Why numerical correspondences must be accompanied by explicit assumptions, compatible dimensions, and a path toward falsification before they can support a physical interpretation.
Measured constants can exhibit suggestive numerical relationships. Such observations may motivate further work, but a numerical match does not by itself establish a physical connection.
A basic requirement
Before interpreting a proposed equality, both sides must be dimensionally compatible. In standard notation, the minimum condition is
[left-hand side]=[right-hand side].(1)Equation (1) is a general statement of dimensional consistency, not a TEF field equation. Passing this test is necessary but not sufficient: many dimensionally valid expressions have no physical significance.
From observation to hypothesis
A candidate relationship should be presented in a fixed order:
- identify the measured quantities and their accepted uncertainties;
- state the mathematical relationship without interpretive language;
- list assumptions, conventions, and units;
- quantify the agreement and its sensitivity to input choices;
- only then propose a geometric interpretation.
The interpretation remains a hypothesis until it follows from a broader derivation or produces an independent test. TEF will treat coincidence as a prompt for calculation, not as proof.