Problem
The affine pair \(p,2p+1\) is realized on the frozen-two carrier. The branch studies the infinitude claim for Sophie Germain primes in the same multiplicative framework.
Geometric formulation
The pair is realized on the carrier \(x=2n\), with \(x\equiv2\pmod4\). The observed event is exactly
Main manuscript claim
Theorem 1.1 claims positivity of the weighted Sophie Germain count on every sufficiently large dyadic block. The stated corollary is infinitude of Sophie Germain primes.
Proof architecture / transport mechanism
The native CRT/local-density ledger and the observed arithmetic ledger are realized on the same affine fibre and pushed to the same retained ledger space. Under zero observation, the retained discrepancy is claimed to carry macroscopic mass.
Same-row closure
The terminal stage uses the same carrier, residual class, transfer map, and fixed readout family for the lower and upper comparisons. This same-channel requirement is one of the mature firewalls of the corpus.
This stage also emphasizes proof dependency: bad atoms are routed by first failure, terminal classes are registered only after material realization, and the paper is structured to avoid hidden companion-manuscript dependencies.
Cite this work
@misc{gotanegra2026sophiegermain,
author = {Jaume Gotanegra},
title = {On the Infinitude of Sophie Germain Primes in a Prime-Specialized Multiplicative Geometric Model},
year = {2026},
month = {Jun},
doi = {10.5281/zenodo.20744219},
url = {https://doi.org/10.5281/zenodo.20744219},
note = {Preprint}
}