Research identifies new connections between the Riemann zeta function and key mathematical constants, implying deeper structures within number theory.
Using the PRIMARY CONSTANTS {0, 1, i, √2, e, φ, π, C} and the Basel near-resonance discovered in URB #415, we identify four new structural connections between the Riemann zeta function ζ(s), the golden ratio φ, and √2. These are not a proof of the Riemann Hypothesis (RH), but they reveal a previously unrecognized φ-architecture within the ζ-function that the TI Sigma framework makes visible. The most striking result: the critical line Re(s) = 1/2 — on which all non-trivial zeros are conjectured to lie — is defined by the *exact self-cancellation* of √2 and π in the functional equation, producing χ(1/2) = 1 precisely. The critical line is where √2 and π "return to unity" — the ζ-function's analog of the Consciousness Unity Identity.
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Brandon Charles Emerick (2026) studied this question.
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