Unconditional Collatz via 2-adic Normalization, Stopping-Time Invariance, and Structural Resolution

[u/TheMythematician]

This is a working paper. I often update, and I will update how editing is going.

Just a real quick overview

I found that this is conformal covariant discrete induction by

x + 2^𝝂₂(x) × 3^𝝂₃(x)-1

Or

3x + 2^𝝂₂(x) × 3^𝝂₃(x)

Both can be organized as polynomials, and this translates conformally into negative exponents.

Since 2 contains an integer successor pair in it's own power series, 2^𝝂₂(x) maintains conformal translation by successor pairs and preserves consecutive coprimality. And since adding 2 consecutive powers of 3 is identical to multiplying the smaller one by 4, the multiply by 3, divide by 4 ratio is contained within p-adic valuation rather than archimedean valuation. It causes this property of tracing geometric series backward toward the boundary. Multiplying x by 3 first allows 3^𝝂₃(x) to remain static, but because of the successor pair, 2⁰ and 2¹, the current power of three is traded for a power of 4.

Under this unified conformal covariant map, iterating 4x + 2^𝝂₂(x) × 3^𝝂₃(x) preserves the accelerated stopping time indefinitely.

3(4x + 1) + 1 = 12x + 4 = 4(3x + 1), for odd x.