Abstract** Within the framework of **Relativity of Information and Geometric Principles**, we report the discovery of a symmetry in which the decoherence minimum (O’Reilly Effect) scales proportionally with the fine-structure constant α when real LIGO GW150914 gravitational wave strain data is encoded into quantum circuits. Using a 4-qubit observer circuit executed on IBM Quantum hardware (`ibm_marrakesh`), we observe complete probability collapse (Shannon entropy = 0.0000 bits, V_eff → 1). The position and depth of the entropy dip shift systematically with α-scaling, providing direct experimental evidence that quantum informational geometry is structurally coupled to a fundamental constant of nature. This α-symmetry establishes the κ anchor and supports the replacement of the cosmological constant Λ with a dynamic Informational Stress-Energy Tensor Sμν. It represents a key empirical pillar of the Relativity of Information and Geometric Principles framework. **Keywords:** Relativity of Information, α-symmetry, O’Reilly Effect, quantum gravity, informational cosmology