Let's understand the problem that led to the neutrino's prediction:

1. **Observation:** Scientists observed a type of radioactive decay called beta decay, where an electron is emitted from an atomic nucleus.
2. **Expectation (Energy Conservation):** Based on the law of conservation of energy, the electron emitted should always have a specific, fixed amount of energy, like a ball rolling down a smooth ramp always reaching the bottom with the same speed.
3. **Reality (The Puzzle):** However, experiments showed that the emitted electrons had a range of energies, from very low to the expected maximum. It was like the ball rolling down the ramp sometimes stopped halfway or went slower, meaning some energy was 'missing'.
4. **Pauli's Prediction (1930):** To save the law of energy conservation, physicist Wolfgang Pauli proposed that another tiny, undetected particle must be carrying away the 'missing' energy. He called it the 'neutron' initially, which was later renamed 'neutrino' by Enrico Fermi.
5. **Reines and Cowan Experiment (1956):** It took decades, but physicists Clyde Cowan and Frederick Reines finally built an experiment to detect these elusive particles. They used a nuclear reactor as a strong source of neutrinos and a detector filled with water and cadmium chloride.
6. **Detection:** When an antineutrino from the reactor hit a proton in the water, it produced a neutron and a positron. The positron quickly annihilated with an electron, creating two gamma rays. The neutron was then captured by cadmium, releasing more gamma rays a few microseconds later. Detecting these specific sequences of gamma rays confirmed the neutrino's existence.

**Answer:** The detection of specific gamma ray signals in the Reines-Cowan experiment, occurring in a precise sequence after exposure to a strong neutrino source, provided the experimental proof for the neutrino's existence, confirming Pauli's prediction.