What question did this study set out to answer?

To establish that complex numbers have ontological priority over real numbers and introduce a structural constant T.

April 4, 2026Open Access

The Prior Number: On the Ontological Primacy of Complex Structure and the Invariant T

Key Points

To establish that complex numbers have ontological priority over real numbers and introduce a structural constant T.
Restatement of the Riemann Hypothesis using T-language.
Demonstration of T-symmetry in the Riemann zeta function's functional equation.
Identification of the pair correlation function of Riemann zeros in relation to T.
Proposition of a falsifiable prediction regarding the Montgomery pair correlation function.
Utilization of experimental confirmations from previous studies.
Establishment of T = 1/2 as a fundamental structural constant.
Identification of T-symmetry in key mathematical equations.
Prediction that the Montgomery pair correlation function can be derived without random matrix theory.
Evidence supporting the necessity of complex structure in physical systems.

Abstract

This paper argues that the complex number is ontologically prior to the real number, and introduces T = 1/2 as the prior structural constant of any system capable of making distinctions. The Riemann Hypothesis is restated in T-language, the functional equation of the Riemann zeta function is shown to be T-symmetric, and the pair correlation function of Riemann zeros is identified as traceable to T through Γ(T) = √π. A falsifiable prediction is proposed: that the Montgomery pair correlation function is derivable from T-symmetry without appeal to random matrix theory. Experimental confirmation that complex structure is physically necessary is drawn from Renou et al. (2021) and Chen et al. (2022). The ontological status of time is also addressed within the framework.

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Authors

Nassim El Hassouni

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Oldham Council

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The Prior Number: On the Ontological Primacy of Complex Structure and the Invariant T

Key Points

Abstract

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Authors

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References and Citations

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