A projective twistor correspondence for local analytic Einstein germs
Year: 2026
Type: preprint
Abstract: For each prescribed numerical cosmological constant, including zero, we establish a convergent projective twistor correspondence recovering every marked four-dimensional local analytic Einstein germ of any algebraic Weyl type. The inputs are two independent analytic Čech classes of weights $2$ and $-6$ on a fixed flat twistor germ $T_0$ along its whole marked zero line, encoding both complete chiral curvature records. The fixed source correction and calibration select a unit optical section, an intrinsic projective extension condition recognizes Einstein geometry, and the prescribed normalized contact, optical and affine maps and their inverses converge on common neighborhoods of the whole physical sky for bounded holomorphic input families. On independently admitted ordinary and operator domains we prove both inverse comparisons, with the two source operations acting in one projective analytic Heisenberg model. The same comparisons preserve the nonlinear source, compact point objects, optical evaluation and calibrated infinity forms, together with physical point and full spin-frame changes and coupled Lorentz reality. For fixed positive Schwarzschild mass, we obtain finite horizon-crossing presentations, a calibrated local primitive comparison and optical approximation bounds for the entire specified compact nonradial crossing family using finite local readouts and the exact benchmark cuts, coordinate comparisons and Sachs reference frames. This record archives the fixed v1.0 manuscript and publication source package also available in the GitHub v1.0 release. Licensing. The manuscript and scholarly documentation are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Build and validation code under scripts/ and rendering support under common/styles/ are licensed under the Apache License, Version 2.0. The source package includes LICENSE and both license texts with the exact file scope. AI-use disclosure. AI systems were used extensively throughout this research and the preparation of this manuscript. The models used were GPT-6 Pro, gpt-6.1-sol (xhigh), and Claude Opus 5.5 (xhigh).
Author: Isthmus, Lior
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225337709