Twin primes

Problem

The twin-prime branch removes the additive width available in Goldbach. The fixed fibre is \(Q_n=(n,n+2)\).

Geometric formulation

Setting \(x=n+1\) converts the pair into the exact terminal factorization trace

Main manuscript claim

The manuscript defines the dyadic weighted twin-prime count \(T_X\) and claims \(T_X>0\) for every sufficiently large \(X\), yielding infinitely many twin-prime pairs on successive dyadic blocks.

Proof architecture / transport mechanism

Under the contrary assumption \(T_X=0\), the observed primitive ledger vanishes while the native principal prediction retains macroscopic mass. Their discrepancy is compressed into a finite terminal residual complex while preserving the rows needed for the final readout.

Primitive-zero principle

The manuscript explicitly avoids the implication “locally primitive ⇒ observed prime-prime.” Observed primality enters only through the observed ledger; zero observation creates the residual class that the terminal channel must both detect and annihilate.

@misc{gotanegra2026twin,
  author       = {Jaume Gotanegra},
  title        = {On the Twin Prime Problem in a Prime-Specialized Multiplicative Geometric Model},
  year         = {2026},
  month        = {May},
  doi          = {10.5281/zenodo.20478342},
  url          = {https://doi.org/10.5281/zenodo.20478342},
  note         = {Preprint}
}