What question did this study set out to answer?

To explore a discrete system linking combinatorial games and the Riemann xi-function, aiming to clarify connections to the Riemann Hypothesis.

June 2, 2026Open Access

A Discrete Reflection Algebra and its Convergence to the Riemann xi-Function: The Matchstick Game, the Heat-Kernel Bridge, and the Remaining Step to RH

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Authors

TKThomas Krause

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Implication

Establishes a combinatorial framework that connects the Riemann xi-function to discrete structures, hinting at implications for the Riemann Hypothesis.

Key Points

To explore a discrete system linking combinatorial games and the Riemann xi-function, aiming to clarify connections to the Riemann Hypothesis.
Introduced a finite combinatorial system called the Matchstick Game with two operations: expansion and reflection.
Established reflection uniqueness and created a heat-kernel bridge linking a spectral function to the Jacobi theta function.
Formulated geometric conjectures addressing gaps in proving the Riemann Hypothesis, alongside numerical tests.
Demonstrated that the reflection algebra is uniquely characterized by its initial data.
Proved the completed function Xi(s) coincides with Riemann’s xi(s) across the complex plane, aligning their non-trivial zeros.
Identified a remaining open condition regarding off-equatorial orbits of the reflection algebra that must connect on the critical line.

Cite This Study

Thomas Krause (2026) studied this question.

synapsesocial.com/papers/6a1e72e830b38c64201b61ef https://doi.org/10.5281/zenodo.20479975

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Implication

Establishes a combinatorial framework that connects the Riemann xi-function to discrete structures, hinting at implications for the Riemann Hypothesis.

A Discrete Reflection Algebra and its Convergence to the Riemann xi-Function: The Matchstick Game, the Heat-Kernel Bridge, and the Remaining Step to RH

Discussion

Member takes

Implication

Key Points

Cite This Study

A Discrete Reflection Algebra and its Convergence to the Riemann xi-Function: The Matchstick Game, the Heat-Kernel Bridge, and the Remaining Step to RH

Discussion

Member takes

Implication

Key Points

Cite This Study

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