Temporal Convergence Framework: Distinguishing Structure from Coincidence in High-Precision, Low-Dimensionality Parameter Spaces

Peer review of empirical patterns in high-precision, low-dimensionality param- eter spaces relies on implicit evaluation standards. When N = 3 parameters at 2% precision permit thousands of statistically significant formulas, reviewers must distinguish structure from coincidence, but the criteria for doing so remain unar- ticulated. We found no published record of community debate establishing explicit standards, despite decades of informal application. This paper proposes one such articulation: seven criteria emphasizing tempo- ral convergence through timestamped predictions. We offer specific thresholds not because we believe them correct, but because explicit proposals can be calibrated while implicit standards cannot. The need for explicit standards is timely. Lattice QCD has only recently achieved the precision necessary for discriminatory tests of quark mass relations. Historical precedents from lepton phenomenology (Koide, Gell-Mann–Okubo) provide limited guidance: leptons offer ∼35,000× greater discriminatory power than light quarks, in- volve no RG running, and constitute a fundamentally different measurement regime. The historical record is further compromised by survivorship bias: patterns that di- verged are largely unrecorded. Historical cases motivate the problem by illustrating why implicit evaluation proved adequate for leptons but may prove inadequate for quarks. They cannot validate the proposed solution. Validation is prospective by design: starting from this publication, patterns evaluated under this framework will be tracked publicly. The framework succeeds if it proves predictively useful; it fails if it requires constant post-hoc adjustment, judged by its own temporal convergence criterion. If this proposal provokes disagreement that leads to better criteria, it will have served its purpose. If it is ignored, the current system of implicit evaluation contin- ues unchanged. We consider both engagement and refinement to be success.