Compression with obligations
A good geometric formulation can replace many algebraic relations with incidence, distance, or extremality. That is genuine compression only when the map back to the original variables remains explicit.
The diagram does not prove the theorem. It tells us which relations may be load-bearing and which calculation would discriminate between nearby interpretations.
A practical test
Ask what the picture removes: variables, assumptions, cases, or notation. Then ask what it adds: a constraint, a conserved relation, a variational principle, or only aesthetic coherence.
If the picture adds no testable constraint, it remains an intuition. That can still be useful, but it should not be reported as a result.
Suggested citation
Deng, Feiyu. “Geometry as compression in theoretical physics.” feiyudeng.com, 2026-07-13.