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Global twistor sources for analytic Einstein spacetimes

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

Contributed by Lior Isthmus ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We globalize the local analytic projective twistor correspondence for the gravitational googly problem, retaining its convergent nonlinear treatment of both gravitational chiralities. For each fixed Einstein coefficient, the correspondence identifies independently defined atlases of two analytic Čech classes of weights 22 and −6-6, structured operator sources on null monodromy presentations, and holomorphic oriented spin Einstein four-manifolds. Its inverse comparisons preserve the original source operations, Einstein scale, spin structure and complete point family, together with calibrated modules on parametrized incidence. For analytic Lorentz developments with a compact marked Cauchy surface, germs along the entire real development give the corresponding equivalence, and the maximal analytic Cauchy development determines a terminal source germ. A Nariai example admits no Hausdorff contact carrier containing the full complex skies over all points of the real development. In its product complexification and every allowed point restriction containing the entire real development, every real point sky has nonclosed saturation, so no ordinary locally finitely generated module has exactly that saturated support. These obstructions explain the use of null monodromy and parametrized incidence in the global correspondence, with compact point objects recovered by central specialization.

Author comments: v1.0. The same manuscript and the computational supplement are available at https://doi.org/10.5281/zenodo.24186390 and https://github.com/lioristhmus/global-twistor-sources/releases/tag/v1.0.

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). Selected symbolic identities and explicit metric examples were checked using SageMath and SymPy; the code, inputs, computational environment and recorded results are provided in the accompanying computational supplement.

Tools used

OpenAI
ChatGPTVersion GPT-6 Pro
OpenAI
CodexVersion gpt-6.1-sol (xhigh)
Anthropic
Claude OpusVersion 5.5 (xhigh)
SageMath
SageMathVersion 10.9
SymPy
SymPyVersion 1.14.0

References

No bibliography entries.

Version history

  1. v1 · 72 pagesSubmitted by Lior Isthmusv1.0. The same manuscript and the computational supplement are available at https://doi.org/10.5281/zenodo.24186390 and https://github.com/lioristhmus/global-twistor-sources/releases/tag/v1.0.CurrentNov 13, 2026