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Dimensional Consistency Before Interpretation

A minimum standard for candidate relationships

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:

  1. identify the measured quantities and their accepted uncertainties;
  2. state the mathematical relationship without interpretive language;
  3. list assumptions, conventions, and units;
  4. quantify the agreement and its sensitivity to input choices;
  5. 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.