Major Conjectures and Cosmological Tests H; The Cosmological Falsifiability of the ABC Conjecture

This paper explores the potential connection between the ABC conjecture in
number theory and physical phenomena in the early universe. Based on the ax
iomatic assumptions of ”the universe as an information processing system” and
”information conservation” and ”computability”, we reinterpret the arithmetic in
equality implied by the ABC conjecture as an efficiency constraint on the ”addi
tive” synthesis processes in the cosmic information flow. This constraint is mapped
to a suppression of specific non-Gaussian signals in the cosmic microwave back
ground (CMB) radiation: namely, on collinear triangular configurations satisfying
the scalar wavenumber addition relation (k1+k2 = k3), the non-Gaussian amplitude
should exhibit a characteristic exponential decay at high wavenumbers (correspond
ing to small angular scales). We performed the first test of this prediction using
Planck 2018 satellite data and observed a suppression signal qualitatively consistent
with the model in the multipole range ℓ > 500, with a global significance of approx
imately 2.9σ. Further simulation analysis indicates that next-generation CMB-S4
experiments will have the capability to conduct a decisive test of this signal. This
study provides a new, operational and falsifiable path for testing the physical rele
vance of fundamental mathematical structures through cosmological observations.