HDBLAST v28: Copula-free (kernel-free) robustness certificate result for PTA spectral knees — NANOGrav 15-year KDE FreeSpectra (HD)

Release focus (v28 / NANOGrav result add-on): First real-data application of the HDBLAST copula-free (“kernel-free”) robustness certificate to a public PTA KDE FreeSpectra product, with PASS/FAIL scorecards.

Status: Robustness diagnostic result only (about covariance artifacts). This deposit does not claim a physical explanation for any PTA signal feature. Any “Big Bang spark / higher-dimensional” notes remain exploratory scaffolding, not established conclusions.

Core question (HDBLAST)

Could an apparent PTA free-spectrum “knee / turnover” be produced by correlated frequency bins (covariance / smoothness / GP-kernel choices), rather than a physical spectral feature?

HDBLAST reframes this in terms of an effective degrees-of-freedom scalar:

n_eff(R) = (tr R)^2 / tr(R^2),

for the N×N correlation matrix R across N spectral bins (so tr R = N).

Calibration (killswitch anchor)

The HDBLAST reference covariance frontier defines a “knee-crossover” effective DOF:

• n_eff* = 4.418580431 (for N=10)

Under the conservative AR(1) envelope (slowest-decaying stationary kernel at fixed adjacent correlation), the critical adjacent-bin correlation that reaches this same n_eff* at N=10 is:

• rho_adj,crit(AR1; N=10) = 0.658866

(For context at N=10: rho_adj,crit(SE)=0.767109, rho_adj,crit(Matérn 3/2)=0.727821, rho_adj,crit(Matérn 5/2)=0.744382.)

Input data product (real PTA KDE grids)

This run uses only per-bin 1D marginal posteriors from:

• NANOGrav 15-year KDE FreeSpectra v1.1.0 (HD-correlated) (Zenodo DOI: 10.5281/zenodo.10344086)

Kernel-free / copula-free bound

Using the Fréchet–Hoeffding comonotone coupling (copula-free) on the KDE marginals, we compute conservative pairwise correlation upper bounds, then enforce stationary Toeplitz consistency (lagwise feasibility) to obtain a conservative adjacent-bin bound:

• rho_adj,max <= 0.514141 (from U1 = min_i rho_max(i,i+1))

Headline result (PASS/FAIL)

Because rho_adj,max < rho_adj,crit(AR1; N=10), no stationary kernel in the HDBLAST kernel family {AR(1), squared-exponential, Matérn 3/2, Matérn 5/2} can drive n_eff <= n_eff* for this KDE product under the conservative AR(1) envelope.

Scorecard summary

• N=10: rho_adj,max=0.514141; rho_crit(AR1)=0.658866; margin=0.144725; n_eff(AR1 at rho_adj,max)=6.169172 ⇒ PASS

• N=30: rho_adj,max=0.514141; rho_crit(AR1)=0.878779; margin=0.364638; n_eff(AR1 at rho_adj,max)=17.792662 ⇒ PASS

Interpretation: the specific “stationary-kernel covariance artifact” mechanism targeted by the HDBLAST killswitch is ruled out for this KDE product at this conservatism level. This does not by itself identify the physical origin of any spectral feature.

Included artifacts (this version)

• HDBLAST_SCORECARD_NANOGrav15yr_HD.pdf (one-page PASS/FAIL summary)

• HDBLAST_KERNELFREE_CERTIFICATE_NANOGrav15yr_HD_PREPRINT_DRAFT_ASCII_v2_20260106.pdf(short note describing method + result)

• HDBLAST_NANOGrav15yr_HD_RESULT_RELEASE_BUNDLE_20260106.zip (recommended download; includes the PDFs + machine-readable outputs + checksums + script)

• HDBLAST_RESULTS_NANOGrav15yr_HD_20260106.zip (machine-readable outputs only; included for convenience)

• (Optional) HDBLAST_free_spectrum_knee_estimator_20260106.py

Reproducibility (outline)

1. Download and unzip the NANOGrav KDE FreeSpectra product (DOI 10.5281/zenodo.10344086).

2. Use the HD-correlated directory: ceffyl_data/30f_fs{hd}_ceffyl (quote or escape braces in shells).

3. Run the HDBLAST KDE-grid killswitch for N=10 and N=30 and generate scorecards using the included scripts and threshold tables.

Disclaimer: This deposit reports a robustness diagnostic only. It does not claim a physical explanation for any PTA signal feature.

Recommended download is the RESULT_RELEASE_BUNDLE zip; the RESULTS zip is provided separately for convenience (machine‑readable outputs only). (corrected title)