What question did this study set out to answer?

To evaluate whether place-selective deformation weights in the Arithmetic Teichmüller Space framework can satisfy product formulas while preserving parameter dependence in projective height calculations.

August 16, 2026Open Access

Repairing the ATS Chain? A Rigidity Theorem for Product-Formula Weights and an Effective-Weight Test for the Height Subchain (DRAFT)

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Authors

LGLukas Geiger

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Implication

Theoretical analysis proves an unconditional rigidity theorem for product-formula weights in number fields, showing that place-selective height variations collapse to classical values.

Key Points

To evaluate whether place-selective deformation weights in the Arithmetic Teichmüller Space framework can satisfy product formulas while preserving parameter dependence in projective height calculations.
Derived an unconditional rigidity theorem for real exponent families satisfying standard product formulas across arbitrary number fields.
Applied a finite-fibre factorization lemma and an exhaustion analysis to the normalization identities and weighted projective height definitions of the Arithmetic Teichmüller Space series.
Proved that any family of exponents satisfying the standard product formula across a number field must be globally constant, regardless of class number.
Demonstrated that deformation parameter dependencies in normalization weights and absolute values cancel exactly, reducing weighted degrees and heights to classical, parameter-independent values.

Cite This Study

Lukas Geiger (2026) studied this question.

synapsesocial.com/papers/6a817a91f2fb91fc834ae889 https://doi.org/10.5281/zenodo.21952487

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Implication

Theoretical analysis proves an unconditional rigidity theorem for product-formula weights in number fields, showing that place-selective height variations collapse to classical values.

Repairing the ATS Chain? A Rigidity Theorem for Product-Formula Weights and an Effective-Weight Test for the Height Subchain (DRAFT)

Discussion

Member takes

Implication

Key Points

Cite This Study

Repairing the ATS Chain? A Rigidity Theorem for Product-Formula Weights and an Effective-Weight Test for the Height Subchain (DRAFT)

Discussion

Member takes

Implication

Key Points

Cite This Study

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