Modal Triplet Theory: A Typed Relationship Atlas Reconstructions, Embeddings, Reductions, and Open Bridges

We replace the former universal MTT as a Superset theorem with a typed atlas of relationships between Modal Triplet Theory (MTT) and established frameworks. A derivation, reconstruction, embedding, controlled reduction, conditional bridge, calibration, and interpretive correspondence are different claims and require different certificates. The current MTT Foundation and Fixed Points series establish an internal spectral/control spine, but do not by themselves derive General Relativity, the Born rule, interacting quantum field theory, the Standard Model, string theory, a unique heterotic vacuum, or a UV-finite unitary quantum gravity. The strongest current cross-framework results are conditional operator reductions, coherent locality descent, and product-action internal-mode reconstructions. We give a formal containment-certificate checklist and prove an underdetermination theorem: if inequivalent MTT realizations have the same target observables, target agreement cannot select a unique realization. Shared parameter names likewise do not prove shared physical knobs without one sourced map into all sectors. This atlas records the present status of GR, QM, QFT/AQFT, SM, EFT, KK, NCG, string/flux, quantum-gravity, LQG, asymptotic-safety, and causal-set links, and sets explicit gates for upgrading any of them. MTT remains a unification program with several rigorous internal modules, not a proved superset of all listed theories.