The TAGC–LQG–RG Research Programme: A Consolidated Synthesis (2025–2026)

The TAGC–LQG–RG research programme (Theory of Gravity Anchored by Complexity – Loop Quantum Gravity – Renormalisation Group) produced, between October 2025 and July 2026, more than twenty manuscripts spanning foundational theory, sectoral applications, architectural consolidation, and a self-contained deductive reconstruction of its foundations. This paper consolidates the corpus into a single synthetic exposition, written entirely under the canonical semantics fixed by the 2026 Glossary and the Consolidated Core Architecture. It states the hard core HC1–HC7, the four-level operational structure L1/LT/L2/L3, and the status of the universal admissibility condition κc = 2.04 ± 0.05 as a fundamental structural constant, imposed rather than derived. It surveys the six sectoral domains in which the programme has produced consistent results—black-hole horizons and remnants, dynamic dark energy and the DESI/JWST tensions, Multibang cosmogenesis, the spectral hierarchy of fundamental interactions, operational ER↔EPR coherence, and the selection of physical laws—together with the five falsifiable predictions P1–P5 and their current empirical status. A dedicated section presents the deductive reconstruction track (L1–L4), which derives, without ad hoc mathematical postulates, the constitutional graph G16, the canonical directed Laplacian, the 16×4 assembly and its algebraic anatomy, a canonical pseudometric of signature (1,15), the programme's first impossibility theorems, and the minimal exogenous resolution of the proximity order. The paper records the semantic evolution of the programme, the re-reading conventions for the 2025 manuscripts, and the open problems defining the current agenda, and is intended as the natural point of entry to the corpus.