What question did this study set out to answer?

The aim is to create a mathematical structure that incorporates fundamental physical equations through the Hessian in a Helmholtz field.

June 21, 2026Open Access

Physical Structures Contained in the Hessian of a Harmonic Phase: a Spectral Functional Framework

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This work constructs a mathematical framework that derives equations unifying key physical theories, indicating potential new insights.

The aim is to create a mathematical structure that incorporates fundamental physical equations through the Hessian in a Helmholtz field.
Developed a tensor decomposition of the Hessian in Euclidean ℝ⁴.
Derived emergent metrics and key equations (Maxwell, Einstein, Dirac) from a unified geometric framework.
Presented quantitative predictions including lepton mass ratios and (g−2)/2 deviation.
Predicted lepton mass ratios with a deviation of 2–5%.
Calculated (g−2)/2 = 0.001157 with a deviation of −0.20%.
Established a geometric framework that incorporates multiple fundamental equations.

Roberto Pavani (2026) studied this question.

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June 21, 2026Open Access

View Full Paper

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Authors

This work constructs a mathematical framework that derives equations unifying key physical theories, indicating potential new insights.

The aim is to create a mathematical structure that incorporates fundamental physical equations through the Hessian in a Helmholtz field.
Developed a tensor decomposition of the Hessian in Euclidean ℝ⁴.
Derived emergent metrics and key equations (Maxwell, Einstein, Dirac) from a unified geometric framework.
Presented quantitative predictions including lepton mass ratios and (g−2)/2 deviation.
Predicted lepton mass ratios with a deviation of 2–5%.
Calculated (g−2)/2 = 0.001157 with a deviation of −0.20%.
Established a geometric framework that incorporates multiple fundamental equations.

Roberto Pavani (2026) studied this question.

View Full Paper

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