Totient inequality at consecutive integers is still open

Establish whether there exist infinitely many primes p such that Euler’s totient function satisfies φ(p+1) > φ(p).

Background

The authors explicitly note the longstanding conjecture that φ(p+1) > φ(p) for infinitely many primes p remains unresolved. They then provide an analogous result for the modified function φ⁺(n) for a specific infinite subsequence of primes.