Methodological Foundations of the TAGC–LQG–RG Research Programme: A Lakatosian Framework for Informational Quantum Gravity

We present an exhaustive methodological analysis of the TAGC–LQG–RG research programme under Lakatos’s philosophy of science. The programme proposes that classical spacetime emerges from an informational substrate governed by a universal critical threshold κc = 2.04±0.05. We explicitly identify the hard core (informational primacy, Landauer’s principle, GKSL dynamics) and the protective belt (18 third-party works) of the programme. We present a formal effective derivation of κc from first informational principles based on variational stability, renormalizationgroup analysis, and spectral criteria. The programme generates five falsifiable predictions (P1–P5) verifiable within 2–20 years. We demonstrate that κc possesses the same epistemological status as the fine-structure constant α before QED.