Two-Axis Residual Map: Testing Vortex-Return Predictions with Pantheon+ SN Ia Data

# Two-Axis Residual Map: Testing Vortex-Return Predictions with Pantheon+ SN Ia Data **Author:** Shino Sanada **Affiliation:** Independent Researcher, Hokkaido, Japan **Date:** July 2026 --- ## Summary This analysis tests a specific prediction of the vortex-return model (Sanada, 2026) against the Pantheon+SH0ES Type Ia supernova dataset (Scolnic et al. 2022, Brout et al. 2022). ### Prediction The vortex-return model predicts that the Hubble tension is not a simple discrepancy between measurements, but a phase-return residual left in the inner projection of a toroidal return field. Specifically: 1. Deviation from λ = 1 concentrates near a phase-crossing redshift z_phase ≈ 0.452. Deviation carries θ dependence from the CMB dipole axis — directional asymmetry peaks at z_phase3. Isotropic ΛCDM predicts no θ dependence4. Smooth dark energy models predict z dependence but no θ dependence5. **Only vortex return predicts both z and θ coupling** This prediction was posted on the FQXi forum prior to the present analysis. ### Method - **Data:** Pantheon+SH0ES (1,590 SNe Ia after z > 0.01 cut)- **ΛCDM baseline:** Flat ΛCDM with H₀ = 73.04 km/s/Mpc, Ωm = 0.334- **Residual:** Δμ = m_b_corr − μ_ΛCDM(z) − ⟨offset⟩- **Binning:** (z, θ) where θ = angular separation from CMB dipole direction (RA=167.99°, Dec=−6.94°)- **z bins:** [0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.5, 2.5]- **θ bins:** 6 bins of 30° from 0° to 180° ### Results At z ∈ [0.35, 0.55), the distance modulus residual shows θ dependence: | θ range | N_SNe | ⟨Δμ⟩ (mag) | σ_mean ||---------|-------|-------------|--------|| 0°–30° | 30 | +0.026 | 0.024 || 30°–60° | 6 | +0.091 | 0.036 || 60°–90° | 47 | −0.005 | 0.024 || 90°–120° | 26 | −0.012 | 0.024 || 120°–150° | 66 | −0.029 | 0.014 || 150°–180° | 30 | −0.014 | 0.030 | - Linear slope: −0.00054 mag/deg- Total Δμ change over 180°: 0.097 mag (~5% in distance)- Toward the CMB dipole: supernovae appear slightly brighter (closer)- Away from the dipole: supernovae appear slightly fainter (more distant) Isotropic ΛCDM predicts zero slope. The observed gradient is consistent with the direction predicted by the vortex-return model. ### Caveats - The 30°–60° bin contains only 6 SNe and is statistically unreliable- Per-bin sample sizes (6–66) limit statistical significance- This is a preliminary directional analysis; systematic uncertainties (dust, survey footprint, selection effects) have not been fully characterized- The result should be interpreted as **indicative, not conclusive** ### Significance No prior analysis of the Pantheon+ dataset has applied (z, θ) binning relative to the CMB dipole axis to test for coupled directional asymmetry. The prediction of θ dependence at z_phase was made before this analysis was performed. The data shows a signal consistent with the predicted direction, pending confirmation with larger datasets (e.g., Nancy Grace Roman Space Telescope, launching August 30, 2026). ### Files - `vortex_analysis.py` — Complete analysis code (Python 3.8+, requires numpy, pandas, matplotlib, scipy, astropy)- `two_axis_residual_map.png` — Figure: Two-axis residual map Δμ(z, θ)- `theta_dependence_z045.png` — Figure: θ dependence at z ∈ [0.35, 0.55) ### Data Source Pantheon+SH0ES Data Release: https://github.com/PantheonPlusSH0ES/DataRelease ### References - Scolnic et al. (2022), "The Pantheon+ Analysis: The Full Data Set and Light-curve Release," ApJ 938, 113- Brout et al. (2022), "The Pantheon+ Analysis: Cosmological Constraints," ApJ 938, 110- Riess et al. (2022), "A Comprehensive Measurement of the Local Value of the Hubble Constant," ApJ 934, L7