Sandhi: Proof of Necessity as a Primitive Causal State Beyond Binary Logic

This paper proves that Sandhi — the primitive causal state of irreversible commitment without realization, situated between inaction (0) and full outcome (1) — is not a modelling choice. It is a mathematical necessity. Through six formal definitions, an impossibility lemma, and a theorem by contradiction, we demonstrate that any causal decision system exhibiting irreversible commitment cannot derive its stopping boundary from within a binary framework — because the binary state space is structurally blind to what is already there. The proof holds bidirectionally: during activation (0 → S → 1) and cessation (1 → S → 0). Part of the Sandhi Framework Series. Foundational paper: DOI: 10.5281/zenodo.19665865