methods. Our independent MCMC yields \(H_0 = 67.68 \pm 1.06\) km/s/Mpc, consistent with the standard Planck ΛCDM value.

Figure: Hubble constant measurements from key probes. Our spin-torsion MCMC result (Full Tension dataset, blue) is consistent with the Planck ΛCDM value and does not bridge the Hubble tension. The 4.8σ discrepancy between early- and late-universe measurements persists.

Cosmic Birefringence: The Surviving Positive Result Paper 1

Cosmic birefringence — a frequency-independent rotation of CMB polarization — is a clean signature of parity violation. A spectator ALP with \(f_a \sim M_{\rm Pl}\), \(m \sim H_0\), and \(\theta_i \sim \mathcal{O}(1)\) predicts a rotation angle \(\beta\) that is independent of the ALP decay constant (due to \(f_a\) cancellation in the observable).

Measurement	\(\beta\) (deg)	\(\sigma\) (deg)	Significance
Planck (Minami & Komatsu 2020)	0.35	0.14	2.4σ
Planck NPIPE (Eskilt 2022)	0.30	0.11	2.7σ
ACT DR6 (2025)	0.215	0.074	2.9σ
Combined	0.242	0.061	3.9σ
ALP Prediction (this work)	0.27	—	—

Sources: Minami & Komatsu (2020), Eskilt (2022), ACT Collaboration (2025).

Figure: Cosmic birefringence measurements with 1σ error bars. The dashed line shows the ALP prediction \(\beta = 0.27°\) from this work. All measurements are consistent with the prediction within 1σ.

The prediction \(\beta = 0.27°\) from a spectator ALP with \(f_a \sim M_{\rm Pl}\) is independent of the ALP decay constant (\(f_a\) cancellation). This is the program's strongest surviving positive result, testable by LiteBIRD (\(\sigma \sim 0.03°\)) within a decade.

External Data Sources

Datasets used in the MCMC analysis and for comparison constraints.

Planck 2018 NPIPE

CamSpec TTTEEE + lowl TT/EE + lensing. Primary CMB likelihood for all four dataset combinations.

CMB

DESI 2024–2025 BAO

DR1 + DR2 baryon acoustic oscillation measurements. Used in Planck+BAO, Planck+BAO+SN, and Full Tension datasets.

BAO

Pantheon+

1701 Type Ia supernovae light curves. Distance ladder calibration. Used in Planck+BAO+SN and Full Tension datasets.

SNIa

ACT DR6

Atacama Cosmology Telescope Data Release 6. CMB power spectra and birefringence measurement (\(\beta = 0.215 \pm 0.074°\)).

CMB

SH0ES 2022

Cepheid-calibrated distance ladder. \(H_0 = 73.04 \pm 1.04\) km/s/Mpc. Used as a prior in the Full Tension dataset only.

Prior only

DES Y3 / KiDS-1000

Weak lensing \(S_8\) constraints. Used as priors in the Full Tension dataset only. HSC Y3, eROSITA used for comparison.

Prior only

Galaxy Spin Data Contested

9–12 order-of-magnitude coupling gap. The galaxy spin dipole was a component of the original Paper 1 hypothesis. Independent reanalyses (Patel & Desmond 2024, Philcox & Ereza 2025) report null results. Additionally, the theoretical coupling between the ECH framework and galaxy spin amplitudes has a 9–12 order-of-magnitude gap. This prediction is effectively falsified.

Show galaxy spin dipole data (Shamir 2024)

Survey	Objects	CW excess	Dipole \((l, b)\)	\(\sigma\)
Pan-STARRS	33,028	1.8%	(34°, 55°)	4.0σ
SDSS (z < 0.1)	67,788	1.2%	(240°, −27°)	3.6σ
HST (GOODS-N/S)	8,690	2.1%	(280°, −17°)	2.8σ
DECam	17,045	1.5%	(22°, 48°)	3.1σ

Source: Shamir (2024). Independent null results from Patel & Desmond (2024) and Philcox & Ereza (2025).

Cobaya Configuration

Key MCMC sampler parameters used across all dataset combinations.

Show Cobaya YAML configuration

theory: camb: extra_args: num_massive_neutrinos: 1 nnu: 3.046 # baseline; dneff added as sampled parameter theta_H0_range: [20, 100] sampler: mcmc: Rminus1_stop: 0.01 Rminus1_cl_stop: 0.2 burn_in: 0.3 max_tries: 40d learn_proposal: true learn_proposal_Rminus1_max: 30 oversample_power: 0.4 covmat: auto drag: true # Convergence achieved: # Full Tension: R-hat - 1 < 0.001 (176,840 samples) # Planck+BAO+SN: R-hat - 1 < 0.003 (132,949 samples) # Target: R-hat - 1 < 0.01 # Theory: Stock CAMB v1.6.5 (no custom modifications)

Downloads

Raw data, configuration files, and the compiled manuscript.

File	Description	Size	Link
`arxiv/main.pdf`	Compiled manuscript (latest)	~200 KB	Download
`dneff/full_tension/*.yaml`	Cobaya config — Full Tension	~4 KB	GitHub
`dneff/planck_bao_sn/*.yaml`	Cobaya config — Planck+BAO+SN	~4 KB	GitHub
`dneff/planck_bao/*.yaml`	Cobaya config — Planck+BAO	~4 KB	GitHub
`dneff/planck_only/*.yaml`	Cobaya config — Planck Only	~4 KB	GitHub
MCMC chain files	All chains (64 total, 148 MB)	~148 MB	GitHub
Full repository	Complete codebase, data, and paper	—	GitHub

Figures

All publication figures — including parameter posterior plots, the vacuum-scale sensitivity diagram, birefringence consistency window, and dataset comparison panels — are collected on the dedicated Figures page.