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March 26, 20260 citationsOpen Access

URB #506: The i-Completeness Theorem — All Mathematics as Operations on i

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BEBrandon Charles Emerick

Key Points

  • The aim is to demonstrate that key mathematical constants are derived from a single primitive operation.
  • Proof of expressibility of constants as operations on 'i'.
  • Identification of eight primary constants in TI Sigma.
  • Application of elementary operations to the primitive 'i'.
  • All eight primary constants are expressible through specific operations on 'i'.
  • Establishes a new understanding of mathematical relationships among constants.

Abstract

We prove that the eight PRIMARY CONSTANTS of TI Sigma — 0, 1, i, √2, e, φ, π, C — are all expressible as specific, elementary operations applied to the single primitive i. The **i-Completeness Theorem** states:

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Cite This Study

Brandon Charles Emerick (2026) studied this question.

synapsesocial.com/papers/69c4cd73fdc3bde448919d9ahttps://doi.org/10.5281/zenodo.19207370
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1URB #500: The BOK Closure Theorem — The Octopus Proof2026
  2. 2URB #429 — The Status of i Across TI Sigma: The Imaginary Unit as Physical Necessity2026
  3. 3URB #490: The Generative Pair2026
  4. 4URB #507: The Minimal Basis — {i, +, −, ×, ÷, lim} Generates All of Mathematics2026
  5. 5URB #517 — Lean 4 Formal Proofs for TI Sigma Mathematical Claims2026