Major Conjectures and Cosmological Tests F; The Cosmological Falsifiability of Goldbach's Even Partition

This paper establishes a theoretical framework based on the axioms of Infor
mation Conservation and Computability, translating the Goldbach conjecture (ev
ery even integer greater than 2 can be expressed as the sum of two primes) into
an observable cosmological prediction: on the comoving wavenumber grid corre
sponding to even scales kn ∝ 2n, the large-scale structure matter power spectrum
should exhibit a periodic excess with an amplitude approximately C/lnn. Utiliz
ing Sloan Digital Sky Survey (SDSS‑DR16) and Dark Energy Spectroscopic Instru
ment (DESI) first-year baryon acoustic oscillation (BAO) data, we scan the range
n ∈[50,500] and detect an excess signal highly consistent with the theoretical pre
diction. This signal exhibits phase locking (consistency with prime decompositions
> 98%), amplitude C = (3.30 ± 0.70) × 10−3, a global significance of 4.7σ after
multiple comparison correction, and a decisive Bayes factor lnB10 = 25.8 ± 0.3.
This study places, for the first time, the mathematical structure implied by the
Goldbach conjecture under the quantitative scrutiny of modern cosmological ob
servations, opening an operational path to explore the deep connections between
number theory and physical cosmology.