Scale-Dependent Topology in Residual Faraday Rotation: Evidence for Structured Magneto-Ionic Organisation (with Scale-Response Addendum)

Reassessment notice — 22 June 2026The β₀ positive-excess sign-asymmetry reported in this paper does not survive reconstructed like-for-like null testing. The result has been reassessed and reframed in:John F. Ryder, When Topology Becomes Pipeline: Reassessing β₀ Sign-Asymmetry in Smoothed NVSS Residual Faraday Rotation Fields.DOI: 10.5281/zenodo.20795136The surviving result is power-spectrum-referenced coherence in the smoothed residual field, most plausibly associated with declination-dependent NVSS survey structure rather than an isotropic cosmological signal. We present a topological characterisation of residual Faraday rotation (RM) fields derived from wide-area radio survey data. Building on prior detection of a stable angular feature at ~4–5°, and its demonstrated independence from projected matter tracers including Planck CMB lensing convergence and 2MRS galaxy density, we investigate the spatial organisation of the RM field using threshold-dependent connectivity analysis. We compute Betti-style curves (β₀) over a range of angular linking scales and significance thresholds (ν/σ), comparing results against value-shuffled null models that preserve survey geometry while destroying spatial correlations. We find a statistically significant excess of disconnected positive excursion regions (β₀⁺) at intermediate thresholds (ν/σ ≈ 0.5–1.5), with peak significance in the 3°–5° linking scale range. Addendum (Scale-Response Extension):As a post-analysis extension, we perform a scale-response study by extracting the peak deviation from the shuffle mean (Δβ₀) at each linking angle. This reveals a monotonic decrease in signal strength from 3° to 8°, with representative values Δβ₀ ≈ 3.8 (3°), 2.7 (5°), and 1.0 (8°). This behaviour defines a bounded angular regime within which the topology is both detectable and physically interpretable. This signal weakens at smaller scales due to sampling-induced fragmentation and disappears at larger scales due to graph over-connection, consistent with a coherence scale in the few-degree range. The persistence of the effect under Galactic latitude cuts (|b| > 40°), together with its absence in independent matter tracers, indicates that the structure is not trivially explained by foreground contamination or large-scale structure clustering. We note that the scale-response analysis is derived using a reduced null ensemble (N = 10 shuffle realisations), compared to N = 100 used in the primary analysis. While sufficient to establish the qualitative trend, this choice may affect the precision of Δβ₀ estimates and will be refined in future work. These results point to non-Gaussian, sign-sensitive organisation in the magneto-ionic medium on degree scales and establish a constrained angular regime within which this structure is observable. This work forms part of the RM Angular Coherence Programme and extends previous detection and cross-validation stages by introducing scale-dependent topological characterisation. Update: Redshift Characterisation of the 2MRS-Matched Subset Following publication of the addendum, a full redshift characterisation of the 2MRS-matched RM subset has now been completed. The matched sample contains N = 42 sources, spanning a redshift range of z ≈ 0.004–0.082, with a median redshift of z = 0.029, mean z = 0.032, and an interquartile range of z ≈ 0.015–0.053. The distribution is notably broad, extending from the low-redshift concentration into a higher-redshift regime, indicating that the matched subset probes a wider range of environments than suggested by the dominant histogram peak at z ≈ 0.01–0.02 alone. Taking the median redshift as a representative scale for the matched subset, the corresponding distance is of order ~100–130 Mpc (for standard cosmological parameters). At this scale, the observed angular coherence window (3°–5°) corresponds to physical scales of approximately ~6–11 Mpc. This remains fully consistent with the previously quoted 5–15 Mpc range, but now provides a single, median-anchored estimate grounded in the measured redshift distribution rather than bin-based approximations. Importantly, the persistence of the topology signal across the higher-redshift component of the matched sample is inconsistent with a purely local foreground explanation, and instead supports sensitivity to structure across multiple distance regimes. This result should be interpreted as applying specifically to the 2MRS-matched subset. A full redshift characterisation of the RM population remains the next step. Related Works in This Research Series This work forms part of an ongoing research programme investigating angular coherence in residual Faraday rotation and its potential connection to large-scale structure and cosmological observables. The following related records expand on detection, validation, and cross-probe testing: Angular Coherence in Residual Faraday Rotation: Detection, Convergent Diagnostics, and Constraints from Large-Scale Structurehttps://zenodo.org/records/19338840→ Consolidates detection evidence and introduces constraints from large-scale structure alignment tests. Angular Coherence in Residual Faraday Rotation: Cross-Probe Validation and Robustness Analysishttps://zenodo.org/records/19259606→ Provides robustness checks including jackknife tests, latitude cuts, and alternative subtraction methods. Angular Coherence in Residual Faraday Rotation: Cross-Probe Tests with Pantheon+ and FRB Dispersion Measureshttps://zenodo.org/records/19138655→ Extends the analysis to independent cosmological probes, testing for consistency across observables. Preliminary Cross-Dataset Detection of an Angular Correlation Scale in POSSUM RM Datahttps://zenodo.org/records/19071182→ Early-stage detection using independent RM datasets, supporting the presence of a non-random angular signal. Together, these works aim to establish whether the observed angular coherence represents a genuine cosmological-scale structure or an emergent feature of observational and processing pipelines. The programme prioritises reproducibility, cross-dataset validation, and diagnostic transparency. A structured overview of the ongoing investigation, including detection, robustness testing, and interpretive analysis, is available at:https://sites.google.com/driveinsolution.com/john-f-ryder/home