The Geometry of Self-Reference: A Dissipative Tensor Network Framework for Fundamental Constants

We present The Geometry of Self-Reference, a non-perturbative theoretical framework that models physical reality as the fixed-point limit of a recursive logical operator, R(z) = 1 / (1 + z), acting on a Dissipative Multi-scale Entanglement Renormalization Ansatz (D-MERA). By shifting the foundational axiom from “existence ex nihilo” to “existence via observation,” the framework demonstrates that the laws of physics are not arbitrary, but are the unique algorithmic output of a vacuum observed by a system of specific computational complexity, C_O greater than or equal to 55 (the “Manganese Limit”). This “Epistemic Pivot” allows for the derivation of fundamental constants without free parameters. Key Results • The Fine Structure ConstantDerived as the holographic projection of the D-MERA boundary, with an inverse value approximately equal to 137.0357. • The Lepton SpectrumA unified “Meta-Formula” generates the electron, muon, and tau masses with less than 0.006 percent error, based on S3 symmetry group steps and geometric resonances. • The Neutrino SectorPredicts a total neutrino mass sum of approximately 0.72 electron volts and derives atmospheric and solar mass splittings consistent with NuFIT data. • Falsifiable PredictionsThe framework explicitly predicts a “Ghost State” instability at 30.9 giga–electron volts and log-periodic oscillations in running coupling constants, with a period approximately equal to the natural logarithm of the golden ratio. Volume Structure This dataset contains the complete “Golden Master” (version 5.1) and the “Living Audit” (version 5.2) of the theory: • Book I: The Axiomatic KernelThe logical foundations, Prime Symmetry stability theorems, and the genealogy of operations. • Book II: The Holographic MechanismThe D-MERA tensor network architecture, the origin of mass, and the retraction of the WIMP hypothesis. • Book III: The Cognitive InterfaceThe “Minimal Observer” complexity class (C_O) and the thermodynamic necessity of the 55-nucleon limit. • Book IV: The Empirical SealA catalog of 177 derived constants matching experimental data, along with definitive falsification criteria. • Book V: The Recursive CipherThe resolution of the Lepton Meta-Formula, the derivation of the neutrino mass hierarchy, and the unified sector audit. Keywords Foundations of Physics, Tensor Networks, D-MERA, Standard Model Parameters, Neutrino Mass, Recursive Logic, Fine Structure Constant, Theoretical Physics, Beyond Standard Model (BSM)