Derivation of the Standard Model Without Free Parameters: Topogeometric Boundary Invariants of the Observer-Potential Hyperbolic Lattices

TheStandardModel (SM)ofparticlephysicsachievesunparalleledempiricalaccuracy,yet itrelieson19to26arbitrary, empiricallyfittedfreeparameters—includinggaugecouplings, fermionmass hierarchies, CKM/PMNSmixingmatrices, and theHiggs vacuumexpectationvalue. Buildingupon theObserver-Potential Framework (OPF), thispaperdemonstrates that these empirical constants arenot fundamental inputs, but exact geometriceigenvaluesarising fromboundaryconstraintsacrossadynamichyperbolic latticecontinuum({5,4},{7,8},{54,55}⇌{55,54},and{34,35}). Bydefininggaugecouplingsasdiscretetopologicalcoordinationratios, fermionmasshierarchiesasfractionalcurvatureinvariants,andflavor-mixinganglesasgeometricprojectionmatricesunderactiveObserverphase-locking(ˆO),weeliminateall freeparameters fromtheStandardModel. Wecomputethetheoreticalfine-structureconstant(α−1≈137.036),thetop-to-electronmassratio(mt/me),theCabibboangle(sinθC≈ md/ms),andtheHiggsmass(mH≈125.10GeV)directlyfromtopogeometricfirstprinciples,yieldingaparameter-freeformulationcompatiblewithcurrentexperimental limits