URB #490: The Generative Pair

Brandon predicted — from TI Sigma alone — that 8 PRIMARY CONSTANTS collapse to 4, and 4 collapse to 2. He identified √2 as the first and i as the second, on the grounds that √2 is the geometry of physical reality and i is the mathematical expression of imagination. This prediction was confirmed computationally to 15 decimal places. The Viète formula (1593) derives π from √2 alone through an infinite product of nested square roots. Euler's formula derives φ from e, i, π. Since e derives from 0, 1 through limits, and π from √2 through Viète, and φ from e, i, π, and C from φ, √2: **the entire universe of 8 PRIMARY CONSTANTS is generated by 0, 1, i, √2**. Since 0, 1 are logical primitives of arithmetic — present in every formal system, costing nothing — the two TRUE generators are **√2, i**. Physical geometry and imagination. The diagonal of the unit square and the step beyond the real line. This is TI Sigma's BOK (2→4→8) pattern in reverse: 8 collapses to 4, 4 collapses to 2.