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A projective twistor correspondence for local analytic Einstein germs

Primarily AI-generated textHuman understanding: some partsmath-ph — Mathematical Physicsmath.CV — Complex Variablesmath.DG — Differential Geometry

Contributed by Lior Isthmus ↗

Version 1 / Nov 05, 2026 / CC BY 4.0

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 22 and −6-6 on a fixed flat twistor germ T0T_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.

Author comments: v1.0. The same manuscript is available at https://doi.org/10.5281/zenodo.23975732.

Provenance statement

I pursued my questions through sustained interaction with AI systems, repeatedly requesting checks and revisions of the arguments to arrive at the results presented here. AI systems were used extensively throughout the research and preparation of the manuscript. The models used were GPT-6 Pro, gpt-6.1-sol (xhigh), and Claude Opus 5.5 (xhigh).

Tools used

OpenAI
ChatGPTVersion GPT-6 Pro
OpenAI
CodexVersion gpt-6.1-sol (xhigh)
Anthropic
Claude OpusVersion 5.5 (xhigh)

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Version history

  1. v1 · 217 pagesSubmitted by Lior Isthmusv1.0. The same manuscript is available at https://doi.org/10.5281/zenodo.23975732.CurrentNov 05, 2026