Definition: Source rule and interpretation ledger

A proposed source rule $\mathfrak{S}$ assigns to admitted data either:

1. a symmetric covariant tensor in a declared finite jet or comparison space; or

2. a symmetric tensor field or distribution on a justified geometric extension.

Its ledger must state:

1. the actual process, preparation, instrument, and residual data used, including every operative enlargement of ${\mathsf{A}}_0$;

2. the explicit rule producing its components and its covariance under the permitted matched equivalences;

3. the energy-momentum interpretation, units, localization, density or smearing convention, and apparatus contributions;

4. the balance or response principle supporting that interpretation;

5. the status of symmetry, conservation, renormalization, and any energy condition invoked;

6. whether the output is a real expectation tensor, an operator-valued object, or a statistical estimate, with its domain and allowances.

Absent an interpretation theorem, the output is called a source candidate, not a derived physical stress-energy tensor.