Listening Beyond Four Dimensions: Higher-Dimensional Blast (HDBLAST): Canonical Snapshot & Tool‑Kit

Scope (blast-only / screening-level): This record provides a reproducibility kit for testing a falsifiable hypothesis that an early-universe “higher-dimensional blast” seeded a cosmological SGWB whose PTA-band spectrum is well described by a smooth broken power law (SBPL) with a knee near ~3×10⁻⁸ Hz. Key methodological upgrade in this release (vNEXTLEVEL+): covariance-limited inference. We quantify the exact covariance frontier (smooth bin-to-bin covariance in log₁₀ f modeled with a squared-exponential kernel) at which the PTA-band knee preference becomes neutral in this binned-Gaussian screening framework. Covariance frontier (SBPL vs SMBHB): Zero-cross correlation length: ℓ* ≈ 0.358 decades in log₁₀ f Adjacent-bin correlation at the frontier: ρ_adj(ℓ*) ≈ 0.775 Effective independent-bin count at the frontier (participation ratio): n_eff(ℓ*) ≈ 4.34 (out of 10 bins) Interpretation (falsifiable): If the true PTA free-spectrum covariance is smoother than this (ρ_adj ≳ 0.78 / n_eff ≲ 4.3), the SBPL-vs-SMBHB knee preference can be erased in this screening framework. If it is less smooth (ρ_adj ≲ 0.78 / n_eff ≳ 4.3), smooth covariance cannot explain away the knee within this screening framework. New in this version: Scripts to evaluate model evidence given an explicit bin covariance matrix Σᵢⱼ (enables “drop-in” PTA-provided covariance products). Notes on extracting covariance proxies from public products and mapping the PTA knee to early-universe epochs (temperature/horizon-mass diagnostics). Honest caveat: The PTA comparisons here use a binned-Gaussian approximation to published free-spectrum points (not collaboration-grade likelihoods). The decisive missing product is the PTA bin covariance matrix or full likelihood object. Most important data request: Σᵢⱼ for the published free-spectrum bins (or posterior draws of the free-spectrum vector, or full timing-residual likelihood). Main reproducibility bundle: HDBLAST_ZENODO_UPLOAD_BUNDLE_REALONLY_v24_20251224_vNEXTLEVEL_PLUS.zip Integrity: SHA256SUMS file Status summary: GrandStatus JSON Data request: HDBLAST_DATA_REQUEST_v3.md