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This paper reports the detection of a stable angular coherence feature in residual Faraday rotation (RM) data at a characteristic scale of approximately 5°, identified in the NVSS RM catalogue and independently cross-validated in POSSUM pilot survey data. Five independent statistical diagnostics converge on this feature, including angular correlation analysis, bootstrap resampling, structure function analysis, jackknife sky partitioning, and angular power spectrum decomposition. The feature persists under multiple robustness tests and is not reproduced in null configurations based on coordinate randomisation or RM value permutation. Cross-correlation with the 2MRS galaxy catalogue reveals a measurable RM–large-scale structure (LSS) signal only at low redshift (cz < 3000 km/s), with no consistent angular scale reproduced across redshift shells and no evidence of the monotonic θ ∼ 1/dₐ scaling expected from projection of a fixed physical scale. Cross-probe tests using Pantheon+ supernova distance residuals and CHIME FRB dispersion measures yield non-detections, consistent with an observable kernel framework in which RM, as a phase-sensitive signed line-of-sight integral, retains coherent magnetic structure that is not accessible to scalar observables. At plausible source redshifts (z ∼ 0.05–0.3), the observed angular feature corresponds to a physical transverse scale of approximately 80–200 Mpc. The result is presented as a constrained empirical anomaly with a defined set of physical requirements, motivating targeted follow-up investigation into the spatial organisation of intergalactic magnetic fields. Addendum: Environmental Conditioning with 2MRS Density Field A supplementary analysis conditions the full RM sample (~22k sources) on projected foreground galaxy density derived from the 2MRS catalogue. Each sightline is assigned a local density based on galaxy counts within an angular aperture (5–8°), exceeding the characteristic signal scale to avoid circular conditioning. Partitioning the sample into low- and high-density environments reveals: A stable zero-crossing scale (~4–5°) across both density regimes A systematic suppression of small-angle coherence (≲2–3°) in high-density sightlines A tendency toward more negative correlation at larger separations in denser regions The density partition is based on projected counts and is therefore not strictly spatially independent; neighbouring sightlines contribute to overlapping density estimates, inducing covariance between subsets. However, the persistence of the angular scale under environmental conditioning indicates that the ~5° feature is not dominated by local foreground structure, while the amplitude modulation is consistent with increased stochastic Faraday contributions along high-density lines of sight. 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 About the Author This research was conducted independently, without institutional affiliation or external funding. All analysis was performed using limited personal computing resources and publicly available data and tools. AI-based systems were used to assist with structuring, coding, and drafting; however, all scientific reasoning, methodological decisions, and interpretations are solely those of the author. The work was carried out using only widely accessible, non-specialised tools. This work represents an ongoing line of investigation.