What does this research mean for the field?

Imaginal Number Theory provides a framework that unifies Frobenius and quaternionic spectra, producing unified imaginal zeta and L-functions that link arithmetic geometry with prime emergence. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

To establish a unified mathematical framework connecting arithmetic geometry and prime emergence through shared spectral mechanisms.

September 8, 2026Open Access

Imaginal Number Theory A Spectral Unification of Arithmetic Geometry and Prime Emergence

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To establish a unified mathematical framework connecting arithmetic geometry and prime emergence through shared spectral mechanisms.
Modeled a generative mathematical process comprising fluctuation, image formation, and spectral gluing.
Synthesized Frobenius spectra with quaternionic spectra into a cohesive algebraic structure.
Constructed unified imaginal zeta and L-functions across arithmetic and geometric domains.
Demonstrated a coherent spectral bridge directly linking arithmetic geometry with the emergence of prime numbers.

Implication

Theoretical analysis reveals unified imaginal zeta and L-functions across geometric spectra, suggesting a shared mechanism behind prime emergence.

Abstract

Imaginal Number Theory unifies Frobenius and quaternionic spectra through a shared generative process of fluctuation, image formation, and spectral gluing, producing unified imaginal zeta and L-functions that coherently link arithmetic geometry with prime emergence.

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Cite This Study

Shin Tamaki (2026) studied this question.

synapsesocial.com/papers/6a9fd76758e84d0ff5b45fcd https://doi.org/10.5281/zenodo.22557814

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Implication

Theoretical analysis reveals unified imaginal zeta and L-functions across geometric spectra, suggesting a shared mechanism behind prime emergence.

Imaginal Number Theory A Spectral Unification of Arithmetic Geometry and Prime Emergence

Key Points

Implication

Abstract

Discussion

Cite This Study

Imaginal Number Theory A Spectral Unification of Arithmetic Geometry and Prime Emergence

Key Points

Implication

Abstract

Discussion

Cite This Study

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