The Root Theorem of Context Engineering
Every system that maintains a large language model conversation beyond a single session faces two inescapable constraints: the context window is finite, and information quality degrades with accumulated volume. We formalize these constraints as axioms and derive a single governing principle -- the Root Theorem of Context Engineering: \emph{maximize signal-to-token ratio within bounded, lossy channels.} From this principle, we derive five consequences without additional assumptions: (1)~a quality function $F(P)$ that degrades monotonically with injected token volume, independent of window size; (2)~the independence of signal and token count as optimization variables; (3)~a necessary gate m...
| Authors | Borja Odriozola Schick |
|---|---|
| Primary category | cs.CC |
| Published | 29 March 2026 |
| Last updated at source | 29 March 2026 |
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