Internal critical-line alignment

Problem

This stage studies zero localization in the prime-specialized multiplicative model. The prime-specialized manuscript identifies the free multiplicative state space with positive integers and fixes the geometric length of a prime direction by \(\lambda_p=\log p\).

Geometric formulation

The partition function becomes \(\zeta(s)\), while the quotient coordinate \(w=\log(n/m)\) supplies the local geometry used for transport.

Main manuscript claim

Theorem 0.1 states that, within the prime-specialized multiplicative geometric model developed in the paper, every nontrivial zero of the Riemann zeta function has real part \(1/2\).

Proof architecture / transport mechanism

The argument is organized in two stages. First, aligned and nonaligned shellwise transport are separated and the nonaligned branch is quantitatively excluded for the concrete packet family. Second, a zero-pinned jetwise transfer inserts a hypothetical off-critical zero into the already rigid geometry.

Terminal contradiction

The manuscript derives a quantitative off-critical lower bound at the pinned origin and combines it with exact zero-pinned vanishing. The intended contradiction is therefore same-channel: the same transferred profile is forced to be both nontrivial and annihilated.

@misc{gotanegra2026criticalline,
  author       = {Jaume Gotanegra},
  title        = {Internal Critical-Line Alignment and Zero Localization in a Multiplicative Geometric Model Specialized to Primes},
  year         = {2026},
  month        = {Apr},
  doi          = {10.5281/zenodo.19388932},
  url          = {https://doi.org/10.5281/zenodo.19388932},
  note         = {Preprint}
}