Twin Prime Conjecture: Computational Pattern Detection Through Temporal Dynamics Framework — Honest Negative Result and Three-Body Gap Structure Discovery

This paper investigates twin prime detection using the Temporal Dynamics Framework resonance analysis. The paper reports an honest negative result: the Psi-UPR standing wave acts on all integers equally regardless of twin status, with bump primes, dip primes, and node primes all producing twins at identical rates (approximately 20.8% at 10^6). High resonance magnitude does not discriminate twins from non-twins. The paper discovers three-body gap structure: twin primes are governed by a three-state Markov chain with forbidden transitions, meaning the gap before a prime carries information about the gap after it. All 67 verification tests pass. Paper 3 in the Temporal Dynamics Framework Research Series.