![Finite scalar spectral-cube reference at the channel centers nearest 0.76, 1.25, and 2.20 µm. -- full graphic below [astro-ph.IM]](https://i0.wp.com/astrobiology.com/wp-content/uploads/2026/10/A-Covariance-Aware-Framework.png?fit=1200%2C670&ssl=1)
[astro-ph.IM] Assessing possible life on an exoplanet requires spatial, spectral, temporal, and environmental context. We develop a covariance-aware Solar Gravitational Lens (SGL) framework for regional biosignature inference from reconstructed Einstein-ring measurements.
A controlled 0.45-2.40 um Stokes-I experiment uses ten illuminated cells, 128 channels, and R=70 to compare resolved and exactly projected disk spectra with common parameters and priors. Across 96 synthetic scenes, the joint gas, vegetation, and mineral block gains (1.52+/-0.03) nats after marginalizing cloud and calibration/response parameters; adding independently trained surrogate-discrepancy covariance gives (1.49+/-0.03) nats.
Held-out mismatch nevertheless produces linearized shifts up to 6.08 posterior standard deviations; preserved precision does not establish unbiased recovery or evidence for life. For fixed Gaussian hypotheses, the expected log-likelihood-ratio loss under disk integration equals half the squared whitened contrast discarded by the projection.
A separate 0.40-20 um continuum calculation provides absolute photon rates and observing-time estimates for an Earth-radius planet at 30 pc, observed from 650 AU. It includes source-averaged SGL amplification, finite-aperture extraction, coronal and host-star photons, detector noise, and a declared calibration floor.
A reconstruction-covariance bracket reduces an 8 x 8 coadd gain from 7.77 to 3.00, costing 6.7 times the exposure in the statistical-noise limit. The framework connects regional spectroscopy and co-location tests to the physical and instrumental validation needed to assess exoplanet biospheres and possible biological activity.
Finite scalar spectral-cube reference at the channel centers nearest 0.76, 1.25, and 2.20 µm. Columns: source S, measurement HS +ϵ, and Wiener reconstruction Sb, on a common radiance scale. The 128×128 fields retain blur/noise outside the illuminated support; outlines mark the limb and 60◦ terminator. Lower panel: RMS total error, regularization bias and response-centered noise over 128 channels and 7, 872 selected pixels, with covariance-predicted σrec = 0.003015. Appendix A defines the scene, scalar blur, noise, inverse, and boundaries. This scalar test is distinct from the ten-cell Fisher reference and does not establish wave-optical SGL reconstruction performance. — [astro-ph.IM]
Slava G. Turyshev
Comments: 43 pages, 13 figures, 15 tables
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:2606.29138 [astro-ph.IM] (or arXiv:2606.29138v3 [astro-ph.IM] for this version)
https://doi.org/10.48550/arXiv.2606.29138
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Submission history
From: Slava G. Turyshev
[v1] Sun, 28 Jun 2026 00:55:47 UTC (4,533 KB)
[v2] Wed, 7 Oct 2026 02:16:52 UTC (4,534 KB)
[v3] Sat, 24 Oct 2026 19:33:16 UTC (623 KB)
https://arxiv.org/abs/2606.29138
Astrobiology,
