Systematic Comparison of Trinity Framework Mass Predictions with CERN Particle Observations

This paper presents a systematic phenomenological comparison between mass scales generated by the π–φ–e Trinity framework and experimentally observed particle masses reported by CERN and the Particle Data Group. Starting from the resolved invariant E0=π2E_0 = \pi^2E0=π2, derived independently from the Carol Equation, the study explores how this dimensionless scale and its simple combinations with the fixed transcendental constants π\piπ, φ\varphiφ, and eee align numerically with known fermion, boson, and composite particle masses under standard dimensional rescalings. All constants used are fixed and parameter-free. No regression, tuning, or optimization is performed. The analysis documents numerical correspondences within stated tolerances while explicitly distinguishing between analytic results, dimensional consequences, and exploratory pattern searches. Where geometric constructions are discussed, a clear distinction is maintained between Euclidean metric geometry and logarithmic scaling space. Euclidean results (such as the Trinity Triangle circumradius) are treated separately from scaling invariants (such as the Resolution Gap), which arise from logarithmic comparison rather than metric length. The purpose of this work is documentation rather than interpretation. No physical mechanism is asserted, no new particles are claimed, and no replacement of the Standard Model is proposed. Instead, the paper provides a transparent, reproducible catalogue of numerical alignments that may be of interest for further theoretical or statistical investigation, particularly in light of the independently derived Carol Equation invariant. All computations are reproducible and are accompanied by openly available scripts. For further information about the ENSO Framework, please contact Eric Needham: ensotheory1@gmail.com