[trissim]

Here ‘formalize SSOT’ means: treat the codebase as an encoding system with multiple places that can hold the same structural fact (class shape, signature, etc.). Define DOF (degrees of freedom) as the count of independent places that can disagree; coherence means no disagreement. Then prove:

- Only DOF=1 guarantees coherence; DOF>1 always leaves truth indeterminate, so any oracle that picks the ‘real’ value is arbitrary.

- For structural facts, DOF=1 is achievable iff the language provides definition‑time hooks plus introspectable derivation; without both (e.g., Java/Rust/Go/TS) you can’t enforce SSOT no matter how disciplined you are.

It’s like turning ‘consistency’ in distributed systems from a principle into a property with necessary/sufficient conditions and an impossibility result. SSOT isn’t a predictive law; it’s an epistemic constraint. If you want coherence, the math forces a single independent source. And if the same fact lives in backend and UI, the ‘truth’ is effectively in the developer’s head; an external oracle. Any system with >1 independent encoding leaves truth indeterminate; coherence only comes when the code collapses to one independent source (DOF=1).