Within the FKGP (Fractal Quantum Holographic Paradigm) framework we propose and experimentally verify a scaling law for the second-order Rényi entanglement entropy S2 (A) in graph states of varying topological dimension D. The key result is S2 (A) = rankGF2 (Gamma) · ln 2, where the GF (2) -rank of the A-B boundary adjacency matrix increases by exactly one at each step of the dimensional ladder. On IBM Heron r2 (ibmfez) with 65, 536 shots per circuit, four steps are confirmed: D=2. 00 (ΔSNR=76. 9σ), D1=2. 05 (34. 3σ), D2=e (7. 8σ), and D=3 (5. 1σ). All detections exceed the 5σ threshold. Cosmological hypotheses are advanced: D1 = 2 + Ωb (baryon fraction) and D2 = e (informational efficiency). This paper includes a complete reproducibility appendix (Batches 1–10): all QASM circuits, measured P₀ values, noise corrections, and ΔSNR calculations.
Pavel Trojan (Mon,) studied this question.