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

# HDBLAST: Covariance Killswitch & Closed-Form n_eff Mapping (vKILLSWITCH++) This release extends **HDBLAST** with a **falsifiable “covariance killswitch”** for the PTA spectral knee, and adds new closed-form mathematics that makes the threshold analytically transparent. ## What is the “covariance killswitch”?We ask: *Could the apparent spectral “knee” be an artifact of bin-to-bin covariance / smoothing?* We define a **Covariance Frontier**: for a fixed binning (N=10) and a squared-exponential (SE) correlation model, we find the correlation length (or adjacent-bin correlation) where evidence for **SBPL vs SMBHB** crosses unity. **Canonical threshold (SQEXP, N=10):**- Adjacent-bin correlation: **ρ_adj\* ≈ 0.775**- Correlation length: **ℓ\* ≈ 0.358 decades in log10 f**- Participation-ratio effective bins: **n_eff\* ≈ 4.34 (out of 10)** Interpretation: if the *true* covariance is smoother than this threshold, the knee can be explained as a covariance artifact; if it is rougher (lower correlation), the knee is robust. ## New in vKILLSWITCH++### 1) Killswitch without Σ (copula-free marginal bounds)A key operational problem is that public releases may provide **only per-bin marginal posteriors** (KDEs), not the full joint covariance matrix Σ. This release adds a **copula-free bound** workflow:- Compute rigorous pairwise correlation bounds using **quantile coupling** (Fréchet–Hoeffding bounds).- Use these bounds to upper-bound adjacent-bin correlation **ρ_adj,max** *without assuming any copula*.- If **ρ_adj,max < ρ_adj\***, the knee is robust to *any* dependence structure consistent with the marginals. ### 2) Closed-form mapping n_eff(ρ_adj) for SE Toeplitz correlation For R_{ij}=\rho_{\rm adj}^{(i-j)^2}, we provide… - Exact expression for tr(R^2) and thus n_eff = N^2 / tr(R^2).- Practical mapping between (ρ_adj, ℓ, n_eff), including a large-N approximation. ### 3) Ready-to-run NANOGrav pipeline + spreadsheet calculatorIncludes:- Local Python autorun script- Google Colab notebook- Spreadsheet “killswitch calculator” ## Run itSee:- `HDBLAST_RUN_NANOGRAV_KILLSWITCH_NOW.md`- `HDBLAST_RUN_NANOGrav_KILLSWITCH_COLAB.ipynb`- `HDBLAST_NANOGrav_KILLSWITCH_AUTORUN_20251226.py` ## FilesDownload the zip bundle in this Zenodo record for full reproducibility (scripts, docs, plots, tables, calculator).