SWhat changed
Friedmann shows that the Einstein equations under a positively curved pressureless cosmological ansatz allow a time-dependent curvature radius, and classifies monotone and expanding-contracting possibilities depending on constants.
Scientific scope
Friedmann shows that the Einstein equations under a positively curved pressureless cosmological ansatz allow a time-dependent curvature radius, and classifies monotone and expanding-contracting possibilities depending on constants. The target is the 1922 positively curved, pressureless matter construction with Einstein equations and a cosmological constant, plus explicit coordinate and metric assumptions. It is not the complete modern FLRW geometry, arbitrary-pressure cosmology, spatially flat models, or the 1924 negative-curvature extension. A later scholarly note flags incomplete geometric precision; the full tensor reduction was not independently certified. Positive spatial curvature does not alone force recollapse: sufficiently large positive cosmological constant permits a monotone branch. Periodic-radius descriptions do not independently prove regular spacetime continuation through zero-radius singularities. The paper does not derive cosmic redshift, fit galaxy recession data, prove our actual universe expands, or determine its age; its numerical period is explicitly illustrative. Lemaître’s later observation connection and Robertson/Walker developments remain separate. Extracted formula glyphs were not visually certified; the normalized first-integral check confirms a narrow root interpretation, not the full proof or singular boundary behavior.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Alexander Friedmann · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- A. Friedman, Über die Krümmung des Raumes (Zeitschrift für Physik 10,377-386,1922), original German scan
- Ellis and Krasiński, Editor’s Note on Friedmann 1922/1924 (General Relativity and Gravitation 31,1985-1990,1999), selected scholarly scope commentary
- Instituut-Lorentz, Friedmann papers: institutional manuscript catalogue and work identification
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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