Is the S₈ Tension Structural? A Provenance-Based Reanalysis of Cross-Survey Covariance

Paper S tests the structural hypothesis that published late‑time S₈ measurements share cross‑survey and cross‑probe correlated residuals arising from common calibration fields, shear pipelines, analysis codes, and cosmological priors. Using a 36‑measurement compilation spanning CMB, weak lensing, 3×2pt, RSD, cluster, and joint analyses, we construct a provenance‑encoded correlation matrix and apply literature‑supported residual systematic corrections. Under the canonical archived covariance matrix Σ generated by the deterministic reproducibility pipeline, the apparent CMB–late‑time tension reduces from 3.11σ (baseline) to 1.0σ in the primary archived configuration. Residual systematic corrections drive the central‑value shift, while the provenance‑encoded covariance regulates effective information content and enforces statistically consistent weighting. This work does not claim definitive resolution of the S₈ tension. Instead, it demonstrates a viable, falsifiable structural mechanism that materially reduces the discrepancy and can be adjudicated by forthcoming independent datasets (Euclid, Roman, DESI full release). A fully deterministic, self‑auditing reproducibility archive accompanies this paper. The methodology extends the reproducibility and covariance‑governance principles introduced in Paper 0 and applies the cross‑probe correlation framework developed in Paper 1 to the late‑time structure‑growth domain. This paper examines whether the commonly assumed independence of published S₈ measurements remains valid at the cross‑survey, cross‑probe level. Modern cosmological analyses combine constraints from CMB, weak lensing, clustering, redshift‑space distortions, and cluster counts. While individual survey pipelines rigorously model internal systematics and covariances, structural dependencies may arise across surveys due to shared calibration fields (e.g., COSMOS), shear pipelines (METACALIBRATION, LENSFIT, re‑Gaussianisation), analysis codes (CosmoSIS, CosmoLike, CAMB, CLASS), shared priors, and partial footprint overlap. Paper S constructs a provenance‑based correlation framework encoding these structural relationships using fixed correlation categories (ρ = 0.82, 0.45, 0.25). Literature‑supported residual systematic corrections are applied without parameter fitting. Inverse‑covariance synthesis is performed deterministically using the archived pipeline. Quantitative results • Baseline CMB–late‑time tension: 3.11σ • Primary archived configuration tension: 0.97σ • Upper‑bound envelope: 1.89σ Residual systematic corrections drive the dominant central‑value shift, while the provenance‑encoded covariance regulates effective information content and prevents over‑counting of shared structure. The precise S₈ value is not the central claim; the key result is the demonstrated compatibility between CMB and late‑time probes under a transparent, falsifiable structural model. Reproducibility archive A complete audit‑grade reproducibility archive accompanies this paper. The archive includes: • the full 36‑measurement dataset • provenance‑encoded correlation‑matrix construction • deterministic inverse‑covariance synthesis • sensitivity sweeps over correlation parameters • golden‑output validation (tolerance = 0.0) • SHA‑256 checksum manifest and ROOT_HASH chain‑of‑custody • continuous‑integration workflow All numerical values reported in the paper are exactly reproducible from the archived version 1.0.0 pipeline. Relation to the Precision Cascade series This work extends the deterministic reproducibility and covariance‑governance principles introduced in Paper 0 (Precision Cascade Engine) and applies the cross‑probe correlation methodology developed in Paper 1 (Hubble tension analysis) to the late‑time structure‑growth domain. Paper S provides an independent application of the same structural‑covariance mechanism to a distinct cosmological tension.