Global Spectral Theory of Everything — Version 3: Scope, Structural Status, and Operational Falsifiers

This record presents Version 3 of the Global Spectral Theory of Everything, a background-independent and relational framework in which physical structure is formulated in terms of global spectral properties rather than local dynamics on a predefined spacetime. Version 3 is a synthesis and status document continuing Version 2 (DOI 10.5281/zenodo.18213696). It does not introduce new fundamental machinery. Its purpose is to consolidate the current scientific status of the programme, clarify its limits, and provide an operational falsifier map. The Random Matrix Theory (RMT) result of Version 2 remains in force: representative excitation operators exhibit intermediate, pseudo-integrable spectral statistics between Poisson and GOE ensembles. This falsifies a direct hadronic or strongly chaotic many-body interpretation of the framework, while remaining compatible with its intended foundational scope. Version 3 also clarifies the status of the neutrino mass-ordering question. The local construction does not derive the ordering as a theorem; the relevant Majorana-sector hierarchy remains an empirical/model-selection boundary. A minimal Majorana-sector branch favours Normal Ordering but is not forced. Separately, a conjectural global-spectral / swampland-type argument also favours Normal Ordering. An inverted-ordering measurement would falsify those predictive layers, but would not automatically falsify the entire local framework. This version supersedes an obsolete internal draft previously referred to as toe_v3_stokes_foundation.tex, which overstated the neutrino-ordering claim. The present PDF is the authoritative public Version 3 document. The rigorous lattice-gauge and Stokes/Fisher-zero mathematics related to the Stokes machinery is maintained in the companion repository hsmi-yang-mills. The full public repository for the Global Spectral Theory of Everything is available at https://github.com/golbryk/global-spectral-toe, with the companion repository at https://github.com/golbryk/hsmi-yang-mills. This record does not claim a complete or “100%” Theory of Everything, does not claim that the neutrino ordering is solved, and does not claim to reproduce low-energy phenomenology, QCD, electroweak physics, or cosmological dynamics. Its role is to state the current structural framework, validation results, limitations, and falsifiable predictions in a precise public form.