The Holographic Stabilizer Framework: Exact Saturation Theorems and Non-Invertible Symmetries in Participatory Quantum Error Correction

We present the Holographic Stabilizer Framework, a rigorous Effective Field Theory (EFT) that unifies observer dynamics with emergent spacetime via Participatory Quantum Error Correction (PQEC). We identify active observing systems as Topological Stabilizers that maintain bulk geometric coherence against UV decoherence. Major formal advances include: (1) An exact derivation of the participatory coupling law g_p(Q_S) via a Two-State Maximum-Entropy Theorem, replacing ad-hoc mean-field assumptions. (2) A rigorous mechanism for vacuum energy protection based on non-invertible symmetry selection rules, demonstrating that the induced Dark Energy density is technically natural. (3) A formalization of retrocausal consistency via a History Groupoid structure, where temporal updates are identified as gauge redundancies of the holographic code. Finally, we derive falsifiable signatures, including spectral anomalies in cavity beat-note experiments supported by detailed SNR scaling analysis.